set2 maths explanation


GMAT SET 2 has traditionally been the most confusing and difficult Set to work with. However, Set 2 has some of the best and most difficult Quant questions and I strongly recommend all test takers to go through it. I have provided my personal answer and explanation below. To prevent this from turning into a big discussion, please PM me with questions or corrections. Let's keep this thread clean with Answers and Explanations only.

Quant Part 1

Q1:

Country

Consumption (in millions of kilograms)

J

1,080

K

600

L

360

M

330

N

310

The table above gives the coffee consumption in 1994 for five countries. If the total coffee consumption of these countries was 40 percent of the world's coffee consumption, what was the world's coffee consumption, in millions of kilograms, in 1994?

A. 4,320

B. 4,470

C. 5,400

D. 6,480

E. 6,700

X=world's total coffee consumption. 4x/10=2680, x=6700

Answer: E.

Edited by greenclover on 31 January 2006 at 11:33am

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Q2:

When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

A. 96

B. 75

C. 48

D. 25

E. 12

If x/y=96.12 and y is a factor of x, then the value of y must be 9/.12=75

Answer: B.

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Q3:

Is the standard deviation of the salaries of Company Y's employees greater than the standard deviation of the salaries of Company Z's employees?

(1) The average (arithmetic mean) salary of Company Y's employees is greater than the average salary of Company Z's employees.

(2) The median salary of Company Y's employees is greater than the median salary of Company Z's employees.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. Average salary of Y and average Salary of Z does not give us the standard deviation. Insufficient.

Statement 2. The median salary does not give us the standard deviation. Insufficient.

Combined. Median and Mean does not give us any information on the standard deviation of the company. Insufficient.

Answer: E.

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Q4:

What is the value of v3 - k3?

(1) v k > 0

(2) v - k = 6

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. Tells us either y and k are both positive, or they are both negative. Insufficient.

Statement 2. Tells us the difference between y and k. Insufficient.

Combined. Still Insufficient.

Answer: E.

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Q5:

In the figure, points A, B, C, D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle, and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?

(1) AB = 3 and BC =2

(2) CD =1 and DE = 4

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Highly debated question between A and D.

Statement 1. We can easily find out the area of two circles. Sufficient.

Statement 2. Since CD + DE = radius of bigger circle, AC=5. AC + CD = 6 = diameter of small circle. Sufficient.

Answer: D.

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The figure above shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?

A. 5 ft

B. 7 ft

C. 8 ft

D. 9 ft

E. 10 ft

The radius of this semicircle is 10 ft and the 12ft lane is centered. This gives us 6ft of lane each side from the center of the semicircle. X^2 + 6^2 = 10^2, x=8. 8 ft - ft of clearance = 7 .

Answer: B.

Edited by greenclover on 31 January 2006 at 11:54am

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Q7:

Square S is inscribed in circle T. If the perimeter of S is 24, what is the circumference of T?

A. 6p

B. 12p

C. 3Ö2 p

D. 6Ö2 p

E. 12Ö2 p

Since the perimeter of S is 24, that means square S has 6 on each sides. Find the diagonal of the square for the diameter of the circle. 6^2 + 6^2 = d^2, d= 6 root 2. Circumference = 6 root 2 * pi.

Answer: D.

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Q8:

The operation Ä is defined for all nonzero numbers a and b by a Ä b = a/b - b/a. If x and y are nonzero numbers, which of the following statements must be true?

I. x Ä xy = x(1 Ä y)

II. x Ä y = -(y Ä x)

III. 1/x Ä 1/y = y Ä x

A. I only

B. II only

C. III only

D. I and II

E. II and III

I. x/xy - xy/x = x(1/y-y), x/xy-y=x/y-y. Not true.

II. x/y-y/x = -(y/x-x/y), x/y-y/x = x/y-y/x. True.

III. (1/x)/(1/y) - (1/y)/(1/x) = y/x-x/y, y/x-x/y=y/x-x/y. True.

Answer: E.

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Q9:

What was the price at which a merchant sold a certain appliance?

(1) The merchant's gross profit on the appliance was 20 percent of the price at which the merchant sold the appliance.

(2) The price at which the merchant sold the appliance was $50 more than the merchant's cost of the appliance.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. Does not give us the price. Insufficient.

Statement 2. Does not give us the price. Insufficient.

Combined: We know that $50 is 20% of the price. Sufficient.

Answer: C.

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Q10:

An attorney charged a fee for estate planning services for a certain estate. The attorney's fee was what percent of the accessed value of the estate?

