graph practice

Graph practice

This file contains 25 top-level graphs with 4 to 9 answered and explained questions each.

Good luck on your test.

1. Approximately what percent of all Hydraulic specialists were males during 1996?

A. 15%.

B. 25%.

C. 50%.

D. 75%.

E. 90%.

The best answer is D.

Go to the hydraulic specialists bar, approximately 12,000 are males and 4,000 are females. 12,000 out of the total number of specialists in this category (16,000) is 75%, thus answer D is the best.

2. Which of the following category of mechanical engineering specialists had the lowest ratio between male and female workers in 1996?

A. Hydraulic.

B. Gears.

C. Pneumatics.

D. C.N.C.

E. Electrical erosion.

The best answer is E.

We are actually looking for a category where the bars of the males and the females are the closest. Another way is to calculate each of the ratios but it takes a long time.

By looking at the bars, we can easily notice that the females bar is relatively high in the electrical erosion category and the males bar is relatively low there. In that category the lowest ratio is accepted.

3. In 1996, approximately how many C.N.C specialists were between the age of 49 and 64?

A. 4,500.

B. 5,000.

C. 5,500.

D. 6,000.

E. 6,500.

The best answer is D.

First go to the bar chart and find how many C.N.C specialists were recorded in 1996, the answer to that is 30,000. By the pie chart we know that the required age group is 20% of the total and therefore the answer is (0.2 x 30,000 = 6,000) specialists.

4. If in 1996 all the Hydraulic specialists represented 5.5% of the entire mechanical specialists of Norway, approximately how many specialists were there total?

A. 120,000.

B. 180,000.

C. 240,000.

D. 260,000.

E. 290,000.

The best answer is E.

According to the bar-chart there are approximately (4,000 + 12,000 = 16,000) hydraulic specialists in Norway, which represent 5.5% of the total. 5.5% is a hard number to work with so play with it a little: .

If we take 16,000 and divide it by 5.5% and also multiply by 100 we’ll get the total number of specialists in Norway.

. Therefore answer E is the best.

5. If the number of female C.N.C specialists in the 28 to 35 years old category represents 4.5% of all C.N.C specialists, approximately how many male C.N.C specialists are also between 28 and 35?

A. 1,250.

B. 2,340.

C. 3,450.

D. 4,580.

E. There isn’t enough data.

The best answer is C.

15% of the specialists in the C.N.C category are between the ages of 28 and 35, if 4.5% are woman then the rest must be male, thus 11.5%.

All we need to calculate is 11.5% of the total number of C.N.C specialists.

According to the bar-chart, there are (7,000 + 23,000 = 30,000) specialists in that area of expertise. 11.5% of 30,000 can be easily calculated by dividing the 11.5 to 10% + 1% + 0.5%. The answer is C, 3,450 male specialists.

1. In which of the following years was the fuel consumption closest to 150 Mega-liters?

A. 1965.

B. 1970.

C. 1975.

D. 1980.

E. 1990.

The best answer is D.

In the year 1985 the fuel consumption was approximately 140 mega-liters but this is not one of the answers. The question specifically asked among one of the following years, thus the years presented as one of the answers. In 1980 the consumption was 125 and in 1990 it was 195 and therefore the closest year is 1980 and D is the best answer.

2. Which of the following years presented the lowest increase of consumption compared to the previous year of sampling?

A. 1970.

B. 1975.

C. 1980.

D. 1985.

E. 1990.

The best answer is C.

With our calculating anything, we can easily see that between 1975 and 1980 the line is almost horizontal. The angle of the line relative to the year axis represents the degree of change in the consumption. Since the line has the lowest inclination between these years, 1980 is the year we are looking for.

3. In 1985, how many of the categories shown use greater than 25 mega-liters?

A. 0.

B. 1.

C. 2.

D. 3.

E. 4.

The best answer is C.

Using the graph we can conclude that in 1985 approximately 140 mega-liters of fuel were consumed. 25 mega-liters are approximately a little under 20% (17%). Look in the bar-chart in the year 1985 for categories that surpass 20% of fuel.

The only categories that fit the description are Private cars and industrial, thus two categories among the categories shown.

4. In 1965, approximately how many mega-liters are consumed by industrial use only?

A. 10.

B. 15.

C. 20.

D. 25.

E. 30.

The best answer is C.

Go to the bar-chart, you can see that 80% of the total fuel consumption goes to industrial use only. In the year 1965, according to the graph, approximately 25 mega-liters are consumed and therefore 80% of 25, which is 20 mega-liters, goes to industrial use.

5. In which of the following years was the consumption of the public transportation the greatest?

A. 1995.

B. 1985.

C. 1975.

D. 1965.

E. There isn’t enough data.

The best answer is A.

There are two ways to answer this question, the first is to calculate all the necessary numbers and the second is to evaluate.

We can see that the bars of the public transportation are nearly even yet the line chart is inclining as the years go. The highest fuel consumption would be in the latest year, thus 1995. The consumption there is approximately 25% of 220, which are 55.

If you look up close you’ll also notice that the 1995 bar is the greatest and therefore answer A is undoubted.

6. In which of the following years was the consumption of the industrial use the greatest?

A. 1995.

B. 1985.

C. 1975.

D. 1965.

E. Answers B and C.

The best answer is C.

This time the only way is to find the real consumptions in each year.

Use both the line chart and the bar graph to answer this question.

In 1995- 15% out of 220, which is 33.

In 1985- 35% out of 140, which is 49.

In 1975- 60% out of 120, which is 72.

In 1965- 80% out of 25, which is 20.

The largest industrial consumption is in the year 1975.

7. If the number of cars grew by 30% between the years 1972 and 1975, what was the fuel consumption in the year 1972?

A. 65.

B. 72.

C. 84.

D. 93.

E. It cannot be determined from the information given.

The best answer is E.

We don’t know the connection between the number of cars to the fuel consumption. Although this correlation seems logical, this is not the place to work by intuition.

The answer is E because more sufficient data is required.

8. Which of the following can be inferred form the graphs?

A. The fuel consumption of private cars increased from 1965 to 1995.

B. The fuel consumption of public transportation in 1985 is larger than that in 1975.

C. New roads were built due to the increase in the number of cars between 1965 and 1975.

D. Answers A and B.

E. Answers A, B and C.

The best answer is A.

Check all the answers.

A- The fuel consumption in 1995 was much higher than in 1965 according to the line chart. B- The public transportation fuel consumption in 1985 was 21 while in 1975 it was 24, thus B is incorrect which leaves us with answer A by itself.

9. Assume that there were 2,800 private cars in the year 1985 in the Fiji islands. What is the average fuel consumption per car (in liters)?

A. 6,500.

B. 8,200.

C. 10,000.

D. 12,500.

E. It cannot be determined from the information given.

The best answer is C.

In 1985, approximately 140 mega-liters were consumed. 20% of that amount goes to private cars (0.2 x 140 = 28). That is 28 million liters of fuel.

28 million divided to 2,800 is 10,000 liters per car and thus C is correct.

1. How many of the presented car systems cost more than a thousand dollars to produce?

A. 0.

B. 2.

C. 3.

D. 4.

E. 5.

The best answer is E.

This is an easy question, go to the graph that presents the price of production and see how many categories are over a $1000- the answer is 5, all but the last.

2. How many of the car systems cost more than $1,500 and took more than 7 hours to produce?

A. 0.

B. 1.

C. 2.

D. 3.

E. 4.

The best answer is B.

In this question you need to use both graphs. From the first graph (the money graph), you can see that the only systems that surpass $1,500 are the first two. Now go to the second graph and see how much time it takes to produce each of the two systems. The only system which answers both categories is the Engine Machinery system.

3. Approximately how many more minutes does it take to produce the internal design system than the Electric system?

A. 0.5.

B. 10.

C. 30.

D. 600.

E. 120.

The best answer is C.

Go to the relevant graph. The difference between the bars of the internal design system to the electric system is approximately 0.5 hour, which is 30 minutes and therefore answer C is the best.

4. What is the ratio between the cost of two radiator and cooling systems to a system of engine machinery?

A. 1:3.

B. 1:6.

C. 12:1.

D. 6:1.

E. 3:1.

The best answer is A.

According to the graph with the cost data, the price of a radiator and cooling system is approximately $750 and the price of the engine system is $4500.

The ratio between two radiator systems to one engine systems is the ratio between 1500 and 4500, which is 1:3.

5. Approximately what is the average cost of the two median systems?

(Median in terms of cost)?

A. $1,300.

B. $1,550.

C. $1,700.

D. $1,850.

E. $2,000.

The best answer is B.

The median systems are the ones that have two more expansive systems and two less expansive systems. Look for two bars that have two bars smaller and two bars larger than them. The two median systems are the Tinsmith’s work and the internal design.

The average is (1700 + 1400)/2 = 1550.

6. Approximately what percent of the entire cost of the car is the cost of the engine machinery system?

A. 12%.

B. 22%.

C. 30%.

D. 38%.

E. 47%.

The best answer is D.

Refer to the cost graph; the cost of the engine system is $4,500.

Sum up all of the other systems, including that of the engine, to get approximately $12,000 as the cost of the entire car.  4500 out of 12000 is approximately 38% and therefore answer D is the best.

7. Approximately what percent of the total does it take to produce the electricity system and the steering system?

A. 10%.

B. 20%.

C. 30%.

D. 40%.

E. 50%.

The best answer is C.

Add the two relevant bars; the time it will take to produce them is (7.5 + 6.5 = 14 hours).

Add all the systems up; the result is approximately 43 hours.

14 out of 43 are approximately 32% and thus C is the closest answer.

8. Which of the following systems has the lowest ratio between time and cost of production?

A. Engine machinery.

B. Steering.

C. Electricity.

D. Internal design.

E. Radiator and cooling.

The best answer is C.

There is no other way, check the approximate ratio in each of the categories.

A. 13 hours to 4500 dollars, which is approximately 1:350.

B. 6.5 hours to 2400 dollars, which is approximately 1:370.

C. 7.5 hours to 1250 dollars, which is approximately 1:170.

D. 8 hours to 1400 dollars, which is approximately 1:175.

E. 3 hours to 750 dollars, which is approximately 1:250.

And therefore the closest ratio is C.

