GMAT数学真题精选（一）

GMAT数学真题精选（一）

1.If Mario was 32 years old 8 years ago, how old was he x years ago? 

A. x – 40 

B. x – 24 

C. 40 – x

D. 24 – x

E. 24 + x

Explanation: 

Since Mario was 32 years old 8 years ago, his age now is 32 + 8 = 40. x years ago, Mario was x years younger, so his age  then was 40 – x. The correct answer is C. 

2． Running at the same constant rate, 6 identical machine can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes? 

A. 648 

B. 1,800 

C. 2,700 

D. 10,800 

E. 64,800 

Explanation: 

The production rate of each machine is 6 270= 45 bottles per minute. The production rate for 10 machines is 45 (10) = 450 bottles per minute. Therefore, the 10 machines can produce 450 (4) = 1, 800 bottles in 4 minutes. The correct answer choice is B. 

3. Three business partners, Q, R, and S, agree to divide their total profit for a certain year in the ratios 2:5:8, respectively. If Q’s share was $4,000, what was the total profit of the business partners for the year? 

(A) $26,000 

(B) $30,000 

(C) $52,000 

(D) $60,000 

(E) $300,000 

Explanation:

Based on the ratio 2:5:8, the total profit T was divided as follows: 

T

15

2

was given to Q, T

15

5

was given 

to R, and T

15

8

was given to S. Since 

T

15

2 = $ 4,000, T = 

(4,000) $30,000

2

15 = . So the correct 

answer choice is B. 

4. Of the five coordinates associated with points A, B, C, D, and E on the number line above, which has the greatest absolute value? 

(A) A

(B) B

(C) C

(D) D

(E) E

Explanation:

The absolute value of a number x may be thought of as the distance between x and 0 on the number line. By inspection of the five points, the coordinate of point A is farthest from 0 and thus has the greatest absolute value. 

The correct answer is A. 

5. A restaurant meal cost $35.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal then the total amount paid must have been between 

(A) $40 and $42 

(B) $39 and $41 

(C) $38 and $40 

(D) $37 and $39 

(E) $36 and $37 

Explanation:

If P is the total amount paid, then P must be greater than $ 35.50 (1.1) but less than $ 35.50 (1.15). That is, P is between $ 39.05 and $ 40.825. It follows that P must be between $ 39 and $ 41. Each of the other choices excludes a possible value of P. So B is the correct answer. 

6. Harriet wants to put up fencing around three sides of her rectangular yard and leave a side of 20 feet unfenced. If the yard has an area of 680 square feet, how many feet of fencing does she need? 

(A) 34 

(B) 40 

(C) 68 

(D) 88 

(E) 102 

Explanation:

The area of the yard is 20w= 680 square feet, so w =680/20 = 34 feet. The length of fencing needed is then 34 + 20 + 34 = 88 feet. So D is the correct answer. 

7. If u>t, r > q, s > t, and t > r, which of the following must be true? 

Ⅰ. u>s

Ⅱ. s>q

Ⅲ. u>r

(A)Ⅰonly 

(B)Ⅱonly 

(C)Ⅲ only 

(D)Ⅰand Ⅱ

(E) Ⅱand Ⅲ

Explanation:

From the given inequalities, we can conclude that q < r < t < u, and it is helpful to know s > u or t < s < u. Thus, II and III must be true, but I may be untrue. So, E is the correct answer. 

8. Increasing the original price of an article by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by 

(A) 32.25% 

(B) 31.00% 

(C) 30.25% 

(D) 30.00% 

(E) 22.50% 

Explanation:

A is the correct answer. If p is the original price, then the 15 percent increase in price results in a price of 1.15p. the next 15 percent increase in price results in a price of 1.15(1.15p), or 1.3225p. Thus, the price increased by 1.3225p – p = 0.3225p, or 32.25% of p. 

9. If k is an integer and 0.0010101×10k is greater than 1,000, what is the least possible value of k? 

(A) 2 

(B) 3 

(C) 4 

(D) 5 

(E) 6 

Explanation:

Since 0.0010101 is being multiplied by the kth power of 10, k is the number of decimal places that the decimal point in 0.0010101 will move to the right (if k > 0) in the product 0.0010101×10k. By inspection, 6 is the least number of decimal places that the decimal point must move to the right in order for the product to be greater than 1,000. Therefore, E is the correct answer. 

10. If ) 0 2 ( − 3)(4 + = b

b and b≠3, 

then b = 

(A) –8 

(B) –2 

(C) 2

1 −

(D) 2

1

(E) 2 

Explanation:

Since ) 0 2 ( − 3)(4 + = b

b , it follows that either b − 3 = 0 or 0 2 4 + = b . That is, either b = 3 or 2

1 b = − . 

But b ≠ 3 is given, so 2

1 b = − . C 

is the correct answer.