(1) The accessed value of the estate was $1.2 million.

(2) The attorney charged $2,400 for the estate planning services.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. Does not give us the attorney fee. Insufficient.

Statement 2. Does not give us the estate value. Insufficient.

Combined: We know both information so we can find the percentage. Sufficient.

Answer: C

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Q11:

Is the sum of the integers x and y a prime number?

(1) x is an even prime number.

(2) y is a prime number between 10 and 20.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. Only even prime number is 2, so X=2, but we do not know Y. Insufficient.

Statement 2. Tells us Y=11,13,17,19 but we do not know X. Insufficient.

Combined: We have the following possibilities for X+Y: 13,15,19,21. Insufficient.

Answer: E

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Q12:

There are 11 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?

A. 120

B. 720

C. 1,060

D. 1,520

E. 1,980

11C2 * 9C2 = 1980

Answer: E.

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Q13:

An integer greater than 1 that is not prime is called composite. If the two-digit integer n is greater than 20, is n composite?

(1) The tens digit of n is a factor of the units digit of n.

(2) The tens digit of n is 2.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. If the tens digit is a factor of units digit, then the number must be composite i.e. 24, 36, 63, 48. Sufficient.

Statement 2. Number can be 21, composite, or 23, non composite.

Answer: A

Edited by greenclover on 31 January 2006 at 11:36am

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Q14:

C(m,n) = m! / [(m-n)! n!] for nonnegative integers m and n, m ³ n. If C(5,3) = C(5,x) and x ¹ 3, what is the value of x?

A. 0

B. 1

C. 2

D. 4

E. 5

5!/(5-3)!3! = 10. 5!(5-x)!x! = 10, x=2. Back solving works very well in this question.

Answer: C.

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Q15:

If w, x, y, and z are integers such that 1 < w < x < y < z and wxyz = 462, then z =?

A. 7

B. 11

C. 14

D. 21

E. 42

462 = 11*7*3*2. Z must be 11.

Answer: B.

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Q16:

The sum of three integers is 40. The largest integer is 3 times the middle integer, and the smallest integer is 23 less than the largest integer. What is the product of the three integers?

A. 1,104

B. 972

C. 672

D. 294

E. 192

Assume the three integers, from largest to smallest are XYZ. X+Y+Z=40, X=3Y, Z=X-23. X=27 Y=9 Z=4 X*Y*Z = 972

Answer: B

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Q17:

If a and b are positive, is (a-1 + b-1)-1 less than (a-1b-1)-1?

(1) a = 2b

(2) a + b > 1

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Simplify this problem first: (a^-1 + b^-1)-1 = (1/a + 1/b)^-1 = (a+b)/ab)^-1 = ab/(a+b). (a^-1*b^-1)^-1 = ab

So question is asking ab/(a+b) > ab?

Statement 1. Does not give us enough information. Insufficient.

Statement 2. Does not give us enough information. Insufficient.

Combined: Since ab>0 and a+b>0, we know that ab/(a+b)<ab. Sufficient.

Answer: C.

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Q18:

On a certain transatlantic crossing, 20 percent of a ship's passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship's passengers held round-trip tickets?

A. 33 1/3%

B. 40%

C. 50%

D. 60%

E. 66 2/3%

0.4 R = 0.2 P, R/P * 100 = 50

Answer: C.

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Q19:

If x is an integer, which of the following must be an odd integer?

A. 2x + 2

B. 4x + 3

C. 12x - 6

D. 13x

E. 14x

You could either realize that odd*even or even*even always comes out even, and even + odd always equals odd. Or honestly, just plug in 2.

Answer: B.

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Q20:

A collection of 36 cards consists of 4 sets of 9 cards each. The 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?

(1) The units digit of the sum of the numbers on the remaining 35 cards is 6.

(2) The sum of the numbers on the remaining 35 cards is 176.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. Since the cards are in sequential order, we know the total digit sum so we can backsolve to know which card is missing. Sufficient.

Statement 2. Since we know the total sum of the numbers, we can also backsolve to know which car is missing. Sufficient.

Answer: D.

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Q21:

If xy ¹ 0, is x/y = 1?

(1) x2 = y2

(2) xy > 0

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. Only tells us |x| = |y|, does not give indication on positive or negative. Insufficient.

Statement 2. Tells us x and y should either be both negative or positive. Insufficient.

Combined. Sufficient.

Answer: C.

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Q22:

A construction company was paid a total of $500,000 for a construction project. The company's only costs for the project were for labor and materials. Was the company's profit for the project greater than $150,000?