9. If there are 87 working hours per day in the factory of car X, approximately how many cars can be manufactured in 3 days?

A. 2.

B. 4.

C. 6.

D. 8.

E. There isn’t enough data to determine.

The best answer is C.

If you sum up the entire time of building a car, you’ll get approximately 43.5 hours.

If there are 87 working hours in one day then two cars can be made, thus 6 cars can be manufactured in 3 days.

1. Approximately what percent of all appliances sold in the Arnolds electric store were Ovens and televisions?

A. 10%.

B. 20%.

C. 30%.

D. 40%.

E. 50%.

The best answer is C.

In this question you’ll need to use the data from both graphs.

Sum up the bars of both the ovens and the televisions. They both sum up to 58.

Sum up the bars of all the appliances in all the categories, they will sum up to approximately 200 or so. Now, 58 out of 200 are a little under 30% and therefore answer C is the best answer.

2. If X represents the number of DVD’s that were made in U.S and were sold during December, how many Televisions that were made in the China sold that month?

A.    X.

B.     1.5X.

C.     2X.

D.    X/2.

E.     6X.

The best answer is E.

According to the bar chart, X represents approximately 5 DVD’s that were sold.

Go to the T.V category, you can see that approximately 30 televisions that were made in china were sold in December and therefore the answer is 30/5 = 6X.

3. For the individual category in which the second greatest number of appliances made in the U.S were sold, the number of appliances made in the U.S exceeded the number of appliances made in China by how much approximately?

A. 0.

B. 1.

C. 2.

D. 3.

E. 4.

The best answer is C.

First identify the category in which the number of appliances made the U.S is the second in size, which would have to be the “ovens” category. In that category 14 (U.S) ovens were sold and (China) 12 ovens were sold. The difference is 2 ovens and therefore the answer is C.

4. According to the graph, to which of the following categories was the ratio between appliances that were made in China to appliances that were made in the U.S the greatest?

A. Refrigerators.

B. Mixers.

C. Speakers.

D. Televisions.

E. DVD’s.

The best answer is

Check the approximate ratio in each of the options:

A. 6 to 6, which is 1.

B. 11 to 3, which is 3 and two thirds.

C. 15 to 28, not relevant since B is greater.

D. 30 to 2, which is 15- we got a winner.

E. 13 to 5, not relevant since D is better.

And therefore the greatest ratio will be in the Televisions categories.

Geeweez Inc.

Revenue and profit distribution for Organic and Non-organic materials

Over the years 1991 to 1995.

The 3 first graphs should be attached here.

1. Approximately how much did the total revenues increase from 1991 to 1995?

A. $4,400.

B. $5,000.

C. $6,500.

D. $8,000.

E. $11,200.

The best answer is C.

First familiarize your self with the graphs.

The question is about the graph of the revenues, look at the difference between the top value of the column in 1991 and 1995. You can see that the difference between the years is approximately (21,500 – 15,000 = 6,500) and thus the answer is C.

2. In the year which profits from Organic materials decreased over the previous year, the revenues from Non-organic materials were approximately

A. $12,500.

B. $10,000.

C. $7,500.

D. $6,200.

E. $4,000.

The best answer is A.

Refer to both bar graphs. Look for the year in which the Organic bar is lower than its previous year, the only year is 1995. Then go to the other bar graph and look again in the year 1995, the revenues from Non-organic materials are (15,000 – 2,500 = 12,500) and thus the answer is A.

3. In the year which profits from Organic materials are the lowest, what percent approximately of the total revenues belong to the Organic materials?

A. 22%.

B. 28%.

C. 35%.

D. 45%.

E. 65%.

The best answer is C.

Refer to both bar graphs. From the profit graph, we can learn that the question is asking about the revenues of the year 1993. In that year, revenues from Organic materials present approximately $8,000 and the total revenues are approximately $22,000. In percent terms the answer is (8/22 = approximately 36 percent) and so the best answer is C.

4. In 1994, total profits represented approximately what percent of Geeweez’s total revenues?

A. 25%.

B. 30%.

C. 40%.

D. 50%.

E. 65%.

The best answer is C.

Refer to both bar graphs. From the profit graph, we can conclude that the total profits for 1994 are approximately $9,500. From the revenue graph, we can conclude that the total revenues are approx. $24,000.

(9,500 / 24,000) in percent terms is approx. 40% and thus C is the answer.

5. The profits on Non-organic materials in 1992 are approximately what percent of the total revenues in 1994?

A. 15%.

B. 25%.

C. 35%.

D. 45%.

E. 55%.

The best answer is B.

Refer to both bar graphs. Look in the year 1992 in the profit graph, the profits from the upper bar column, which belongs to the Non-organic materials is approx. (10,000 – 4,000 = 6,000). In the year 1994, the total revenues are approx. $24,000 and thus the answer in percent terms is (6/24 = 0.25) 25%.

6. For the first year in which Non-organic materials revenues surpassed $16,000, total profits were approximately

A. $3,200.

B. $6,500.

C. $8,000.

D. $9,500.

E. $10,500.

The best answer is A.

Look at the revenues graph, start in 1991 and go through the years until you find one that the revenues from Non-organic materials is over $16,000, the first possible year is 1994. Now go to the second graph and see how much profits were made that year, the answer is approx. $3,200.

7. For the last year in which profits from Organic materials were under $2,000, approximately what were the total revenues in the previous year?

A. $15,000.

B. $17,500.

C. $22,000.

D. $24,000.

E. $21,000.

The best answer is D.

This is a tricky question, pay attention.

We were asked about the last year so start from 1995 and move down the years. In 1995 the profits from Organic materials were under $2,000 and so the question is asking the total revenues in the previous year, thus in 1994.

The answer is approx. $24,000.

8. In 1994, what were the Non-organic revenues, which belong to the Metal group?

A. $8,500.

B. $9,600.

C. $10,800.

D. $12,000.

E. $13,200.

The best answer is C.

First look at the revenue bar graph, the total Non-organic revenues are $18,000.

Now move to the pie graph, you can see that the metal group is 60% of the total and therefore 60% of 18,000 are the correct answer. (0.6 x 18,000 = 10,800).

9. Of the Non-organic revenues in 1994, how much approximately were not made from metal or glass?

A. $2,150.

B. $3,200.

C. $4,100.

D. $5,000.

E. $5,500.

The best answer is A.

First look at the revenue bar graph, the total Non-organic revenues are $18,000.

Now move to the pie graph, you can see that the metal group is 60% of the total and the glass group is 28% and therefore 12% of 18,000 are left, which are also the clay group. (0.12 x 18,000 = 2,160). The closest answer is A.

10. What percent approximately are the revenues of the Non-organic Metal materials in 1994 relative to the total profits in the years 1994 and 1995?

A. 25%.

B. 35%.

C. 45%.

D. 55%.

E. 65%.

The best answer is D.

First look at the revenue bar graph, the total Non-organic revenues are $18,000.

Now move to the pie graph, you can see that the metal group is 60% of the total and therefore 60% of 18,000 are $10,800.

Now go to the profits graph, the total profits in 1994 and 1995 are approx. $19,000.

In percent terms, 10.8/19 is approximately 55% and thus answer D is the best.

1. The team that made the finals played 50% more games. Which of the following teams made it to the finals?

A. Team A.

B. Team B.

C. Team D.

D. Team E.

E. Answers B and C.

The best answer is E.

We are given a piece of substantial information, a team that made it to the finals played 50% more games than a team that didn’t.

We can see from the graph that some teams played a total of 40 games and the others played a total of 60 games and therefore those teams made it to the finals.

The answer is E, meaning that teams B and D made it to the finals.

2. For the team with the least number of loses, what percent approximately are the tied games of the total number of games?

A. 20%.

B. 33%.

C. 40%.

D. 45%.

E. 50%.

The best answer is B.

The team with the least amount of loses is Team B, you can see that by comparing the sizes of the uni-colored bars for all teams. The number of tied games is 20 and the total number of games is 60 and therefore the percent is 20/60, which is approximately 33%.

3. For the team with the median amount of tied games, won games represented approximately what percent of that team’s total games for that year?

A. 24%.

B. 37%.

C. 44%.

D. 53%.

E. 61%.

The best answer is D.

Look through all the teams for the median number of tied games. The median can easily be found: There are 5 teams and therefore the median number would be the one, which has 2 smaller and 2 bigger tie games than his, the right team is D.

Team D won 32 games, which is approximately a little over 50% and therefore the best answer is D.

4. If Team E won 15 games in the year 2000, Team’s E winnings increased by what percent from 1999 to 2000?

A. 50%.

B. 100%.

C. 200%.

D. 250%.

E. 300%.

The best answer is C.

Team E won 5 games in 1999.

15 are 300% of 5 and therefore there was an increase in 200% in the number of games won from the year 1999 to 2000.

5. If each team receives 3 points for winning a game, 1 point per tie game and 0 points per lose, which team collected the greatest amount of points in the year 1999?

A. Team A.

B. Team B.

C. Team C.

D. Team D.

E. Team E.

The best answer is B.

At first glance, the answer is either B or D since both teams won a lot of games compared to all the other teams. If you were more specific, you will see that team B tied more games than team D and therefore collected a greater amount of points.

The following table describes a certain family with five kids, on Christmas; each kid receives money from each of the older family members. Each family member spends a certain amount of money on gifts per child; the numbers in the middle of the table describes the distribution.  For example, dad gave 15% of his gift money to kid B.

Kid A

Kid B

Kid C

Kid D

Kid E

Total

Mom

30

11

29

20

10

100%

Dad

27

15

16

22

20

100%

Grandmother

8

26

21

35

10

100%

Grandfather

32

10

17

15

26

100%

Uncle Bob

20

8

34

18

20

100%

1.  Which family member gave Kid D one fifth of his Christmas money?

A. Mom.

B. Dad.

C. Grandmother.

D. Grandfather.

E. None of the answers are correct.

The best answer is E.

The numbers in the middle of the table represent the percent of the total money that each family member spent on a certain kid. Don’t be mistaken, mom spent 20% of her gift money on kid D, yet Grandfather's 15% could be more because we don’t know which family member spent more money on gifts.

