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 Section 2 : Mathematical Reasoning 1.     y + 54 + 63 = 180                          y = 180 - 117                          y = 63         Ans : D 2.     Number of miles that the automobile actually travels         = 72 ´ = 96        Ans : A 3.     Units digit   =   4         Tens digit    =   6         4    =   2/3  ´   6         \ The required number is 64         Ans : B 4.     8x + 6x + 3x + x       =    180                             18x       =    180                                 x       =    10         Second largest angle  =     6x                                          = 6 ´ 10                                          = 60        Ans : B 5.    The amount that the person paid for six \$6 shirts and        one \$ 24 shirt    =    6 ´ 6 + 24                                 =    36 + 24                                 =   60        The number of such combinations                                  = =   10        Total number of shirts purchased    =   70        Ans : E 6.       x f y    =   x + y - xy          12 f s   =   12 + s - 12s                78   =     12 - 11 s             11 s   =      12 - 78             11 s   =      - 66                  s   =     - 6          Ans : C 7.     6 f 8    =   6 + 8 - 48                     = 14 - 48                     = - 34        Ans : D 8.    a f b    =   a + b - ab        1 f b    =    1 + b - 1 ´ b                    =    1 + b - b        1 f b    =   1        Ans : A 9.   (64)m      =     2m + 4       (26)m      =     2m + 4         26m       =      2m + 4       [Using the law of indices xm   =   xn ]        6m   =   m + 4        5m   =    4         m    =    4/5       Ans : C 10.  Perimeter of KLMO     =     2 (12 + 8)                                            =    2 ´ 20                                            =     40        Perimeter of square      =     40                                    4x    =    40                                     x     =     10        where x    =     a side of the square        Ans : E Index Part I
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