(1) The company's total cost was three times its cost for materials.

(2) The company's profit was greater than its cost for labor.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Let C=Cost, L=Labor, M=Material. Given C=L+M

Statement 1. C=3M, L=2/3C. Insufficient.

Statement 2. Not sufficient by itself.

Combined. 500,000 - C > L, 300,000>C. Sufficient.

Answer: C.

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Q23:

AMOUNT OF BACTERIA PRESENT

Time

Amount

1:00 P.M.

10.0 grams

4:00 P.M.

x grams

7:00 P.M.

14.4 grams

Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?

A. 12.0

B. 12.1

C. 12.2

D. 12.3

E. 12.4

Simple ratio: 10/x = x/14.4, x=12. Backsolving will also be a good approach here.

Answer: A.

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Q24:

The value of (9107)(9108) is closest to which of the following?

A. 1016

B. 1017

C. 1056

D. 1057

E. 1058

Close to 10^8 * 10^9

Answer: B.

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Q28:

Of the goose eggs laid at a certain pond, 2/3 hatched, and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?

A. 280

B. 400

C. 540

D. 600

E. 840

(2/3)(3/4)(2/5)x=120, x=600

Answer: D.

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Quant Part 2

Q2:

If n is a positive integer and the product of all the integers from 1 to n, inclusive, is divisible by 990, what is the least possible value of n?

A. 8

B. 9

C. 10

D. 11

E. 12

990 = 11 * 5 * 3 * 3 *2, N's least possible value must equal to 990's largest prime factor.

Answer: D

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Q3:

What is the remainder when the positive integer n is divided by 2?

(1) When n is divided by 5, the remainder is an odd integer.

(2) When n is divided by 10, the remainder is an odd integer.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. Possible values are 6,8,11,16, which can or cannot be divided by 2. Insufficient.

Statement 2. Possible values are 11,13,15,17, remainder is always 1 when divided by 2. Sufficient.

Answer: B

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Q4:

What is the hundreds digit of the integer z?

(1) 10z = 93,120

(2) z rounded to the nearest hundred is 9,300.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. z=9310. Sufficient.

Statement 2. z can be 9310 or 9279. Insufficient.

Answer: A

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Q5:

The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3:2:2. In terms of x, which of the following equals the height of the carton, in feet?

A. 3ãx

B. 3ã[(2x)/3]

C. 3ã[(3x)/2]

D. (2/3) 3ãx

E. (3/2) 3ãx

Volume = LBH. LBH are in the ration of 3 :2 :2. So Volume = 3x * 2x * 2x. V=12x^3 or x=(V/12)^(1/3). Since H=2x, H=(2x/3)^1/3

Answer : B.

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Q6:

Leo can buy a certain computer for p1 dollars in State A, where the sales tax is t1 percent, or he can buy the same computer for p2 dollars in State B, where the sales tax is t2 percent. Is the total cost of the computer greater in State A than in State B?

(1) t1 > t2

(2) p1t1 > p2t2

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. Does not give us the actual dollar purchase. Insufficient.

Statement 2. Only tells us the discount in State A is larger than State B. Insufficient.

Combined. Still Insufficient.

Answer: E.

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Q7:

Last year, 36 houses in a certain development had roof repairs and 48 houses were repainted. If 20 houses in the development had roof repairs but were not repainted last year, how many houses were repainted but did not have roof repairs?

A. 12

B. 16

C. 20

D. 28

E. 32

Drawing a quick Venn diagram will tell you there are 20 houses in roof repair, 16 houses doing both and 32 houses repainted but did not have roof repairs.

Answer: E.

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Q8:

Which of the following is equal to [1/(¡Ì3-¡Ì2)]2?

A. 1

B. 5

C. ¡Ì6

D. 5 - ¡Ì6

E. 5 + 2¡Ì6

Math Basic - In this situation, one cannot square the top and bottom directly. So multiple root 3 + root 2 on both top and bottom = (root 3 + root 2)^2 = 5 + root3*root2

Answer: E.

Edited by greenclover on 31 January 2006 at 11:40am

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Q9:

If n and t are positive integers, is n a factor of t?

(1) n = 3n-z

(2) t = 3n

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. We do not know what Z is. Insufficient.

Statement 2. n=1, t=3 or n=2 t=9. Insufficient.

Combined. Still don't know what Z is. Insufficient.

Answer: E.

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Q10:

On a certain date, Hannah invested $5,000 at x percent simple annual interest and a different amount at y percent simple annual interest. What amount did Hannah invest at y percent simple annual interest?

