Aptitude Day 34

Problems on Numbers 

1. The average of 4 consecutive even numbers is 29. Find the largest of these numbers.

Solution:
                Let the 4 consecutive even numbers be x,(x+2),(x+4) and (x+6).
                Average = sum of the observations / Number of observations
                      29    =  [x+(x+2)+(x+4)+(x+6)] / 4
                       116 = 4x+12 
                        104= 4x
                            x=26.
               The 4 numbers are 26, 28, 30, 32.
               Here the largest one is 32.

2. The sum of the squares of the 3 consecutive odd numbers is 83. Find the numbers.

Solution:
                Let the numbers be x, (x+2) and (x+4).
                x²+(x+2)²+(x+4)²=83 [Given]
                x²+x²+4x+4+x²+8x+16 = 83
                 3x²+12x+ 20= 83
                    3x²+12x- 63 = 0
                     x²+4x-21=0
                     (x+7)(x-3)=0
                           x= 3, -7
                           x=3 (Considering the postive value)
                    The numbers are 3, 5 and 7.