GRE
Practice Test 3
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Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P ?

 

  • Solution

    Let Ben's age now be B
    Anita's age now is A.
    (A - 6) = P(B - 6)
    But A is 17 and therefore 11 = P(B - 6)
    11/P = B-6
    (11/P) + 6 = B

12 litres of water are poured into an aquarium of dimensions 50cm length, 30cm breadth, and 40cm height. How high (in cm) will the water rise?
(1 litre = 1000cm³)

  • Solution

    Total volume of water = 12 liters = 12 x 1000 cm3
    The base of the aquarium is 50 x 30 = 1500cm3
    Base of tank x height of water = volume of water
    1500 x height = 12000; height = 12000 / 1500 = 8

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In the following correctly worked addition sum, A,B,C and D represent different digits, and all the digits in the sum are different. What is the sum of A,B,C and D?

 

  • Solution

    First you must realize that the sum of two 2-digit numbers cannot be more that 198 (99 + 99). Therefore in the given problem D must be 1.
    Now use trial and error to satisfy the sum 5A + BC = 143
    A + C must give 3 in the units place, but neither can be 1 since all the digits have to be different. Therefore A + C = 13.
    With one to carry over into the tens column, 1 + 5 + B = 14, and B = 8.
    A + C + B + D = 13 + 8 + 1 = 22

For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?

  • Solution

    1 < 4n + 7 < 200
    n can be 0, or -1
    n cannot be -2 or any other negative integer or the expression 4n + 7 will be less than1.
    The largest value for n will be an integer < (200 - 7) /4
    193/4 = 48.25, hence 48
    The number of integers between -1 and 48 inclusive is 50

♠n denotes the number obtained when n is rounded to the nearest tenth. For example ♠4.31 = 4.3
♠0.089 – ♠1.135 =

 

  • Solution

    0.089 to the nearest tenth = 0.1
    1.135 to the nearest tenth = 1.1
    0.1 - 1.1 = -1

-20 , -16 , -12 , -8 …

In the sequence above, each term after the first is 4 greater than the preceding term. Which of the following could not be a term in the sequence?

Indicate ALL such numbers.

 

  • Solution

    Correct Answer: E,G

    Explanation:

    All terms in the sequence will be multiples of 4.
    762 and 902 are not multiples of 4

(65 – 64) / 5

  • Solution

    65 = 64x 6
    (64 x 6) - 64 = 64(6 - 1) = 64 x 5
    Now, dividing by 5 will give us 64

If pqr = 1 , rst = 0 , and spr = 0, which of the following cannot be zero?
Indicate ALL such answers.

 

  • Solution

    Correct Answer: A,B,C

    Explanation:

    If pqr = 1, none of these variables can be zero. Since spr = 0 , and since p and r are not zero, s must be zero. Now rst = 0, and so either s or t must be zero. Even though we have established that s is zero, there is still the possibility that t could be zero as well.

√5 percent of 5√5 =

 

  • Solution

    We can write the statement mathematically, using x to mean of and /100 for percent. So ( √5/100) x 5√5 = 5 x 5 /100 = 0.25

The distance from town A to town B is five miles. C is six miles from B. Which of the following could be the distance from A to C?

Indicate ALL such distances.

 

  • Solution

    Correct Answer: A,B,C

    Explanation:

    Do not assume that AB and C are on a straight line. Make a diagram with A and B marked 5 miles apart. Draw a circle centered on B, with radius 6. C could be anywhere on this circle. The minimum distance will be 1, and maximum 11, but anywhere in between is possible.

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