2.  Which family member spent a quarter of his gift money on kid B and kid D?

A. Dad.

B. Mom.

C. Grandmother.

D. Grandfather.

E. Uncle Bob.

The best answer is D.

You are looking for a family member that spent 25% on both B and D.

If you add the percentages in columns B and D, you will know what percent each family member spent on those kids. The sum of grandfather adds up to 25% and therefore he is the only family member who spent a quarter of his money on kid B and D.

3. Which of the following arguments must be true?

A. The amount of money that dad gave to kid D is twice the amount that mom gave to kid B.

B. Kid E received the same amount of money from mom and from grandmother.

C. Grandfather gave one of the kids the same amount of money that he gave to two other kids together.

D. One of the family members gave kid B more money than any other family member.

E. Answers A and B are correct.

The best answer is C.

Go over all the answers.

Answers A and B are not necessarily true since the numbers presented in the table are in percent and not in actual figures of money. Answer D is incorrect for the same reason.

Answer C is the best one since it compares two percentages of the same family member. Grandfather spent 32% on kid A and (17% + 15% = 32%) on kids C and D and therefore this argument is correct.

4. If it turns out that grandfather spent twice as much money, in total, as dad, then

A. Kid B received more money from grandfather than from dad.

B. One of the Kids received more money from Dad than from Grandfather.

C. The amount of money that dad gave to kid A and B is identical to the amount of money that grandfather gave to kid A and B.

D. Uncle Bob spent more money on kid C than grandfather.

E. Answers A and B are correct.

The best answer is A.

The question tells us that the 100% of grandfather is equal to 200% of dad, in other words take 100$ as the money that dad spent and 200$ as the money that grandfather spent. Now that you have real numbers, try all the answers, only answer A is good.

15% of 100$ is smaller than 10% of 200$.

Answer D cannot be related to since we know nothing on Uncle Bob's money.

In the Monopoly world championship, two teams made it to the finals, the Chicago team and the Milwaukee team. Every game, each team can score between 0 and 4 points. The winning team, each game, is the one who earned more points.

There are 100 games in the championship between the teams. The following table represents the scores distribution among the teams.

For example, according to the bottom right square, there were 8 games that both teams received 4 points each.

0

1

2

3

4

0

3

-

4

-

4

1

6

4

3

1

2

2

7

-

8

3

4

3

-

8

7

-

3

4

6

4

6

9

8

1. In how many games was to score 2:3 in favor of Milwaukee?

A. 3.

B. 4.

C. 5.

D. 7.

E. 8.

The best answer is D.

From the data in the question, we need to go to the table and see how many games are in the line 0 and column 1- the answer is 0 games, meaning that there were no games with such a score.

2. In how many games was the score 1:0 in favor of Chicago?

A. 0.

B. 1.

C. 3.

D. 4.

E. 5.

The best answer is A.

From the data in the question, we need to go to the table and see how many games are in the line 3 and column 2- the answer is 7 games.

3. What percent of the total are the games with the score 0:4?

A. 4%.

B. 5%.

C. 7%.

D. 8%.

E. 10%.

The best answer is E.

Prior to the graph, we received sufficient data for this question. We know that there were 100 games in total. Games that ended up in the score 0:4 are 6 games in favor of Milwaukee and 4 games in favor of Chicago. The percent of these games is (10/100), or 10%.

4. In how many games was the sum of the points of both teams over 5?

A. 22.

B. 24.

C. 28.

D. 30.

E. 34.

The best answer is D.

We are looking for games that the sum of the points 6 and up.

The only combinations are 3:3, 4:2, 2:4, 4:3, 3:4 and 4:4.

Sum up these numbers to get: 23 games in total.

5. In how many games was the sum of the points smaller than 3?

A. 16.

B. 20.

C. 24.

D. 28.

E. 32.

The best answer is C.

We are looking for games that the sum of the points is smaller than 3.

The only combinations are: 0:0, 0:1, 1:0, 2:0, 0:2, 1:1.

Sum up these games from the table to get 24 games in total.

6. How many games ended up in a tie?

A. 8.

B. 12.

C. 21.

D. 23.

E. 27.

The best answer is D.

From the data prior to the graph, we know that a team won if she made more points and therefore if two teams made the same amount of points, they're in a tie situation.

The number of tie games is actually the sum of the diagonal of the table.

There were (3+4+8+8 = 23) games that ended up in a tie.

7. Approximately what percent of the games did Chicago win?

A. 15%.

B. 20%.

C. 25%.

D. 30%.

E. 35%.

The best answer is C.

The games that Chicago won are all the games above the diagonal of the table.

The diagonal is the tied games and under the diagonal are all the games that Chicago lost. Sum up these games: (4+2+4+3+1+3+4+3 = 24) games in total.

8. How many games did Milwaukee won where the differences between the points were larger than one?

A. 24.

B. 28.

C. 31.

D. 32.

E. 34.

The best answer is C.

Look under the diagonal of the table, these are the games that Milwaukee won.

We are looking for games that ended up in a score where there is a difference of at least two points between the teams.

The options are: 2:0, 3:0, 4:0, 3:1, 4:1 and 4:2.

Sum up these games: (7+6+4+8+6 = 31).

9. Which team won more games?

A. Chicago.

B. Milwaukee.

C. Both teams won the same number of games.

D. There isn’t enough data to determine the answer.

E. Toronto.

10. In what percent of the games approximately one team scored and the other didn’t?

A. 22%.

B. 27%.

C. 28%.

D. 30%.

E. 32%.

The best answer is D.

The games in which one team scored and the other didn’t is all the games in the first column and the first row except the combinations of 0:0.

There are (4+4+6+7+6 = 27) games.

27 out of 100 are 27%.

Applicants for the musical “Cats”

In the Metropolitan Theater, London

By age and sex in the years 1990 and 2000.

1. In 2000, what percent of the applicants were females under the age of 20?

A. 14%.

B. 24%.

C. 17%.

D. 32%.

E. There isn’t enough data to determine.

The best answer is C.

Familiar you’re self with the graphs.

Go to the graph ascribed to the year 2000, 17% of the females are under the age of 30 and therefore under the age of 20. C is the best answer.

2. In 1990, approximately what percent of females’ applicants were at least 30 years of age?

A. 21%.

B. 22%.

C. 42%.

D. 48%.

E. 65%.

The best answer is D.

In this question, the easiest way is to pick up a number of applicants. Lets say that there were 100 applicants in total. (21% + 22% = 43%, which is 43 applicants) are woman. Only 21% of the applicants are over 30, meaning that 21 out of 43 females are applicants over the age of 30. 21/43 is approximately a little under 50% and therefore D is the best answer.

3. In 2000, approximately what percent of males’ applicants were at least 30 years of age?

A. 20%.

B. 32%.

C. 38%.

D. 42%.

E. 52%.

The best answer is C.

In this question, the easiest way is to pick up a number of applicants. Lets say that there were 100 applicants in total. (32% + 20% = 52%, which is 52 applicants) are man. Only 20% of the applicants are over 30, meaning that 20 out of 52 males are applicants over the age of 30. 20/52 is approximately a little under 40% and therefore C is the best answer.

4. If the total number of applicants in the year 2000 is by 50% greater than in 1990 and there were 240 applicants in 1990, how many males’ applicants are there in the year 2000 over the age of 30?

A. 45.

B. 72.

C. 112.

D. 124.

E. 160.

The best answer is B.

Use all the data. In 1990 there were 240 applicants è in 2000 there are (1.5 x 240 = 360) applicants. We know from the pie graph that 20% of 360 are males over the age of 30, which are exactly 72 applicants.

5. If the number of female applicants in the year 2000 is 96 and there were an equal amount of man applicants in the years 1990 and 2000, approximately how many woman applicants were in the year 1990 less than 30 years of age?

A. 20.

B. 40.

C. 60.

D. 80.

E. 100.

The best answer is B.

Go on step at a time.

96 woman in 2000 are (17% + 31% = 48%) of the total and therefore there are 96/(0.48) = 200 applicants in the year 2000.

Another important piece of information is that the number of male applicants is the same in both years è 0.52 x 200 = 104 males in the year 2000.

If 104 males are (42% + 15% = 57%) of the entire applicants for 1990 than there are approximately (104/0.57) 182 applicants.

We know that 22% are females less than 30 years of age and therefore (0.22 x 182) is approximately 40 applicants.

6. If there were 1,000 applicants in the year 1990, how many more male applicants were there than female applicants?

A. 70.

B. 125.

C. 140.

D. 260.

E. 320.

The best answer is C.

57% of all the applicants are male and therefore 570 are male.

43% of all the applicants are female and therefore 430 are female.

The difference between the groups is 140 applicants.

7. If there were 1,000 applicants in the year 1990 and 10% more in the year 2000, how many more males were there in 1990 than woman in 2000?

A. 12.

B. 24.

C. 38.

D. 42.

E. 56.

The best answer is D.

If there are 1,000 applicants in 1990 then 57% of them are male, which is 570 males.

In 2000 there were 10% more applicants, meaning 1100 applicants.

The women are 48% of 1100, which are 528 applicants.

The difference is (570 – 528 = 42) applicants.

8. If the total number of applicants was 65% higher in 2000 than in 1990, what among the answers is the closest ratio between the numbers of male applicants in 2000 to the number of female applicants 1990?

A. 2:3.

B. 4:1.

C. 1:2.

D. 2:1.

E. 3:2.

The best answer is D.

The question asked for an approximate ratio so make the calculations approximately.

Lets say that there were 100 applicants in the year 1990 and therefore 43 applicants are woman. In 2000 there were 165 (65% more) and therefore approximately 86   (0.52 x 165) are male applicants. 86:43 is the equivalent to the ratio 2:1 presented in answer D.

9. In the year 2002 there was a reunion of all the applicants from the years 1990 and 2000. Approximately what percent of the total are the males?

A. 40%.

B. 55%.

C. 62%.

D. 70%.

E. There isn’t enough data to answer.

The best answer is E.

Be careful, we don’t know the number of applicants in each year and so we cannot compare and make an average (52% + 57%)/2 are approximately 55%.

If we knew that there were an equal number of applicants in both years, the answer would be B.