(1) The total amount of interest earned by Hannah's due investments in one year was $900.

(2) Hannah invested the $5,000 at 6 percent simple annual interest.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. Insufficient by itself.

Statement 2. Does not give us information on the other amount. Insufficient.

Combined. Not enough information on the other invested amount. Still Insufficient.

Answer: E.

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Q11:

The figure shown represents a board with 4 rows of pegs, and at the bottom of the board are 4 cells numbered 1 to 4. Whenever the ball shown passes through the opening between two adjacent pegs in the same row, it will hit the peg directly beneath the opening. The ball then has the probability 1/2 of passing through the opening immediately to the left of that peg and probability 1/2 of passing through the opening immediately to the right. What is the probability that when the ball passes through the first two pegs at the top it will end in Cell 2?

A. 1/16

B. 1/8

C. 1/4

D. 3/8

E. 1/2

There are three ways the ball will row into Cell 2. LRL, LRR, RLL. For each way, the probability of landing in the Cell in that order is * * = 1/8, since there are 3 ways, 3*(1/8).

Answer: D.

Thanks godie for the diagram.

Edited by greenclover on 31 January 2006 at 11:46am

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Q12:

A can manufacturing company has 5 identical machines, each of which produces cans at the same constant rate. How many cans will all 5 machines produce running simultaneously for z hours?

(1) Running simultaneously, 3 of the machines produce 72,000 cans in 2z hours.

(2) Running simultaneously, 2 of the machines produce 24,000 cans in z hours.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. We can find exactly how much 1 machine produce in z hours, and we can find out how much 5 machines will produce. Sufficient.

Statement 2. We can also find exactly how much 1 machine produce in z hours, and we can find out how much 5 machines will produce. Sufficient.

Answer: D.

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Q13:

What is the value of xy?

(1) 2(x+y) = 4

(2) 2(x+3y) = 16

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. 2^(x+y) = 2^2, x+y = 2. Insufficient.

Statement 2. 2^(x+3y) = 2^4, x+3y = 4. Insufficient.

Combined. y=1 x=1. Sufficient.

Answer: C.

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Q14:

The function f is defined by f(x) = - 1/x for all nonzero numbers x. If f(a) = - 1/2 and f(ab) = 1/6, then b =

A. 3

B. 1/3

C. - 1/3

D. -3

E. -12

Straight forward, but be careful with the negative sign.

Answer: D.

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Q15:

Is xy > x/y?

(1) xy > 0

(2) y < 0

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. Tells us x and y are either both positive or negative. Insufficient.

Statement 2. Tells us y is negative. Insufficient.

Combined. Tells us both x and y are negative, but gives no information. Insufficient.

Answer: E.

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Q16:

Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?

A. 75%

B. 80%

C. 100%

D. 120%

E. 125%

Capacity of A / Capacity of B is ((16/pi)^2 *10)/((20/pi)^2 * 8) = 4/5

Answer: B

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Q17:

Meg and Bob are among the 5 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?

A. 24

B. 30

C. 60

D. 90

E. 120

Fastest way is 5!/2 = 60. Since in all possible combinations, half of the time Meg will be ahead of Bob, the other half Bob will be ahead of Meg. So we divide all possible outcomes by two.

Answer: C.

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Q18:

If xy ¡Ù 0 and x2y2 C xy = 6, which of the following could be y in terms of x?

I. 1/(2x)

II. C 2/x

III. 3/x

A. I only

B. II only

C. I and II

D. I and III

E. II and III

Assume xy=k. k^2-k-6=0. k=3 or k=-2. xy=3 or xy=-2, y=3/x or y=-2/x.

Answer: E.

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Q19:

If y is an integer and y =x + x, is y = 0?

(1) x < 0

(2) y < 1

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. We know y=-x+x, y=0. Sufficient.

Statement 2. We also know y must equal to 0. Sufficient.

Answer: D.

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Q20:

In the figure shown, what is the value of x?

(1) y = x

(2) z = x

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. Insufficient by itself.

Statement 2. Insufficient by itself.

Combined we know y=x=z, x must equal to 120. Sufficient.

Answer: C.

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Q22:

If x is negative, is x < -3?

(1) x2 > 9

(2) x3 < -9

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. X must be less than -3. Sufficient.

Statement 2. X can be -2.9 or 4. Insufficient.

Answer: A.

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Q23:

If k = -1, which of the following is (are) true?

