# GMAT Math Test – Solutions

Click the link immediately below to view the GMAT Verbal diagnostic test.

**Test Questions**

1. If x and y are both prime and greater than 2, then which of the following CANNOT be a divisor of xy?

(A) 2

(B) 3

(C) 11

(D) 15

(E) 17

**Correct Answer:** (A)

**Solution:** Since x and y are prime and greater than 2, xy is the product of two odd numbers and is therefore odd. Hence, 2 cannot be a divisor of xy. The answer is (A).

2. For all p not equal 2 define p* by the equation p* = (p + 5)/(p – 2). If p = 3, then p* =

(A) 8/5

(B) 8/3

(C) 4

(D) 5

(E) 8

**Correct Answer:** (E)

**Solution:** Substituting p = 3 into the equation p* = (p + 5)/(p – 2) gives

p* = (3 + 5)/(3 – 2) = 8/1 = 8

The answer is (E).

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3. Seven years ago, Scott was 3 times as old as Kathy was at that time. If Scott is now 5 years older than Kathy, how old is Scott?

(A) 12 1/2

(B) 13

(C) 13 1/2

(D) 14

(E) 14 1/2

**Correct Answer:** (E)

**Solution:** Let S be Scott’s age and K be Kathy’s age. Then translating the sentence “If Scott is now 5 years older than Kathy, how old is Scott” into an equation yields

S = K + 5

Now, Scott’s age 7 years ago can be represented as S = -7, and Kathy’s age can be represented as K = -7. Then translating the sentence “Seven years ago, Scott was 3 times as old as Kathy was at that time” into an equation yields

S – 7 = 3(K – 7)

Combining this equation with S = K + 5 yields the system:

S – 7 = 3(K – 7)

S = K + 5

Solving this system gives 14 1/2. The answer is (E).

4. In the figure shown, y =

(A) 75

(B) 76

(C) 77

(D) 78

(E) 79

**Correct Answer:** (D)

**Solution:** OS and OT are equal since they are radii of the circle. Hence, Triangle SOT is isosceles. Therefore, S = T = 51. Recalling that the angle sum of a triangle is 180 degrees, we get

S + T + y = 51 + 51 + y = 180

Solving for y gives y = 78. The answer is (D).

5. If x = 3y = 4z, which of the following must equal 6x?

I. 18y

II. 3y + 20z

III. (4y + 10z)/3

(A) I only (B) II only

(C) III only

(D) I and II only

(E) I and III only

**Correct Answer:** (D)

**Solution:** The equation x = 3y = 4z contains three equations:

x = 3y

3y = 4z

x = 4z

Multiplying both sides of the equation x = 3y by 6 gives 6x = 18y. Hence, Statement I is true. This eliminates (B) and (C). Next, 3y + 20z = 3y + 5(4z) . Substituting x for 3y and for 4z in this equation gives 3y + 20z = 3y + 5(4z) = x + 5x = 6x. Hence, Statement II is true. This eliminates (A) and (E). Hence, by process of elimination, the answer is (D).

6. The average of four numbers is 20. If one of the numbers is removed, the average of the remaining numbers is 15. What number was removed?

(A) 10

(B) 15

(C) 30

(D) 35

(E) 45

**Correct Answer:** (D)

**Solution:** Let the four numbers be a, b, c, and d. Since their average is 20, we get

(a + b + c + d)/4 = 20

Let d be the number that is removed. Since the average of the remaining numbers is 15, we get

(a + b + c)/3 = 15

Solving for a + b + c yields

a + b + c = 45

Substituting this into the first equation yields

(45 + d)/4 = 20

Multiplying both sides of this equation by 4 yields

45 + d = 80

Subtracting 45 from both sides of this equation yields

d = 35

The answer is (D).

Directions (Data Sufficiency Problems): Each of the following two problems contains a question followed by two statements, numbered (1) and (2). You need not solve the problem; rather you must decide whether the information given is sufficient to solve the problem.

The correct answer to a question is

A if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient;

B if statement (2) ALONE is sufficient to answer the question but statement (1) alone is not sufficient;

C if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;

D if EACH statement ALONE is sufficient to answer the question;

E if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question.

7. What is the value of the positive, two-digit number x?

(1) The sum of its digits is 4.

(2) The difference of its digits is 4.

**Correct Answer:** (C)

**Solution:** Considering (1) only, x must be 13, 22, 31, or 40. Hence, (1) is not sufficient to determine the value of x.

Considering (2) only, x must be 40, 51, 15, 62, 26, 73, 37, 84, 48, 95, or 59. Hence, (2) is not sufficient to determine the value of x.

Considering (1) and (2) together, we see that 40 and only 40 is common to the two sets of choices for x. Hence, x must be 40. Thus, together (1) and (2) are sufficient to uniquely determine the value of x. The answer is C.

8. If bowl S contains only marbles, how many marbles are in the bowl?

(1) If 1/4 of the marbles were removed, the bowl would be filled to 1/2 of its capacity.

(2) If 100 marbles were added to the bowl, it would be full.

**Correct Answer:** (C)

**Solution:** (1) alone is insufficient to answer the question since we don’t know the capacity of the bowl.

(2) alone is also insufficient to answer the question since we still don’t know the capacity of the bowl.

However, (1) and (2) together are sufficient to answer the question: Let n be the number of marbles in the bowl, and let c be the capacity of the bowl. Then from (1), n – n/4 = c/2, or 3n/2 = c. Next, from (2), 100 + n = c. Hence, we have the system:

3n/2 = c

100 + n = c

This system can be solved for n. Hence, the number of marbles in the bowl can be calculated, and the answer is C.