10. If there were 3,000 applicants in 2000, how many more females over the age of 30 were there than females under the age of 30?

A. 930.

B. 650.

C. 510.

D. 420.

E. 380.

The best answer is D.

There are 31% females over the age of 30, which are 930 applicants.

There are 17% females under the age of 30, which are 510 applicants.

The difference is 420 female applicants.

Crime rate in New York.

Percent change from 1998 to 2001.

1. How did the rate of crimes change from 1998 to 1999?

A. It increased by 4.5 percent.

B. It decreased by 4.5 percent.

C. It increased by 16 percent.

D. It decreased by 16 percent.

E. There isn’t enough data to answer the question.

The best answer is D.

We are asked how did the rate of crimes change. We can easily see from the graph that there was a decrease in the number of crimes and also in the rate of crimes and therefore answers A and C are disqualified.

Between the years 1998 and 1999, there was a decrease of 16 percent per 1,000 people; this data is sufficient to determine that in general there was a decrease of 16%.

2. If there were 2 million crimes in 1998, how many crimes were recorded in 1999?

A. 2,090,000.

B. 2,900,000.

C. 1,910,000.

D. 1,750,000.

E. 1,150,000.

The best answer is C.

First of all, you can eliminate answers A and B since there was a decrease in the rate of crimes from the year 1998 to 1999.

From the graph we can conclude that there was a 4.5 percent decrease in the rate of crimes relative to 1998, in other words, (0.045 x 2,000,000 = 90,000) is the decrease in the number of crimes. (2,000,000 – 90,000 = 1,910,000) crimes.

3. By what percent approximately did the number of crimes decreased from 2000 to 2001?

A. 4.5%.

B. 6%.

C. 6.6%.

D. 7.8%

E. 8%.

The best answer is C.

Pay attention, the answer is not B. Let 1000 be the number of crimes in the year 1998.

In the year 2000, there were 9% less crimes, which is 910 crimes.

In the year 2001, there were 15% less crimes, which is 850 crimes.

There was a decrease in 60 crimes between the years 2000 and 2001.

In percent terms, that number is 60/910, which is approximately a little over 6.5% and therefore the answer is C.

4. To the nearest percent, by what percent did the population of New York increase from 1998 to 2001?

A. 5%.

B. 8%.

C. 13%.

D. 17%.

E. 22%.

The best answer is

Assume that in 1998 there were 1000 people and 100 crimes are recorded.

In 2001, the crimes recorded decreased by 15% to 85 crimes, also the crime rate per 1,000 residents decreased by 25% to 75 crimes per 1,000 residents.

Let N be the number of new residents in New York.

Solve to equation: .  That is an increase in approximately 13%.

A rabbit and squirrel on a racetrack.

The following graph describes the progress of a rabbit and a squirrel on a 13 miles long racetrack. The rabbit and the squirrel started up at the same spot in the same time.

1.  Who won the race?

A. The rabbit.

B. The squirrel.

C. They finished at the same time.

D. One of them didn’t make it all the way.

E. There isn’t enough data to determine.

The best answer is A.

We can see that the dotted line, which represents the rabbit, ended up first at the time 17:00 o’clock while the squirrel finished the track in 17:30.

Therefore the rabbit won the race.

2. How many times did the squirrel by-pass the rabbit? (Meaning that he was behind and then moved in front of the rabbit)

A. 0.

B. 1.

C. 2.

D. 3.

E. There isn’t enough data to determine.

The best answer is B.

The only time where the squirrel by-passed the rabbit was around 10:30, after that the two met around 13:00 but afterwards the rabbit by-passed the squirrel to the finish line.

3. At a certain time and place, the squirrel decided to stop for a little snack, at what time did the squirrel stop?

A. 9:30.

B. 10:30.

C. 12:00.

D. 13:00.

E. 15:30.

The best answer is C.

Look at the graph, find the place where the line becomes horizontal for a while, meaning that the squirrel stopped. You can easily see that it happens around 12:00.

4. Which of the following has the highest speed?

A. The squirrel at 9:00.

B. The squirrel at 10:15.

C. The squirrel at 12:20.

D. The rabbit at 15:30.

E. The rabbit at 8:10.

The best answer is B.

The speed is actually the gradient of the lines, the more vertical, the higher the speed is. Calculate the speed for each of the points. Speed = Distance/Time

A. 2/2 = 1.

B. 4/1 = 1.

C. 0.

D. 2/2 = 1.

E. 3/1 = 3.

You can see that the top speed was at point B.

Another way is to look and see which line has the highest gradient.

5. If the squirrel started out one hour prior to his original time (at 7:00) and did the exact same course only in different times, what would be the distance between the rabbit and the squirrel at 15:00?

A. 0.5 miles.

B. 1 mile.

C. 1.5 miles.

D. 2 miles.

E. 4 miles.

The best answer is B.

I you were to move the path of the squirrel one spot to the right, you’ll see that the squirrel passed 10 miles and not 9.5 as the original path.

The rabbit passed 11 miles until 15:00 and so the distance between them is 1 mile.

Timmy has a very nice and generous grandmother. Every month, she gave little Timmy candies and allowance. The following chart describes the distribution of grandmother’s gifts to Timmy for a period of 4 months.

The chart should be attached here.

1.  What is the average amount of candies that Timmy got each month?

A. 75.

B. 100.

C. 125.

D. 150.

E. 200.

The best answer is D.

Familiar you’re self with the chart.

You can see that the right bars are those of candies, add them up and divide by the number of months. The sum of the candies is 600 and therefore the average is 150 candies per month.

2. What is the average amount of money that Timmy got each month?

A. 75.

B. 100.

C. 125.

D. 150.

E. 200.

The best answer is B.

Familiar you’re self with the chart.

You can see that the left bars are those of allowance in dollars, add them up and divide by the number of months. The sum of the money is 400 and therefore the average is 100 dollars per month.

3. On the first month that the number of candies increased relative to the previous month, what was the ratio between the candies and the money?

A. 2:1.

B. 2:3.

C. 3:2.

D. 1:1.

E. 6:7.

The best answer D.

You can easily see that on the first two months the number of candies stayed the same and on March it increased and thus the question is about March.

The ratio between the number of candies to the amount of money that month is 175:175 or 1:1.

4. On the month with the largest amount of money given to Timmy, what percent of the total are the candies?

A. 25%.

B. 50%.

C. 66%.

D. 75%.

E. There isn’t enough data.

The best answer is B.

The month with the biggest allowance is March. That month Timmy received 175 candies out of 350 in total, which is 50%.

5. How many strawberry candies did Timmy receive over the 4 months period?

A. 150.

B. 240.

C. 350.

D. 400.

E. There isn’t enough data.

The best answer is B.

We know that Timmy received 600 candies during the 4-month period (adding the bars). We also know that 40% of the candies during that period were strawberry candies and therefore 40% of 600 are 240 candies.

6. If up to March (inclusive), Timmy got 160 Tim-Tums’s candies, how much did he get on April?

A. 5.

B. 15.

C. 20.

D. 30.

E. There isn’t enough data.

The best answer is C.

During the 4 months period Timmy got 600 candies. 30% of those candies were Tim-Tums’s, which are 180 candies. If in the first three months he received 160 Tim-Tums’s then on the fourth month (April) he must have gotten 20.

7. If in the first two month Timmy received 120 Lollipops, how many did he receive in April?

A. 0.

B. 10.

C. 15.

D. 20.

E. There isn’t enough data.

The best answer is A.

During the 4 months period Timmy got 600 candies. 20% of those candies were Lollipops, which is 120 candies. By the data in the question we can conclude that he received all of his Lollipops in the first two month and therefore he received none on March and April. The answer must be zero candies.

8. How many Jelly Candies did Timmy receive during February?

A. 10.

B. 20.

C. 35.

D. 80.

E. There isn’t enough data.

The best answer is E.

We know that Timmy received (600 x 10% = 60) Jelly candies during the entire 4 months period but we don’t know how they divide among the months.

There isn’t enough data to determine the answer.

9. What percent are the Jelly candies out of the total amount of gifts that Timmy received during the entire period?

A. 1%.

B. 6%.

C. 10%.

D. 12%.

E. There isn’t enough data.

The best answer is B.

We know that Timmy received (600 x 10% = 60) Jelly candies during the entire 4 months period. Sum up the entire gifts, there are 600 candies and 400 dollars, 1000 altogether. 60 out of 1000 are 6%.

10. If Timmy didn’t receive any Lollipops on the last two months, how many Lollipops did he receive on January?

A. 60.

B. 100.

C. 120.

D. 240.

E. There isn’t enough data.

The best answer is E.

During the 4 months period Timmy got 600 candies. 20% of those candies were Lollipops, which is 120 candies. Therefore he received all of them during January and February, but we don’t know how many he received on January alone.

Perception of specific income

The following chart presents the average perception of the personal income status.

1. What percent of the average income population perceive themselves have just enough money?

A. 5%.

B. 15%.

C. 25%.

D. 35%.

E. 70%.

The best answer is C.

Familiar you’re self with the bar graph.

Go the second bar from the right and find out what percent of this population are satisfied with their income and think they just enough money. The answer would be approximately 25%.

2. The members of which of the four groups have the wrong perception of their income in a way that they can be presumed to be greedy?

A. Low income.

B. Average income.

C. High income.

D. Very high income.

E. There isn’t enough data.

The best answer is D.

As you go over the chart, you’ll notice a pattern: the more you make, the more satisfied you are. We can see that the population, which earns a very high income, is not satisfied with their income. This may come as a surprise in a way that it breaks the previous pattern and so these are the exceptional.

3. If 50% of the low income population start to earn more money and move to the average income population, what would be the percent of people in that category who perceive themselves to have spare money?

A. 5%.

B. 10%.

C. 18%.

D. 25%.

E. There isn’t enough data.

The best answer is E.

We don’t know the amount of people in each group and therefore when people change groups we don’t know anything anymore about those groups with out sufficient information. For example, the average income population could contain 1 million people while the low-income population could include only 7,000 people.

4. In the group with the largest percent of people who perceive to have just enough money, what is the ratio between the people who perceive to have spare money to those who perceive themselves to have a lack in money?

A. 1:2.

B. 3:2.

C. 4:1.

D. 2:3.

E. 1:4.

The best answer is E.

