GRE /GMAT : Sample Questions with Solution

1. If 3/p = 6 and 3/q = 15 then p - q = ?

1. 1/3
2. 2/5
3. 3/10
4. 5/6
5. None of the above

Ans : C

Sol : 3/p = 6 so p=3/6 =1/2

        3/q = 15 so q=3/15=1/5

P – q = ½ - 1/5 =5-2/10 =3/10

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    2.  If x⁴ = 16, then 4^x =

              a) 2   b) 4   c) 8   d) 16

x⁴ = 16    2* 2*2*2=16

2⁴ = 16   S x=2

4^x = 4²  = 16

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     3.  |-5| + |3| - |-5| =

             a) -2  b) -13  c) 8   d) 3  e) 2
          

          Sol: 

          Absolute value of  |-5|=5, |3| = 3

           |-5| + |3| - |-5| = 5 + 3 – 5 =  3

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     4. If 2x > 24 and 3x < 48, which of the following is a possible value for x?

          a) 12  b) 14  c) 16  d) 18

        Sol:  2x > 24  =>  2x/2  > 24/2  =>    x > 12

                3x < 48  =>   3x/3  <  48/3   =>  x <  16

         So from the given choices answers is 14

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   5.  If a cube has a volume of 343 cubic inches, what is the length of one  side?

         A:7square inches B:30square inches C: 7inches D: 49 inches                          

        Sol: Volume of a cube = (length of one side )³  = 343

         So  (length of one side )³ = 7³

              Length of one side = 7 inches

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    6.  If 3x - 6 = 14 - x, then x =

        A: 5       B: 3      C: 4     D: 8       E: 10

        Sol:  It is given that  3x - 6 = 14 – x

        3x – 6 -14 + x = 0

       4x – 20 =0

       4x = 20

        x= 5

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7. Factor: a² -3a - 18

    A: (a - 3)(a - 9)   B: (a - 2)(a - 9)   C: (a + 3)(a + 6)  D: (a + 2)(a + 9)  E: (a - 6)(a + 3)

    It is given a² -3a – 18

   Let (a+ x) (a + y) = a² -3a – 18

    x+ y = -3

    xy = -18

   So  x= -6 and y = 3   factors are (a-6) and (a+ 3)

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8.  If a = 2, then 3a + (a³)² =

    A: 73   B: 70    C: 7   D: 12    E: 27  

   Sol :  It is given a =2

     3a + (a³ ) ² = 3 * 2 + (2³ )² =6 + 8² = 6+ 64 = 70

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9. If a camera purchased for $490 and sold for $460 find the loss percent?

a) 1%    b) 5%   c)  10%   d) 2%

Sol : CP = $490       SP = $465.50

Loss = (490-465.50) = $24.50

Loss % = 24.50* 100/490 = 5%

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10 . A man buys an article for $ 27.50 and sells it for $ 28.60 . Find his gain percent?

a) 3%   b) 1%    c) 4%  d) 5%

Sol: CP = $ 27.50     SP= 28.60

Gain = SP- CP = 28.60 – 27.50 = 1.10

Gain %  = Gain * 100/CP = 1.10 * 100 /27.50 = 4 %

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