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QUESTION: 1

At the end of the year 2002, Monica and Chandler each purchased a certificate of deposit that paid the same rate of interest, and each held the certificate of deposit through the end of 2002. If Chandler invested X dollars and Monica invested $130,000, and if Chandler earned interest in 2002 totaling $45,000, what was the amount of interest that Monica earned on her $130,000 investment?

(1) The rate of interest on the certificate of deposit that Chandler and Monica each purchased was 8.5% annually.

(2) In 2002, Chandler invested $529,412 in the certificate of deposit.

Solution:

The best answer is D.

From statement (1) we know the rate of interest, so we can easily calculate how much Monica earned with her $130,000 deposit.

From statement (2) we know how much Chandler invested and we already know from the question how much he earned, we can calculate the interest and multiply it by the deposit that Monica made.

Therefore, both statements, by themselves, are sufficient to answer the question.

QUESTION: 2

Mickey made an X dollars loan at the beginning of 1996. Travis, who is Mickey’s little brother also made a loan, only twice as large as Mickey’s but with the same interest. If Travis pays $10,000 interest on his loan each year, how big is Mickey’s loan?

(1) The rate of interest on the loan that Travis took is 6% annually.

(2) The loan that Travis made was $166,667.

Solution:

The best answer is D.

From statement (1) we know the rate of interest so we can find how much money Travis loaned and multiply it by 2 to get Mickey’s loan.

From statement (2) we know the amount Travis loaned, which is doubled than that of Mickey.

Therefore, both statements, by themselves, are sufficient to answer the question.

QUESTION: 3

Concentrated orange juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated orange juice, at the most, can fit into 3 wooden boxes?

Solution:

The best answer is A.

You want to waste as little amount of space as possible, therefore make the height of the box 11 and fit 4 boxes at the bottom so you lose only 1 inch of margin at the top and on one of the sides.

You can see that 8 tubes can fit into one box thus 24 tubes fit into 3 boxes.

QUESTION: 4

A certain car’s price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased her price by $1,500. If the price of the car in 1996 was $22,000, what is the car’s price in 2002?

Solution:

The best answer is C.

The price of the car decreased by 2.5% every year on a course of 6 years. That means that the price of the car in 2002 is 15% lower than the original + $1500 of new investments.

The new price is ($22,000 x 0.85 = 18,700 + 1500 = $20,200).

QUESTION: 5

The average price of an antique car increases over the years. If from 1990 to 1996, the price of the car increased by 13% and from 1996 to 2001 it increased by 20%, what is the price of the car in 2001 if the price in 1990 was $11,500?

Solution:

The best answer is A.

The price in 1990 was 11,500. In 1996 the price is (11,500 x 1.13 = 12,995).

The price we are looking for, in 2002, is (12,995 x 1.2 = $15,594).

QUESTION: 6

The apartment on King-Williams street is an asset that it’s value is tramping about.

From the year 1973 to 1983 it’s value decreased by 16% and from 1983 to 1993 it’s value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $40,000?

Solution:

The best answer is C.

Be careful, the value of the asset didn’t stay the same after the two changes in the value.

In the first 10 years, the value decreased by 16% (40,000 x 0.84 = 33,600).

Then, in the next ten years the value increased by 16% (33,600 x 1.16 = 38,976).

Therefore the answer is C.

QUESTION: 7

The value of a “Tin-Rin” stock in the stock market decreased by 15% in the last two years.

The economic experts believe that the value of the stock will increase by 7% during the following year, which will make the value $440. What was the approximate price of the stock two years ago?

Solution:

The best answer is A.

Start from the top, after a 7% increase the price of the stock is $440.

440 are 107% of the price this year à (440/107 x 100 = 411.215).

Two years ago the price was 15% higher, therefore (411.215 x 1.15) is approximately $473.

QUESTION: 8

Which of the following expressions is equivalent to |X| <4 ?

Solution:

The best answer is E.

An absolute value means that the sign of the variable is insignificant, therefore X can be between –4 and 4 and still he will fulfill the original equation.

QUESTION: 9

Which of the following statements is equivalent to (8 + 2X < 18 – 6X < 23 + 2X)

Solution:

The best answer is C.

Take the expression and simplify it: Take (8 + 2x) from each side to get: (0<10 – 8X<15).

Substitute 10, -10<-8X<5.

Divide all by (-8), 5/4 > X > -5/8. Therefore the answer is C.

QUESTION: 10

At the faculty of Aerospace Engineering, 312 students study Random-processing methods, 232 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering?

Solution:

The best answer is D.

Use the group formula.

Total = group_{A} + group_{B} – Both + Neither.