Look at the chart and look for the biggest “diagonal lines” bar (just right bar), you will find it in the high-income population.

In that same group there are 10% people with spare money and 40% with not enough and therefore the ratio is 10:40 or 1:4.

The following chart describes the average working hours of people in different age groups. The horizontal lines represent the minimum criteria of hours per week in order to receive a certain privilege. For example, all the employees that work at least 12.5 hours a week receive a holiday bonus.

1. Which of the following age groups are most likely to receive a free cellular phone?

A. Less than 14.

B. 22-26.

C. 21-23.

D. Over 50 years of age.

E. Answers B, C and D are correct.

The best answer is E.

We can see that all the employees who work at least 27 hours are titled to receive a free cellular phone, that would include ages 18 and up, which makes answer E the best answer.

2. An employee’s “Bonus free hours” are defined to be the total hours needed in order to be entitled for a certain bonus minus the expected working hours per week of its age group. What is the “Bonus free hours” of a 22 years old employee relative to the free cellular bonus?

A. 8.

B. 5.

C. –8.

D. –5.

E. 22.5.

The best answer is C.

As defined in the question, the “Bonus free hours” of an employee who is 22 years of age is 27 (the level of the bonus) minus 35 (the expected working time per week), which is –8, thus answer C is good.

3. What is the ratio between the sums of the expected working hours of employees who are entitled to receive at least 3 bonuses to those who are entitled to only one?

A.    99:92.

B.     63:92.

C.     92:63.

D.    92:99.

E.     92:191.

The best answer is D.

Sum up the hours of all the age groups who cross at least three lines (30-40, 24-30); the sum is 92 hours. Do the same to all the groups who are over one line, which includes all the groups except for the first one. The second sum includes the first one in it and its 191 hours. The ratio is 92:191.

You could have answered right away with out the chart since you know that the second sum should include the first one and much more hours.

4. If employees under the age of 20 receive 8 dollars per hour and employees over that age receive 50% more, what is the ratio between the weekly-expected salary of two employees, 18 years old and 26 years old?

A. 4:3.

B. 3:4.

C. 7:15.

D. 15:7.

E. 6:11.

The best answer is C.

The expected weekly salary of a 18 years old employee is 28 hours times 8 dollars per hour, which is 224 dollars while a 26 years old employee makes (1.5 x 8 = 12) 40 hours times 12, which is 480 dollars per week.

The ratio is 224:480 or 7:15.

1. What is the ratio between the water consumption during the winter of 1994 to the summer of 1998?

A. 25:92.

B. 4:9.

C. 13:72.

D. 1:5.

E. 3:2.

The best answer is A.

Familiar you’re self with the graph. You can see that during the winter of 1994 250 mega-liters of water were consumed and during the summer of 1998 approx. 920 mega-liters of water were consumed and therefore the ratio is 250:920 or 25:92.

2. In which of the following years, was the ratio between the winter consumption to the summer consumption the closest?

A. 1991.

B. 1993.

C. 1996.

D. 1997.

E. 1998.

The best answer is C.

There is no escape from it, find out approximately all the ratios.

A. 80 to 420 or 4 to 21.

B. 110 to 500 or 55 to 250.

C. 300 to 520 or 15 to 26.

D. 280 to 560 or 1:2.

E. 510 to 920 or 51 to 92.

C and E are the closest, which one is the answer. Let’s see which fraction is bigger:

The closer ratio is C since the numerator is bigger.

3. In which of the following years was the greatest increase in consumption between the winter to the summer? (In percent terms).

A. 1991.

B. 1993.

C. 1995.

D. 1996.

E. 1998.

The best answer is A.

The greatest increase should be measured in percent relative to the winter of a certain year. Check the percent increase of each of the years.

1991- From 80 to 420, more than 400% increase.

1993- From 110 to 500, more than 350% increase.

1995- From 150 to 440, a little less than 200% increase.

1996- From 300 to 520, less than a 100% increase.

1998- From 510 to 920, less than a 100% increase.

We can see that the largest increase was during 1991.

4. If one mega-liter of water cost 30$ in 1995, approximately how much would the entire water consumption of 1998 cost assuming that there was an increase of 50% in the cost of water between 1995 and 1998?

A. $32,000.

B. $45,000.

C. $50,000.

D. $64,000.

E. $80,000.

The best answer is D.

The cost of mega-liter of water in 1998 is (30 x 1.5 = $45).

(920 + 510 = 1430 mega-liters) of water were consumed in 1998.

(1430 x 45 = $64,350) is the entire cost of water in 1998 and therefore answer D is the closest and the only one in the nearby region.

1. In the profession where the least number of new female employees are being recruited, what is the ratio between the male recruitments to the female recruitments?

A. 4:3.

B. 3:2.

C. 3:4.

D. 2:3.

E. 7:6.

The best answer is B.

Find the color, which represents the female recruitments, and look for the shortest one, thus the least number of new female employees (the bartenders bar).

You can see that there are 12 male and 8 female and therefore the ratio is 3:2.

2. In which category is the ratio between the female recruitments to the male recruitments the closest?

A. Cooks.

B. Bartenders.

C. Waiters.

D. Hosts.

E. Answers C and D.

The best answer is E.

Find the ratio for each of the categories.

Cooks- 9 to 22.

Bartenders- 8 to 12.

Waiters- 25 to 30, which is 5 to 6.

Hosts- 5 to 6.

We can see that both the waiters and the hosts have a ratio of 5:6, which is the closest and therefore answer E is the best answer.

3. Of all the new catering company recruitments, how many more males than females were recruited?

A. 6.

B. 8.

C. 11.

D. 15.

E. 22.

The best answer is C.

Sum up the male bars and the female bars and find the difference between them.

There are 64 new male and 53 female employees, thus the difference is 11 people.

4. Approximately what is the percent of new male employees that were not recruited to a waiters and a cook’s job out of the total male and female recruitments?

A. 8%.

B. 15%.

C. 22%.

D. 32%.

E. 45%.

The best answer is B.

If the male were not recruited to a cook’s job or a waiter job, they were recruited to a host or a bartender job, which is (5 + 12) 17 males’ employees in total.

The total number of new recruitments (female and male) is 117.

17 out of 117 are approximately 15% and therefore B is the answer.

5. If the manager of the catering company decides to recruit 20 more female employees and spread them evenly across the jobs, what will be the ratio between the female bartenders to the male and female hosts?

A. 12:17.

B. 13:16.

C. 18:11.

D. 8:21.

E. 13:11.

The best answer is B.

If the manager adds 20 female employees to the company and spread them evenly across the jobs, there’ll be 5 more in each job.

The ratio between the bartenders to the hosts will be (8+5 = 13) to (11 + 5 = 16) and therefore answer B is the best.

1. If all the students are on a three years course, how many more students finished with honors in 1997 than in1995?

A. 1%.

B. 2%.

C. 3%.

D. 4%.

E. 5%.

The best answer is C.

Go to the line which represents the percent of third year students, you can easily see that in 1996 5% finished with honors while in 1997 8% finished with honors and thus the difference is only 3%.

2. The class of which of the following years improved most significantly their percent of honor students from first to last year? (Students who finished their third and last year in 1999 for example are considered class of 1999).

A. 2000.

B. 1999.

C. 1998.

D. Answers A and B.

E. There isn’t enough data.

The best answer is A.

Go over each of the classes and see the improvement.

The class of 2000 finished with 19% honor students while they started in 1998 with 2%, which makes an 17% increase. The class of 1999 improved by 15% and the class of 1998 improved by 10% only. And therefore class of 2000 made the biggest increase and A is the answer.

3. In the second year where there was a decrease in the percent of honor students, what was the ratio between the percent of third year to second year honor students?

A. 7:19.

B. 19:3.

C. 21:6.

D. 19:7.

E. 3:19.

The best answer is D.

The first year, which had a decrease in the number of honor students, is the year 2000. In that year the ratio between third to second year honor students is 19 to 7 percent.

4. If every second year honor student in 2000 was also an honor student in 2001 and if 10% of the non-honor students among that group were also honor students in 2001, what percent of the third year students in 2001 honor students?

A. 4.5%.

B. 10.2%.

C. 16.4%.

D. 18%.

E. 20.5%.

The best answer is C.

7% of the second year honor students in 2000 were also honor students in 2001 and 10% of the rest (10% of 94% is 9.4%) are also honor students.

Add up the percentages: 7% + 9.4% is 16.4% percent honor students.

5. Assume that in 1997 there were 3,000 first year students in the University of Berkley. How many more third year honor students were in 1999 than second year honor students in 1998?

A. 320.

B. 380.

C. 400.

D. 420.

E. 550.

The best answer is D.

The same 3000 first year students in 1997 reached their third year in 1999 and therefore we can use the percentages in the graph.

In 1999 there were 18%, which is 540 honor students.

In 1998 there were 4%, which are 120 honor students.

The difference is 420 students.

6. What is the ratio between the second year honor students in 1997 to the second year non-honor students in 1997?

A. 2:23.

B. 2:24.

C. 2:25.

D. 2:26.

E. 1:8.

The best answer is A.

In 1997, second year, there were 8% honor students and therefore 92% of the students were non-honor students. The ratio is 8 to 92 or 2 to 23.

7. If in the class of 2000, each student was an honor student only once during his three years of studying, what percent of the students were honor students once during the trial of their degree?

A. 24%.

B. 25%.

C. 27%.

D. 35%.

E. 49%.

The best answer is C.

If each student wasn’t an honor student more than once in the class of 2000 then by adding up the percentages you’ll receive the percent of the students who were honor students once during the trial of their degree.

The answer is (19% + 6% + 2% = 27%).

8. If every student from 1996 to 2000 received the honor roll appellation only once during his entire trial of studying, which of the following classes contains the largest percent of students who were honor students at least once?

A. 2000.

B. 1999.

C. 1998.

D. Answers A and B.

E. There isn’t enough data.

The best answer is A.

Check the numbers for each of the classes.

In the class of 2000- (19% + 6% + 2% = 27%) were honor students once.

In the class of 1999- (18% + 4% + 3% = 25%) were honor students once.

In the class of 1998- (11% + 4% + 1% = 16%) were honor students once.

