Aptitude Day 170

Problems on Average:

1. Of the 4 numbers, the 1^st is half of the 2^nd, 2^nd is twice the 3^rd and 3^rd is thrice the 4^th. The average of the reciprocal of the numbers is 5/99. The largest number is:

Solution:

                 Let the 4^th number be x.

                 3^rd number = 3x.

                 2^nd number = 2(3x) = 6x.

                 1^st number = 1/2(6x) = 3x.

                 1/x + 1/3x + 1/3x = 5/99

                 1/x[3+1+1/3] = 5/99

                 5/3x = 5/99

                 x = 33.

                 The largest number is 6x = 6(33) = 198.

2. Of the 3 numbers, the average of the 1^st and the 2^nd is greater than the average of the 2^nd and the 3^rd by 9. What’s the difference between the 1^st and the 3^rd of the 3 numbers?

Solution:

                 (x +y)/2 – (y+z)/2 = 9

                 x+ y-y-z = 9*2

                 x-z = 18.