Total = 312 + 232 – 112 + 0 = 432 students

QUESTION: 11

In the faculty of Reverse-Engineering, 226 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 80% of the total?

Solution:

The best answer is D.

Use the group formula.

Total = group_{A} + group_{B} – Both + Neither.

Total = 226 + 423 – 134 + 0 = 515 second year students.

The second year students are 80% of the total amount, therefore (515/80 x 100 = 643.75).

The best answer is D.

QUESTION: 12

In the Biotechnology class of 2000, there were X graduates. 32 of the graduates found a job, 45 continued on to their second degree and 13 did both. If only 9 people didn’t do both, What is X equal to?

Solution:

The best answer is C.

Use the group formula.

Total = group_{A} + group_{B} – Both + Neither.

Total = 32 + 45 – 13 + 9 = 73 graduates.

QUESTION: 13

If a, b, c, d and e are distinct integers, which one is the median?

(1) a < b – c.

(2) d > e.

Solution:

The best answer is E.

Statement (1) tells us nothing about e and d, you can eliminate answers (a) and (d).

Statement (2) tells us nothing about a, b and c, you can eliminate answer (b) .

Try to plug in some numbers, take: a=3, b=7, c=1, d=9 and e=8. The median in that case is 7.

Try other numbers, a=8, b=15, c=6, d=10 and e=9. The median is 9.

First the median was b, then the median was e. More sufficient data is required to answer the question.

QUESTION: 14

a, b and c are three odd and different integers. Which one is the median?

(1) a, b and c are consecutive numbers.

(2) c > a and b < c.

Solution:

The best answer is A.

From statement (1) we can learn that if they are consecutive numbers, the median is B.

From statement (2) we have a connection between c to a and b, but we don’t know if a or b is the smallest among the three, therefore this statement, by itself, is not sufficient.

QUESTION: 15

What is the ratio between W and Q?

(1) Q + W = 23.

(2) W is 25% of Q.

Solution:

The best answer is B.

We are looking for Q/W. From statement (1) we know the sum of the two variables, which is not helpful in our case. From statement (2) we know that W = (0.25)Q, therefore we know the ratio between the two variables.

QUESTION: 16

What is the product of X and Y?

(1) 2X + 2Y = 46.

(2) (X + Y)^{2} = (X – Y)^{2} + 8.

Solution:

The best answer is B.

The product of X and Y is XY.

Statement (1) implies only about their sum.

Statement (2) can be written as: X^{2} + 2XY +Y^{2} = X^{2} – 2XY + Y^{2} + 8 → 4XY = 8 → XY = 2.

Only statement (2) is sufficient

QUESTION: 17

Kramer can pack X boxes of cigarettes per minute. If there are Y boxes of cigarettes in one case, How many cases can Kramer pack in 2 hours?

Solution:

The best answer is B.

Y/X is the time it takes Kramer to fill a case with boxes (in minutes).

In two hours there are 120 minutes, so 120/(Y/X) is 120X/Y, and that is the number of cases that Kramer can fill in two hours.

QUESTION: 18

George can fill Q cans of paint in 3 minutes. If there are R cans of paint in one gallon, how many gallons can George fill in 45 minutes?

Solution:

The best answer is E.

George can fill Q/3 cans of paint in one minute à There are R cans in one gallon, so R/(Q/3) = 3R/Q

Is the time it takes George to fill one gallon (in minutes).

In 45 minutes George can fill up 45/(3R/Q) = 15Q/R.

QUESTION: 19

The junior soccer team is one of the best teams in the state of Alabama. The season is divided into two parts, each part is 4 months. In the first part of the season, the junior soccer team won half of their 32 games. How many games did the team win in the entire season?

(1) In the second part of the season, the team lost 9 games, tied 6 games and won 18 games.

(2) From the 32 games remaining the team won twice as much as she lost.

Solution:

The best answer is A.

From statement (1) we can complete the missing data, in the first part of the season the team won 16 games and on the second part of the season, the team won 18 games. This statement is sufficient enough to answer the question.

Statement (2) is not sufficient by it self, it doesn’t mention how many games were tied, therefore only statement (1) is sufficient.

QUESTION: 20

“Queens” is a game of cards that distinguishes the cards into three groups: reds, blacks and jokers. Four packets of cards are shuffled and only 50 cards are drawn out. How many red cards are in the stack of the 50 cards?

(1) The number of black cards is twice the number of red cards.

(2) There is at least one joker in the stack of cards.

Solution:

The best answer is E.

Statement (1) implies that if we knew the number of jokers, the answer would be clear: take the cards that are not jokers and divide them by 3 to get the number of red cards.

Statement (2) is not clear enough, the number of jokers is not distinct, therefore more data is needed and the two statements taken together are not sufficient.