The class with the largest percent is the class of 2000, thus answer A is the best.

9. Among the honor students in the year 2000, what percent are third year students and learn Aerospace?

A. 1.9%.

B. 6%.

C. 10%.

D. 19%.

E. There isn’t enough data.

The best answer is E.

We know that 19% of all third year students are honor students and we know that 10% of all the honor students study Aerospace (second and first year too) but we can make a correlation between the two groups, we need more sufficient data.

We don’t know how many students are in their third year, that’s the missing link and therefore answer E is correct.

10. Assume that 12,000 students study in the Berkley University in the year 2000 and 50% are in their second year. How many honor students are in their second year and study Agriculture?

A. 900.

B. 126.

C. 98.

D. 63.

E. There isn’t enough data.

The best answer is E.

If 12,000 students are in their second year of study in the year 2000, we know that 50% out of them are in their second year, which is (0.5 x 12,000 = 6,000).

Out of the 6,000, 7% are honor students, which are 420 students.

By the bar graph, we know that 15% of all the students study Agriculture but we don’t know how many of them are in their second year and therefore we lack sufficient information. The answer is E.

1. For how many months in 2000 were the sales of world music CD’s less than any other trends of music?

A. 0.

B. 1.

C. 2.

D. 3.

E. 4.

The best answer is C.

Each line in the graph represents a type of music trend, find the line that represents world music and go over it from January to December and look for months that the line is the lowest among the other 3. You can see that in the months of April and June the line is the lowest one and therefore the answer is 2.

2. Approximately how many more world music CD’s were sold in August than Classic ones?

A. 1.5 million.

B. 2 million.

C. 3.2 million.

D. 4 million.

E. 4.5 million.

The best answer is B.

The question requires data from the months of August, go to that month and find, according to the line style, how many CD’s were sold in each of the music trends necessary. 7 million were sold in the world music category and 5 million were sold in the classic category, approximately 2 million difference.

3. In which of the following months were the total CD’s sales approximately double that of classic CD’s?

A. February.

B. March.

C. April.

D. November.

E. December.

The best answer is A.

This question could take you a long time if you don’t work wisely.

Don’t go over all the months, just the ones that are listed in the answers.

Answers, like December, you can easily disqualify since the classic music trend is relatively low. You can see that in the month of February the total CD sales were approximately 10 million, 5 out of them came from the classic category and therefore the classic music trend represents 50% of the total and A is the answer.

4. What was the approximate increase in the sales of Rock CD’s from February to September as percent of the increase in the sales of world music CD’s over the same period of time?

A.    20%.

B.     25%.

C.     40%.

D.    50%.

E.     75%.

The best answer is A.

In February, 3 million Rock and 1 million world music CD’s were sold.

In September, 4 million Rock and 6 million world music CD’s were sold.

In percent terms, the question is simply is how much is (4-3)/(6-1) = 1/5 = 20%.

And therefore answer A is the best.

5. If 195 million copies of Rock CD’s were made in the year 2000, approximately what percent were sold?

A. 10%.

B. 20%.

C. 30%.

D. 40%.

E. 50%.

The best answer is D.

You need to find how many Rock CD’s were sold during the entire year.

Find the line that represents the Rock category and sum up the sales in each of the months from January to December. Approximately 78 million copies were sold, which exactly 40% of 195 million. (78 x 2.5 = 195), and therefore answer D is the best.

Sales and Net income of two competing companies

1. Approximately what were the average sales of company X during the entire year

(In millions)?

A. 7.5.

B. 11.

C. 13.

D. 15.

E. 16.5.

The best answer is C.

Go to the sales graph and sum up the sales of company X across the seasons and divide by four. The math is (53/4 = approximately 13) and therefore the answer is C.

2. The sales of company Z in the winter were approximately how many times as great as the sales in the spring?

A.    2.5.

B.     3.

C.     4.

D.    5.

E.     5.5.

The best answer is E.

Go to the sales graph and find the pattern which represents company Z.

In the spring approximately 2.5 million dollars were sold while in the winter approximately 14 million were sold. 14 divided by 2.5 is 5.6 and therefore answer E is the closest one.

3. From summer to winter, the decrease in the net income of company X was approximately how much more in dollars than the increase of the net income of company Z during the same period of time?

A. 25,000.

B. 30,000.

C. 50,000.

D. 65,000.

E. 85,000.

The best answer is C.

Go to the net income graph. In the summer, 720 thousand dollars were made by company X while only 110 thousand were made by company Z. In the winter, X made 350 thousand while Z, made 430.

The differences in the decrease of X and the increase of Z is approximately

(720 – 350 – (430 – 110) =  50) thousand dollars.

4. Which of the following ratios was the greatest during the spring?

A. Company’s X sales to company’s X net income.

B. Company’s X sales to company’s Y net income.

C. Company’s Y sales to company’s Y net income.

D. Company’s Y sales to company’s X net income.

E. The sums of both companies’ sales to both companies net income.

The best answer is B

The best and most reassuring way is to check each of the ratios approximately.

A. 12,000,000 to 480,000, which is approximately 25.

B. 12,000,000 to 140,000, which is approximately 85.

C. 2,500,000 to 140,000, which is approximately 18.

D. 2,500,000 to 480,000, which is approximately 5.

E. 14,500,000 to 620,000, which is approximately 23.

The best answer is obviously B.

5. For what company in which season was the net income at least 5% of sales?

A. Company X in the summer.

B. Company X in the winter.

C. Company Z in the winter.

D. Company Z in the fall.

E. Company Z in the spring.

The best answer is E.

In this question you’ll need to cross the data from both of the charts.

Go over each of the possible answers and find the percent of the net income to sales.

A. 720 thousand out of 25 million, which is less than 3%.

B. 350 thousand out of 9 million, which is less than 4%.

C. 430 thousand out of 14 million, which is less than 4%.

D. 290 thousand out of 10 million, which is less than 3%.

E. 140 thousand out of 2.5 million, which is a little over 5% and therefore this is the correct answer.

The following chart represents the range of prices according to category of imported cars to the state of Idaho in the year 1988. The prices are in hundreds of dollars.

1. What two types of cars cannot be bought in the same price?

A. Sports cars and American cars.

B. Japanese cars and Compact cars.

C. Japanese cars and American cars.

D. Sports cars and Japanese cars.

E. European cars and sports cars.

The best answer is E.

The chart represents ranges of prices. Try to find two categories that do not have an overlapping- the only categories among the answers given that don’t have an overlapping are the ones in answer E. European cars range from 250 to 450 while sports cars start only in 500.

2. Which of the following categories have the largest amount of overlapping in their price?

A. Executive cars and American cars.

B. Japanese cars and Europeans cars.

C. Japanese cars and American cars.

D. Sports cars and Japanese cars.

E. European cars and sports cars.

The best answer is C.

Go over each of the answers and find the overlapping between the two.

A- There is a 250 hundred dollars of overlapping.

B- There is a 200 hundred dollars of overlapping.

C- There is a 400 hundred dollars of overlapping.

D- There is a 50 hundred dollars of overlapping.

E- There is no overlapping.

We can see that C is the best answer since the Japanese category is included in the range of the American category according to the graph.

3. Which of the following statements must be false?

A. The average price of a sports car is 600 hundred dollars.

B. The average price of an American car is greater than the average price of an executive car.

C. The average price of a compact car is 300 hundred dollars.

D. The average price of a European car is greater than the average price of a sports car.

E. The average price of a European car is lower than the average price of a compact car.

The best answer is D.

The key to this question is to understand that the average can be anywhere along the range and not necessary in the middle.

All the answers are possible except D because there is no overlapping between the two categories and therefore the higher range must have the higher average, which is contrasting to the statement. And therefore D must be the only statement that must be false.

4. Which of the following statements must be true?

A. The maximum price of an executive car is higher than the minimum price of a sports car.

B. The overlapping between the Japanese cars and the compact cars is larger than the overlapping between American cars and sports cars.

C. The average price of a sports car must be higher than that of an American car.

D. A and B must be true.

E. A, B and C must be true.

The best answer is D.

Let’s go over answers A, B and C.

A- The maximum price of an executive car is 950 while the minimum price of a sports car is 500 and therefore this statement is true.

B- The first overlapping is approximately 250 while the second overlapping is approximately 100 and therefore this statement is also true.

C- The average price can be anywhere in the range and therefore this statement is not necessarily true and D is the answer.

5. A young couple in the state of Idaho bought two cars, an Executive car for the husband and a sports car for the wife. Which of the following amounts is not a possible price for both cars?

A. $65,000.

B. $90,000.

C. $110,000.

D. $125,000.

E. $195,000.

The best answer is A.

The range of prices for the sum of both cars is between the two minimum prices to the two maximum prices. In other words, the minimum price is (50,000 + 35,000 = 85,000) and the maximum possible price is (95,000 + 100,000 = 195,000).

Among the answers given, A is the only one that is out of range.

6. Two cars were stolen from a car dealership in Boise, Idaho. Which of the following cannot represent the loss of the car dealership’s owner?

A. $18,000.

B. $198,000.

C. $10,000.

D. $200,000.

E. There isn’t enough data to determine the answer.

The best answer is C.

Find the possible range of any two cars since we don’t know what kind of cars were there in the dealership.

The minimum price of any car is the low end of the range of the compact cars, which is approximately $7,500. And therefore the minimum price for two cars is $15,000.

The maximum price is determined by the highest price in the chart, the highest price for a sports car, which is $100,000 and therefore the maximum price for two cars is $200,000.

The only answer which is not in the range is C, $10,000.

7. If Michael has $20,000, which of the following cars are in his budget?

A. Compact car.

B. Japanese car.

C. American car.

D. European car.

E. answers A-C are correct.

The best answer is E.

Go to the 200 line in the graph and find out which of the categories have a possible range under that line. Answers A, B and C are possible and therefore E is the answer.

8. Robert bought a sports car in 1988 and sold it after a few weeks in a price that ranges from $35,000 to $43,000. What would be his financial loss on the car?

A. $7,000 to $15,000.

B. $15,000 to $35,000.

C. $12,000 to $42,000.

D. $7,000 to $65,000.

E. $15,000 to $68,000.

The best answer is D.

