Aptitude Day 32

Problems on Numbers

1. A number is as much greater than 20 as is less than 66. Find the number.

Solution:

                  Let the number be x.

                  x-20 = 66-x   [As per the given condition]

                     2x = 86

                       x=43.

                  The number is 43.

             

2. Find the number such that 22 is subtracted from 6 times the number, the result is 2 more than twice the number.

Solution:

                  Let the number be x.

                  6x-22 = 2x+2  [Given condition]

                     4x = 24

                       x = 6.

                  The number is 6.

3. The sum of the rational number and its reciprocal is 13/6. Find the number.

Solution:

                  Let the number be x.

                  x+(1/x) =13/6

                  6(x²+1) = 13x

                   6x²+6=13x

                   6x²-13x+6=0

                  6x²-9x-4x+6=0

                  3x(2x-3)-2(2x-3)=0

                    (2x-3)(3x-2)=0

                       x =3/2, 2/3

                 The number is 3/2 or 2/3.