GRE Math Refresher Diagnostic Test

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					GRE                                                           Math Refresher – Diagnostic Test




               GRE Math Refresher Diagnostic Test




                   Please take the time to complete the following diagnostic test.
      If you have difficulty with any of the topics, you will be directed to one of several short
                                     refresher lessons available.




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GRE                                                          Math Refresher – Diagnostic Test


 Integer Arithmetic


   Evaluate the following (without a calculator)


      a)   ( −5 ) + ( −8 ) =

      b)   ( −2 ) − 10 =

      c) 5 × ( −2 ) × 3 =


           ( 10 )( −2 )( 4 )
      d)                     =
              ( −8 )( 1)

      e) 4 − ( −4 ) =


                                                                                           Answers:
      f)   ( −5 ) + ( −1) − ( −7 ) =                                                         j) -4
                                                                                             i) -6
      g)   ( −10 ) − 8 + 2 =                                                                h) -2
                                                                                           g) -16
      h)   ( −6 )( −1)( −8 )
                             =
             ( −2 )( −12 )
                                                                                             f) 1
                                                                                             e) 8

      i) 8 − 14 =                                                                           d) 10
                                                                                           c) -30

      j)   ( −5 ) − 9 − ( −10 ) =                                                          b) -12
                                                                                           a) -13


   If you had difficulty with any of these questions, you may want to print and complete
   the Math Refresher lesson “Integer Arithmetic.”




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GRE                                                          Math Refresher – Diagnostic Test


 Decimal Arithmetic


   Evaluate the following (without a calculator)


      a) 5.278 + 0.0544 + 17.65 =



      b) 1.2074 + 11.809 =



      c) 6.0287 – 4.55 =



      d) 1.542 – 0.9438 =



      e) 8.5 × 16.3 =
                                                                                               Answers:
                                                                                               h) 8.8
                                                                                              g) 1.35
      f) 6.24 × 48.8 =
                                                                                           f) 304.512
                                                                                            e) 138.55
      g) 57.78 ÷ 42.8 =                                                                     d) 0.5982
                                                                                            c) 1.4787
                                                                                           b) 13.0164
      h) 27.5 ÷ 3.125 =
                                                                                           a) 22.9824




   If you had difficulty with any of these questions, you may want to print and complete
   the Math Refresher lesson “Decimal Arithmetic.”




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GRE                                                          Math Refresher – Diagnostic Test


 Fractions


   Evaluate the following and express your answer in simplest terms

           5 5
      a)    −   =
           8 12


            1   8
      b)      ÷   =
           20 15


           1 1 1
      c)    + + =
           2 3 6

           20 9
      d)     ×   =
           27 16


      e)
           1 3
            +   =                                                                   Answers:
           6 10                                                                         5
                                                                                     a)
                                                                                        24
          1   5
      f) 2 − 1 =                                                                          3
          3   6                                                                      b)
                                                                                          32

           27   1                                                                    c) 1
      g)      ÷1 =
           32   8
                                                                                           5
                                                                                     d)
                                                                                          12
            8 3
      h)     × =
           15 4                                                                            7
                                                                                     e)
                                                                                          15
           7 5                                                                              1
      i)    − =                                                                      f)
           8 6                                                                              2

                                                                                            3
           3  3                                                                      g)
      j) 3 + 1 =                                                                            4
          10  4
                                                                                            2
                                                                                     h)
                                                                                            5
   If you had difficulty with any of these questions, you may want to print and            1
   complete the Math Refresher lesson “Fractions.”                                   i)
                                                                                          24
                                                                                             1
                                                                                     j) 5
                                                                                            20


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GRE                                                         Math Refresher – Diagnostic Test


 Powers


  Evaluate the following:


      a) 5 2 =


      b) 2 −5 =


      c) 10 4 =


      d) ( −3 )
                  −3
                           =


      e) 4 3 =                                                                    Answers:

                                                                                  a) 25

  Simplify the following                                                                1
                                                                                  b)
                                                                                       32
      f) x ⋅ x 2 ⋅ x 11 =
                                                                                  c) 10,000

           x 18                                                                           1
      g)        =                                                                 d) −
           x6                                                                            27

                                                                                  e)   64
           ⎢(     )
                               4
      h) ⎡ x 2             ⎤ =
                       3

           ⎣               ⎥
                           ⎦
                                                                                  f)   x 14

      i)
           (x ) 4 5

                           =
           (x ) 2 7                                                               g) x 12


            x4 ⋅ x2 ⋅ x7                                                          h) x 24
      j)                           =
                (x )   3 3


                                                                                  i)   x6


                                                                                  j)   x4
  If you had difficulty with any of these questions, you may want to print and
  complete the Math Refresher lesson “Powers.”




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GRE                                                                         Quantitative – Algebra


Algebra

   Simplify the following

       a) 8 x + 5 x


       b) 4 x − y + x − 5 y


       c) xy 2 − 8 x 2 y 2 − 4 xy 2


       d)   x + x + 6y + 4 − 3y + 7 x − 5 y − 8 x − 9                             Answers:

                                                                                    a) 13x

   Expand and simplify the following
                                                                                    b) 5 x − 6y

       e) 3 x 2 ( 4 x 4 − 5 x )
                                                                                    c) −3 xy 2 − 8 x 2 y 2

       f)   −4 x 3 y ( 3 xy − x 7 y 2 )                                             d) x − 2 y − 5


       g)   7 x 2 y ( yz − 4 xy )                                                   e) 12 x 6 − 15 x 3


                                                                                    f) −12 x 4 y 2 + 4 x 10 y 3
       h)   ( x − 6 )( x + 5 )
                                                                                    g) 7 x y z − 28 x y
                                                                                          2 2        3 2


       i)    ( 3 x − 5 )( x + 1)
                                                                                    h) x − x − 30
                                                                                        2



       j)    ( 7 x + 1)( 7 x − 1)
                                                                                    i) 3 x 2 − 2 x − 5


                                                                                    j) 49 x 2 − 1


   If you had difficulty with any of these questions, you may want to print and
   complete the Math Refresher lesson “Algebra.”




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GRE                                                             Quantitative – Equation Solving


Equation solving

   Solve each equation for x

      a) 2 x + 5 = 17




      b) −3 x − 11 = 13




      c)   4 x − 8 = 9 x + 22




      d)   18 = 2 ( 3 − x )
                                                                                   Answers:

                                                                                     a) x = 6

      e)   8 − 7x + 2 + 6x = x                                                       b) x = −8

                                                                                     c) x = −6

                                                                                     d) x = −6
      f)   4 ( x + 1) = 3 x + 11
                                                                                     e) x = 5

                                                                                     f)   x =7
      g) x + 2 x + x = 24 − 2 x
                                                                                     g) x = 4

                                                                                     h) x = −1

      h)   15 = 7 x + 22




   If you had difficulty with any of these questions, you may want to print and
   complete the Math Refresher lesson “Equation Solving.”




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