The financial loss also has a range, let’s find it.

The minimum loss would occur if he bought the car at the lowest price (50,000) and sold it in the highest price (43,000), the loss is $7,000.

The maximum loss is exactly the opposite. He bought the car at the highest price and sold it at the lowest price, thus (100,000 – 35,000 = 65,000).

We can see that D is the correct range.

9. Antonio bought a compact car and sold it after a year at 75% of its original price. What was the price of the car that Antonio sold?

A. $15,000 to $25,000.

B. $7,545 to $35,000.

C. $15,000 to $70,000.

D. $5,000 to $25,000.

E. $5,625 to $30,000.

The best answer is E.

Antonio bought a car between $7,500 and $40,000. Take 75% of both edges and you’ll receive the price that he sold the car. 75% of 40,000 is $30,000 and since answer E is the only one with that number, that is the answer.

The following graph represents the prices of apartments in Chicago in different parts of the city. Each shape represents the ranges of prices and sizes of apartments in each of the areas mentioned in the key. For example, point A represents an apartment in the Chicago suburbs that is 140 meters squared and costs 210 thousand dollars.

Key:

v  The rectangle represents apartments in the West side of Chicago.

v  The ellipse represents apartments in the down-town area of Chicago.

v  The triangle represents apartments in the East side of Chicago.

v  The parallelogram represents apartments in the suburbs of Chicago.

1. What size of apartment can be bought only in one area of Chicago?

A.    110 meters squared.

B.     115 meters squared.

C.     125 meters squared.

D.    130 meters squared.

E.     155 meters squared.

The best answer is A.

To each of the possible answers, draw an imaginary vertical line and see where it intersects.

110 meters intersects the rectangle only while all the others intersect at least two geometric shapes and therefore A is the answer.

2. Which of the following sizes of apartments (in meters squared) can be found in the greatest number of place across Chicago?

A. 115.

B. 123.

C. 135.

D. 142.

E. 158.

The best answer is D.

Again, draw a vertical line and count how many different geometric shapes the line intersects. All the lines except for one intersect 2 geometric places. The size 142 meters squared can be found in three different places in Chicago and therefore this is the answer.

3. Ruth and Bill are interested in buying an apartment building that is at least 130 meters squared, in the lowest price possible. In which of the areas of Chicago should they buy an apartment?

A. West side.

B. East side.

C. Downtown area.

D. Suburbs.

E. Answers C and D are both possible.

The best answer is C.

Go to the 130 line (in the horizontal axis) and look to the right of it.

There are three possibilities: downtown, suburbs and East side.

The apartments with the lowest price are the ones in the ellipse and therefore they should buy an apartment in the downtown area of Chicago.

4. In which of the following areas in Chicago, when the size of the apartment increases the price decreases?

A. West side.

B. East side.

C. Downtown area.

D. Suburbs.

E. Answers A and B are both possible.

The best answer is B.

The geometric shape that has a negative slope is the triangle and so when the sizes increase the prices decrease. This is not a logical regularity but this is what the graph gives us.

5.  Which of the following schematic charts represents the difference (in absolute value) between the high and the low price of an apartment building in the suburbs of Chicago?

A.                                      B.                               C.

D.                                         E.

The best answer is D.

Look at the geometric shape that represents the suburbs of Chicago, thus the parallelogram. In the beginning the high and the low price are both the same so the difference graph should start from zero. Then the high price increases and the low price stays the same, thus answers B, C and D are possible. After that the high price and the low price remain equal and so the difference graph should also be horizontal, answers C and D are left. The last part is the same as the first one, only in different direction and therefore answer D is the only one left.

Movie A and movie B are two new successful movies that started to play at the same time. The following graph represents the differences in ticket sales in the first 10 weeks of sampling. The “best movie” is the one that sold more tickets after 10 weeks.

1. In which week was the same number of tickets sold in both movies?

A. 4.

B. 6.

C. 8.

D. 9.

E. 10.

The best answer is C.

The points on the graph represent differences in ticket sales. The week that doesn’t have any point is the week where the same number of tickets was sold; that would be the eighth week and so answer C is the best.

2. If in the first week, 9,560,000 movies A tickets were sold, how many movie B tickets were sold that week?

A. 4,650,000.

B. 9,060,000.

C. 5,650,000.

D. 9,645,000.

E. 4,560,000.

The best answer is E.

The point in the first week represents the number of tickets that movie A sold more than movie B and therefore movie B sold 5 million tickets less than 9,560,000, which is 4,560,000 and therefore answer E is the correct.

3. If movie A sold the same number of tickets each week then in which of the following weeks was the least amount of tickets sold to movie B?

A. 5.

B. 6.

C. 7.

D. 8.

E. 9.

The best answer is E.

If movie A sold the same number of tickets each time all we have to do is look for the week in which movie A sold as many more tickets than movie B, that would be on the ninth week- there movie A sold 9 million tickets more than movie B.

4. In the fourth week, movie B sold 5 million less tickets than in the third week. What would be the difference in the number of tickets sold to movie A between the third and the fourth week?

A. 2.

B. 4.

C. 5.

D. 9.

E. 15.

The best answer is C.

In this question the easiest way is to plug in some numbers.

Let’s say that 20 million tickets were sold on the fourth week for movie B and therefore 25 million were sold in the third week according to the question. Now go to the graph; in the third week movie B sold 4 million more than A, thus A sold 21 million tickets.

As for the fourth week, A sold 6 million more than B, thus A sold 26.

The difference in ticket sales are (26 – 21 = 5 million) and therefore answer C is correct.

5. Which movie won the title “best movie” ?

A. Movie A.

B. Movie B.

C. They both sold the same amount of tickets.

D. There isn’t enough data to answer the question.

The best answer is B.

Each week, we know which movie sold more tickets. If we sum up the differences in each of the weeks we’ll find that movie B sold 4 million tickets more than movie A and therefore it is the “best movie”.

The following graphs represent the total sales of the “Bulletin Newspaper” in the city of Wisconsin, Illinois across a period of 15 years. The lower graph represents the breakdown of production to each of the photographic engraving machines.

1. For how many years did machine D produce more newspapers than any other photographic engraving machine?

A. 4.

B. 5.

C. 6.

D. 7.

E. 8.

The best answer is C.

The question refers solely to the bottom graph. We are looking for years in which the line that represents the machine D is the highest. We can see that in the years 1983 and from 1986 to 1990 machine D had the highest percentage of production and therefore C is the answer.

2. In which of the following years was the number of copies sold closest to 2 million?

A. 1976.

B. 1978.

C. 1980.

D. 1987.

E. 1989.

The best answer is E.

2 million will be represented as 2000 in the upper graph since the units are in thousands.

Go over all the given years (only) and see which one is the closest to 2000.

You can easily see that in the year 1989, the sales stood on approximately 1900, which is the closest.

3. In which of the following years, was the greatest number of active photographic engraving machines?

A. 1977.

B. 1980.

C. 1982.

D. 1987.

E. 1990.

The best answer is C.

This question requires the use of the upper graph only.

Go over all the given years and draw an imaginary vertical line to each one, see how many “machine” line it intersects. You can easily see that in 1982 there were four intersections.

4. In which of the following years was the least amount of active machines?

A. 1976.

B. 1978.

C. 1980.

D. 1984.

E. 1986.

The best answer is A.

This question is exactly the opposite of the previous one. Again draw a vertical line and count the intersections, this time look for the minimum.

You can see that in 1976 only one machine did all the work and therefore A is the answer.

5. In the year in which machine A did four times more work than machine B, how many copies approximately of the “Bulletin Newspaper” were sold in Wisconsin

(In thousands)?

A. 550.

B. 620.

C. 740.

D. 810.

E. 900.

The best answer is C.

Go over the first years (where machine A was active) and find the year in which machine A did 4 times the work machine B did in percent terms. You can see the in the year 1979, 20% of the work was done by B and the rest (80%) was done by A and therefore this is the spoken year. Go to the upper graph and find the amount of copies sold, the answer is approximately 750 and so C is the closest answer.

6. Approximately how many copies of newspapers did machine C make in the year 1988?

A. 675,000.

B. 710,000.

C. 820,000.

D. 875,000.

E. 900,000.

The best answer is C.

Go to the bottom graph; machine C did 35% of the total work.

According to the upper graph, approximately 2,350,000 copies of newspapers were sold.

35% of 2,350,000 are approximately 820,000 and therefore C is the answer.

7. What exactly is the difference between the number of copies that machine D and B did

in 1982?

A. 550,000.

B. 420,000.

C. 270,000.

D. 45,000.

E. 0.

The best answer is E.

Go to the year 1982 in the bottom graph. You can see that machine D and B did the same amount of work and therefore the difference must be zero.

8. By approximately what percent did the yield from machine A increase from 1977 to 1981?

A. 15%.

B. 40%.

C. 50%.

D. 60%.

E. 67%.

The best answer is E.

Let’s find the increase in the yield of machine A.

In 1977, machine A did 100% of the work, which are approximately 450,000 copies.

In 1981, machine A did 50% of the work, which is 50% of 1,500,000, thus 750,000 copies. The difference (or the increase) was by 300,000 copies and in terms of percent the increase was (300/450 = 67%) and therefore E is the answer.

9. In how many years did machine C did the same amount of work as any other machine from 1981 to 1990 inclusive?

A. 0.

B. 1.

C. 2.

D. 3.

E. 4.

The best answer is C.

Remember, intersections are do not count between the years, only when the exact mark of the year comes. In other words there were 3 intersections only, in 1981, 1983 and in 1985.

The intersection between 193 and 1984 does not count as one.

10. Approximately what is the ratio between the numbers of newspapers that machine D produced in 1987 to the number of newspapers that machines A and B produced in 1981?

A. 13:28.

B. 4:5.

C. 2:3.

D. 6:7.

E. 72:75.

The best answer is E.

Use both graphs to answer this question.

In 1987 machine D produced 60% (from bottom graph) of 2400 (upper graph), which is 1,440,000. In 1981 both machine together produced a 100% of the newspapers that were sold, thus 1,500,000. The ratio is 144 to 150; break it down into simpler numbers.

Divide by 2: 72 to 75 and therefore answer E is the best.

