GRE / GMAT : Sample Questions with Solution

1. Define x* by the equation x* = ∏/x . Then ((-∏)*)* =

    a) -1/∏   b) -1/2            c) -∏          d) 1/∏          e)∏

    Sol:  It is given that x* = ∏/x . Then ((-∏)*)* =( -∏/∏)* = ∏/-1 = -∏

          So answer is C.

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2. 2ab5 is a four-digit number divisible by 25. If the number formed from the two digits ab is a multiple of 13, then ab =

(A) 10

(B) 25

(C) 52

(D) 65

(E) 75

Sol: . We have that the number 2ab5 is divisible by 25. Any number divisible by 25 ends with the last two digits 00, 25, 50, or 75. So, b5 should equal 25 or 75. Hence, b = 2 or 7. Since a is now free to take any digit from 0 through 9, ab can have multiple values.

We also have that ab is divisible by 13. The multiples of 13 are 13, 26, 39, 52, 65, 78, and 91. Among these, the only number ending with 2 or 7 is 52. Hence, ab = 52. The answer is (C).

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3. What is the remainder when 7² . 8² is divided by 6?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

Sol: 7². 8²= (7 . 8)²= 56².

The number immediately before 56 that is divisible by 6 is 54. Now, writing 56² as (54 + 2)², we have

56² = (54 + 2)²

= 54² + 2(2)(54) + 2² by the formula (a + b)²= a² + 2ab + b²

= 54[54 + 2(2)] + 2²

= 6 × 9[54 + 2(2)] + 4 here, the remainder is 4

Since the remainder is 4, the answer is (D).

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4. If 42.42 = k(14 + 7/50), then what is the value of k?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

  The given equation is

42.42 = k(14 + 7/50)

42.42 = k(14 + 14/100)

42.42 = k(14 + 0.14)

42.42 = k(14.14)

42.42/14.14 = k

3 = k

The answer is (C).

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5. If x + y = 7 and x² + y² = 25, then which one of the following equals the value of x³ + y³ ?

(A) 7

(B) 25

(C) 35

(D) 65

(E) 91

 We are given the system of equations:

x + y = 7

x² + y² = 25

Solving the top equation for y yields y = 7 – x. Substituting this into the bottom equation yields

X² + (7 – x)² = 25

X² + 49 – 14x + x² = 25

2x² – 14x + 24 = 0

X² – 7x + 12 = 0

(x – 3)(x – 4) = 0

x – 3 = 0 or x – 4 = 0

x = 3 or x = 4

If x = 3, then y = 7 – 3 = 4. If x = 4, then y = 7 – 4 = 3.

In either case, x³ + y³ = 3³ + 4³ = 27 + 64 = 91. The answer is (E).

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