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.





Points of the Chicago team
Points
Of
The
Milwaukee
Team
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.


1990
Males, less
than 30 years
of age
42%
Males, 30
years and over
15%
Females, less
than 30 years
of age
22%
Females, 30
years old and
over
21%


2000
Males, less
than 30 years
of age
32%
Males, 30
years and over
20%
Females, less
than 30 years
of age

17%
Females, 30
years old and
over
31%


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  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  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.

Percent change in crimes
0
-4.5
-9
-15
0
-16
-22
-25
-30
-25

-20
-15
-10
-5
0
1998199920002001
Number of crimes recorded
Crime rate per 1,000 residents


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:
3
1
1133000,8575
85
1000
75
 NN
N
. 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.

The progress of the rabbit and the squirrel
on a 13 miles track
0

2
4
6
8
10
12
14
8
:
00
9
:
00
10
:
00
11
:
00
12
:
00
13
:
00
14
:
00
15
:

00
16
:
00
17
:
00
17
:
30
Distance from start point
Squirrel
Rabbit


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.