GRE/GMAT Sample questions with solution

1. AD is the longest side of the right triangle ABD . What is the length of longest side of ΔABC ?

(A) 2

(B) 3

(C)√ 41

(D) 9

(E) 41

In a right triangle, the angle opposite the longest side is the right angle. Since AD is the longest side of the  right triangle ABD, ∠B must be a right angle and ΔABC must be a right triangle. Applying The Pythagorean Theorem to the right triangle ABC yields

AC² = AB² + BC²

AC = √(AB² + BC²)

AC = √(4² + 5²)

AC = √(16 + 25)

AC = √41

The answer is (C).

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2. From the figure, which of the following must be true?

(I) x + y = 90

(II) x is 35 units greater than y

(III) x is 35 units less than y

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) I and III only

Angle x is an exterior angle of the triangle and therefore equals the sum of the remote interior angles, 35 and y. That is, x = y + 35. This equation says that x is 35 units greater than y. So, (II) is true and (III) is false. Now, if x is an obtuse angle (x > 90), then x + y is greater than 90. Hence,

x + y need not equal 90. So, (I) is not necessarily true. The answer is (B).

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3.  Column A                           x/15 > y/25                                   Column B

            6y + 5x                                                                                10x + 3y

  Multiplying the given inequality x/15 > y/25 by 75 yields 5x > 3y.

Now, subtracting 3y and 5x from both columns yields

Column A                                    5x > 3y                                     Column B

    3y                                                                                                    5x

Since we know that 5x > 3y, Column B is greater than Column A and the answer is (B).

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4. Jane gave three-fifths of the amount of money she had to Jack. Jane now has 200 dollars. How much did she give to Jack?

(A) $80

(B) $120

(C) $200

(D) $300

(E) $500

  Let the original amount of money Jane had be x. Since she gave 3/5 of her money to Jack, she now has 1 – 3/5 = 2/5 of the original amount. We are given that this 2/5 part equals 200 dollars. Hence, we have the equation 2/5 x = 200. Solving for x yields x = 500. Since she gave 3/5 of this amount to Jack, she gave him $300 ( = 3/5  × 500). The answer is (D).

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5. At Stephen Stores, 3 pounds of cashews costs $8. What is cost in cents of a bag weighing 9 ounces?

(A) 30

(B) 60

(C) 90

(D) 120

(E) 150

 

This problem can be solved by setting up a proportion. Note that 1 pound has 16 ounces, so 3 pounds has 48 (= 3 × 16) ounces. Now, the proportion, in cents to ounces, is 800/48

=cents/9

Or   cents = 9 × 800/48 = 150

The answer is (E).

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