The first graph represents the budget breakdown of three major hospitals to factors.

All of the budgets are the same and there are no other allocations besides those in the graphs. The second graph represents the percent of satisfied patients in each of the hospitals by gender. For example, 30% of the males that voted in hospital B are satisfied with the service.

1. In the hospital where the percent of the satisfied female patients is the highest, what is the ratio between the percent of satisfied male patients to the percent of unsatisfied female patients?

A. 1:7.

B. 2:3.

C. 1:3.

D. 4:5.

E. 7:9.

The best answer is C.

Use the bar chart; the hospital in which the percent of the female satisfied patients is the highest is hospital C. There, there are 10% male satisfied patients and 30% unsatisfied female patients. The ratio is therefore 1 to 3.

2. In the hospital where the percent of satisfied male and female is equal, what percent of the budget is being spent on hospital staff?

A. 5%.

B. 10%.

C. 15%.

D. 20%.

E. 25%.

The best answer is E.

According to the bar chart, the hospital in which the percent of the males and the females is the same is hospital B. In that hospital 5% of the budget goes to nurses and 20% of the budget goes to doctors, altogether 25% of the budget goes to staff.

We assume that the staff includes the doctors and the nurses.

3. In which of the following areas doe’s hospital A invests the largest part of his budget?

A. Equipment.

B. Hygiene.

C. Nurses.

D. Food.

E. Medicine.

The best answer is C.

According to the graph, the hospital spends the largest part of his budget on doctors, which are not among the options and therefore go to the second investment, which are the nurses (25% of the budget). The best answer is C.

4. Which of the following is the most expansive investment?

A. Hospital A on Hygiene.

B. Hospital B on Food.

C. Hospital C on Medicine.

D. Hospital A on nurses.

E. Hospital B on equipment.

The best answer is E.

Go over each of the answer and find the percent of investment. Remember that the passage prior to the questions claimed that all the budgets are equal.

Hospital B spent 50% of his budget on equipment, which are the most expansive investments among the other answers.

5. In which of the hospitals the difference between the investment in doctors and nurses is the greatest?

A.    Hospital A.

B.     Hospital B.

C.     Hospital C.

D.    Answers A and B.

E.     Answers B and C.

The best answer is A.

Let’s go over each of the hospital and find the required difference.

Hospital A: 50% goes to doctors and 25% goes to nurses. The difference is 25%.

Hospital B: 20% goes to doctors and 5% goes to nurses. The difference is 15%.

Hospital C: 30% goes to doctors and 15% goes to nurses. The difference is 15%.

And therefore the greatest difference is in hospital A.

6. In which of the following hospitals is the ratio between the investment on medicine and equipment relative to hygiene and food the closest?

A. Hospital A.

B. Hospital B.

C. Hospital C.

D. Answers A and C.

E. Answers A and B.

The best answer is A.

Go over each of the answers and find the necessary ratio.

A: 15% goes to food and hygiene while 10% goes to medicine and equipment.

B: 20% goes to food and hygiene while 55% goes to medicine and equipment.

C: 35% goes to food and hygiene while 20% goes to medicine and equipment.

The closest ratio is in hospital A. The ratio is 10 to 15 or 2 to 3.

7. The number of male patients that participated in the pole of the second graph in all the hospitals is the same. If the number of satisfied patients in hospital C is 68, what is the total number of satisfied male patients in all three hospitals?

A. 476.

B. 544.

C. 622.

D. 856.

E. 1156.

The best answer is B.

If 10% are 68 people then 100% are 680.

The question said that the number of male patients is equal in all the hospitals (680).

Sum up the satisfied male patients in all the hospitals: 68 + (0.3 x 680) + (0.4 x 680) = 68 + 204 + 272 = 544 patients.

8. Based on the two graphs, which of the following statements represents the reality in the hospitals in the best way?

A. The more the hospital invests in doctors the more satisfied male patients.

B. The more the hospital invests on hygiene the more satisfied female patients.

C. The more the hospital invests in equipment the more satisfied female patients.

D. The less the hospital invests on hygiene the more satisfied male patients.

E. The less the hospital invests on food the more satisfied female patients.

The best answer is D.

Ironically, the less hospital spends on hygiene the more satisfied male patience.

Using both graphs, we are looking for a pattern in the general results of the graphs.

We can see that hospital A spends the least amount of money on hygiene while the percent of male patients there is the highest. Answer D reflects the tendency of male patients according to the graphs.

9. Which of the following represents the status of hospital C?

A. A relatively large percent of satisfied male patients and a large investment on nurses.

B. A relatively small percent of female satisfied patients and a large investment on doctors.

C. A relatively small percent of satisfied male patients and a large investment on doctors.

D. A relatively large percent of female satisfied patients and a large investment on doctors.

E. A relatively large percent of female satisfied patients and a large investment on equipment.

The best answer is D.

From the first graph you can conclude that a large portion of the budget goes to doctors. From the second graph you can notice that the percent of satisfied females is relatively high. The answer that reflects this situation is D.

The following chart represents the number of visitors and their origin and the percent of bypasses that only come and go through the gates of the city.

The percent of bypasses is relative to the total number of visitors.

1. In the year where the percent of bypasses was the greatest, approximately what percent of the total visitors came from the United States?

A.    25%.

B.     48%.

C.     65%.

D.    72%.

E.     83%.

The best answer is E.

According to the graph, the year with the greatest amount of bypasses is 1985.

In that year, 48 thousand out of 58 thousand visitors came from the U.S.

In percent terms: 48 out of 58 is approximately 50 out of 60, which is approximately 83% and therefore answer E is the closest one.

2. If 40% of the visitors to Las-Vegas gambled during their stay, how many gamblers were in the year 2000?

A. 22,500.

B. 36,800.

C. 46,000.

D. 55,200.

E. 92,000.

The best answer is B.

In the year 2000 (52 + 24 + 16 = 92) thousand visitors came to Las-Vegas.

40% among them gambled. 40% of 92,000 are .

3. In 1990, what was the ratio between the numbers of visitors that came from South America to those who came from Europe?

A. 8:10.

B. 2:3.

C. 5:4.

D. 3:2.

E. 4:5.

The best answer is C.

Look at the numbers below the graph. You can easily see that 8,000 visitors came from South America while 12,000 came from Europe. In ratio problem the zero’s “fall off” and you are left with 8 to 12, which is 4 to 5.

4. Approximately how many visitors in 1990 are only bypasses?

A. 5 thousand.

B. 7 thousand.

C. 11 thousand.

D. 13 thousand.

E. 15 thousand.

The best answer is D.

We were told that the percent of bypasses is relative to the total number of visitors.

In the year 1990, we can see that there were (45 + 8 + 12 = 65) thousand visitors to Las-Vegas. 20% out of them are bypasses, which is 13,000 and therefore answer D is correct.

5. In 1995, what is the ratio between the numbers of bypasses to the number of visitors that came from South America?

A. 5:9.

B. 2:3.

C. 1:2.

D. 3:2.

E. 9:5.

The best answer is C.

In 1995, the total number of visitors is 90,000; 10% of 90 thousand are bypasses, which is 9,000. Based on the table, the amount of visitors that came from South America is 18,000 and therefore the ratio is 1 to 2.

6. In which year was the greatest amount of real visitors?

(Real visitors are the number of people that are not bypasses).

A. 1985.

B. 1990.

C. 1995.

D. 2000.

E. Answers A and B.

The best answer is

Take each year and find the approximate number of real visitors, do not waste your time and calculate the accurate numbers.

In 1985, 65% (100% - 35%) out of 58,000 is approximately 38,000.

In 1990, 80% (100% - 20%) out of 65,000 is approximately 52,000.

In 1995, 90% (100% - 10%) out of 90,000 is approximately 81,000.

In 2000, 95% (100% - 5%) out of 92,000 is approximately 87,400.

We can see that the greatest amount of real visitors is in the year 2000.

Basically, the whole calculation procedure is unnecessary since we can see that the number of visitors is growing each year and the percent of bypasses is decreasing.

7. Assuming that all the Las-Vegas visitors are mentioned in the graph, how many bypasses didn’t come from Europe in 1990?

A. Between 0 and 8,000.

B. Between 8,000 and 12,000.

C. Between 0 and 13,000.

D. Between 1,000 and 13,000.

E. There isn’t enough data.

The best answer is D.

In 1990 there were 65,000 visitors in total. 20% of them were bypasses and we don’t know their place of origin and so E looks like a good answer, but no.

Even if all the Europeans were bypasses, there will still be 1,000 bypasses left and so the number of bypasses which didn’t origin in Europe is more than 1,000 but we already know that its less than 13,000 and therefore D is the answer.

8.Which of the following statements is true?

A. In 1995 there were Europeans and Americans among the bypasses.

B. The bigger the number of visitors, the bigger the number of bypasses.

C. The number of real visitors from Europe in 1990 is larger than the number of real visitors from Europe in 1985.

D. The number of real visitors from Europe in 1995 is larger than the number of real visitors from Europe in 1990.

E. Answers C and D are correct.

The best answer is D.

Let’s eliminate each of the answers until we find the best one.

(A) In 1995 there could have been any types of visitors in the groups of bypasses including people from South America and therefore this answer is disqualified.

(B) We saw in the first questions that the bigger the number of visitors, the lower the percent of the bypasses and therefore this answer is also disqualified.

(C) If all the Europeans in 1990 came from Europe and in 1985 none of them came from Europe than the statement wouldn’t be true and therefore it isn’t necessarily.

(D) This is the only correct answer. Even if all the bypasses came from Europe there’ll still be more Europeans than in 1990.

9. In the year with the greatest percent increase in the number of visitors from South America, how many bypasses didn’t come from South America?

A. Between 0 and 18,000.

B. Between 0 and 9,000.

C. Between 9,000 and 18,000.

D. Between 18,000 and 90,000.

E. There isn’t enough data to answer the question.

The best answer is B.

First, find the relevant year. You can see that in the year 1995 there are 18 thousand visitors from South America while in 1990 there were only 8 thousand- that’s the largest increase. In that year there are (0.1 x 90,000 = 9,000) bypasses and therefore there could be zero or even 9,000 from different places than South America.

The answer is B.