QUESTION: 21

Ron has three kinds of shirts in his closet, white shirts, black shirts and fancy shirts. What is the ratio between the shirts in the closet?

(1) The total number of shirts is 100.

(2) 30% of the shirts are black, which is twice as much as the fancy shirts.

Solution:

The best answer is C.

From statement (1) we know the total amount of shirts in the closet.

Statement (2) gives us the ratio between the shirts.

30% of the shirts are black (which is 30 shirts), this number is twice as much as the fancy shirts (15).

The remaining shirts must be white. We know the ratio; therefore both statements are required in order to answer the question correctly.

QUESTION: 22

The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 784 feet squared, what is the difference between the length and the width of the roof?

Solution:

The best answer is C.

The area of a rectangle is (length) x (width), let X be the width of the roof → 4X^{2} = 784 →

X^{2} = 196 à X = 14.

The width of the roof is 14 and the length is 56. The difference is (56-14 = 42).

QUESTION: 23

The length of a cube is three times its width and half of its height. If the volume of the

Cube is 13,122 Cm cubed. What is the height of the cube?

Solution:

The best answer is C.

Normalize each dimension to the width of the cube (W).

The length is 3 times the width, therefore its 3W, which is half of the height (6W).

The volume of the cube is 13,122 = 6W x 3W x W = 18W^{3} → W^{3} = 729 → W = 9.

The height of the cube is six times the width, therefore its 54 meters.

QUESTION: 24

The width of a cube is half the length and one third of the height. If the length of the cube is 4 meters, what is the volume of three identical cubes?

Solution:

The best answer is A.

Normalize all the dimensions to the width. Let the width be X.

The length is twice the width, thus 2X.

The height is 3 times the width, thus 3X.

The volume of the cube is X.2X..3X = 6X^{3}.

The length is equal to 4 → 2X = 4 → X = 2 → Volume = 6 x 8 = 48.

The volume of two cubes will be 96.

QUESTION: 25

Two brothers took the GMAT exam, the higher score is X and the lower one is Y. If the difference between the two scores is equal to their average, what is the value of Y/X ?

Solution:

The best answer is D.

If the difference is equal to the average, then we could write the equation: X – Y = (X +Y)/2.

→ X – 3Y = 0 →Y/X = 1/3

QUESTION: 26

Two people measure each other’s height, the height of the taller person is H and the height of the other person is L. If the differences in their height is equal to their average height, what is the Value of H/L ?

Solution:

The best answer is D.

If the difference is equal to the average, then we could write the equation: H – L = (H+L)/2.

→ H – 3L = 0 → H/L = 3.

QUESTION: 27

If building X is less than 40 store’s high, is building Y taller than X?

(1) Building Y is at least three times as high as building X.

(2) On the fortieth floor of the Y building there is a gift shop.

Solution:

The best answer is D.

Statement (1) tells us clearly that the Y building is taller than the X one.

Statement (2) implies that there is a gift shop on the 40’Th floor; therefore there are at least 40 floors on the Y building, which make it taller than X.

Both statements, by themselves, are sufficient enough to answer the question.

QUESTION: 28

There are two major statues in Tasmanian County; the first is no more than 45 meters high. How tall is the second statue?

(1) The second statue is 10 meters higher than the first statue.

(2) Both statues together are 80 meters high.

Solution:

The best answer is C.

The information on the first statue in the question is confusing and irrelevant.

Statement (1) tells us that: B = A + 10 (A is the first and B is the second statue).

Statement (2) tells us that: A + B = 80, therefore we have two equations with two variables and so we can solve the problem.

Therefore, both statements are required in order to answer the question.

QUESTION: 29

Tower X is smaller than tower Z. Is tower Y bigger than tower X?

(1) Tower Z higher than tower Y.

(2) Tower Y is one of the tallest in the world.

Solution:

The best answer is E.

We can write the data that is given to us: X < Z.

From statement (1) we can learn that: Y < Z also, this is not enough.

From statement (2) we know that Y is very tall, __one__ of the highest in the world, but X can still be higher. Therefore, more sufficient data is required to answer the question.

QUESTION: 30

How many steaks did the restaurant sell between 20:00 P.M and 21:00 P.M on Wednesday?

(1) On Tuesday the restaurant sold 25 steaks between the hours of 20:00 P.M and 21:00 P.M.

(2) The average amount of steaks that are sold on Wednesdays is 25 steaks per hour.

Solution:

The best answer is E.

Both statements do not provide us with any vital information about the specific number of steaks that were sold on that specific hour. The average is not accurate enough for the question and the sales of Tuesdays could be different than those in Wednesdays. Therefore, more sufficient data is required.

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