I. kk = k

II. k = -k

III. k0 = -k

A. I only

B. I and II only

C. I and III only

D. II and III only

E. I, II, and III

I. -1^-1=-1. True

II. 1=1. True.

III. 1=1. True.

Answer: E.

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Q24:

A certain computer program generates a sequence of numbers a1, a2, ¡­ , an such that a1 = a2 = 1 and ak = ak-1 + 2ak-2 for all integers k such that 3 ¡Ü k ¡Ü n. If n > 6, then a7 = ?

A. 32

B. 43

C. 64

D. 100

E. 128

Just use brute force to solve this one. a3=a2+2a1=3, a4=5, a5=11, a6=21, a7=43

Answer: B.

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Q25:

If n is an integer greater than 6, which of the following must be divisible by 3?

A. n (n+1) (n-4)

B. n (n+2) (n-1)

C. n (n+3) (n-5)

D. n (n+4) (n-2)

E. n (n+5) (n-6)

Answer: A.

Edited by greenclover on 31 January 2006 at 11:31am

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Q26:

If n is a positive integer that is less than 10, what is the value of n?

(1) n is the tenth digit in the decimal representation of 1/n.

(2) n is the hundredth digit in the decimal representation of 1/n.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1.Only possible number is n=3, 1/3=0.3333. Sufficient.

Statement 2.Two possible numbers, 1/3=0.3333 or 1/6=0.1666. Insufficient.

Answer: A.

Edited by greenclover on 31 January 2006 at 11:43am

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Q28:

At a monthly meeting, 2/5 of the attendees were males and 7/8 of the male attendees arrived on time. If 9/10 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time?

A. 11/100

B. 3/25

C. 7/50

D. 3/20

E. 4/25

Try plugging in 400 as total number of attendees.

Answer: A.

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Q29:

In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle?

A. 3Î

B. 3ã2 Î

C. 3ã3 Î

D. 9Î

E. 18Î

3^2 * 3^2 = radius of circle^2, radius of circle=3 root 2, area equal to 18 pi

Answer: E.

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Q34:

What is the median number of employees assigned per project for the projects at Company Z?

(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project.

(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Often discussed problem on ST.

Statement 1. Insufficient.

Statement 2. Insufficient.

Combined. If 25% of projects have 4+ employees and 35% of projects have 2 or less employees, this MUST mean the middle 40% of projects have EXACTLY 3 employees. This is sufficient and I promise it's the last time I'll explain this problem!

Answer: C.

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Q35:

p is an integer; n is an integer; and p/n is an integer. Is p/n odd?

(1) p is divisible by 4.

(2) n is divisible by 4.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. Nothing is given about n. Insufficient.

Statement 2. Nothing is given about p. Insufficient.

Combined. p and n can both be 1, which will have odd result, or p can be 8 and n can be 4, which will have even results. Insufficient.

Answer: E.

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Q36:

What is the value of the integer N?

(1) 101 < N < 103

(2) 202 < 2N < 206

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. Hopefully I'm not blind. Only 102 is possible. Sufficient.

Statement 2. Divide by both sides and n=102. Sufficient.

Answer: D.

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Quote: greenclover Q9:

If n and t are positive integers, is n a factor of t?

(1) n = 3n-z

(2) t = 3n

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. We do not know what Z is. Insufficient.

Statement 2. n=1, t=3 or n=2 t=9. Insufficient.

Combined. Still don't know what Z is. Insufficient.

Answer: E.

I think the answer to this question is C.

From statement one and also than n is a positive integer, n can only be values - 3,9,27,243,729...that is all powers of 3.

Now take the second statement - we say that t is also 'n' power of three. The question is 'n' a factor of p. As 3 power n will always be greater than n and as n is some power of 3 this means that n will be a factor of t.

We do not need to know the value of z.

for example n = 243. than t = 3243 => n is a factor of t. Please correct me if I am wrong.

Amit.

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Q20:

A collection of 36 cards consists of 4 sets of 9 cards each. The 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?

(1) The units digit of the sum of the numbers on the remaining 35 cards is 6.

(2) The sum of the numbers on the remaining 35 cards is 176.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1. Since the cards are in sequential order, we know the total digit sum so we can backsolve to know which card is missing. Sufficient.

Statement 2. Since we know the total sum of the numbers, we can also backsolve to know which car is missing. Sufficient.

Answer: D.

But, statement 1 is not sufficient.

ex: The total of all the 36 cards is 180

2 says that last digit of remaining cards is 6 so the sum maybe 176(missing card is 1) and also 156(missing card is 6)

Ans is B



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