Question

Arithmetic mean of two numbers whose sum is equal to 28, is equal to the geometrical mean of two perfect square numbers. Sum of these perfect square number out of given ten option will be
OPtion
1) 42
2) 45
3) 48
4) 49
5) 51
6) 52
7) 53
8) 56
9) 58
10)60

Answer 1

let the number be a and b,
now according to given conditions...
a+b=28
and
(a+b)/2 = √(a*b)
( since geometric mean is equal to square root of product of two number)
28/2=14=√(a*b)
squaring both sides
14*14=7*2*7*2=a*b
the possible combinations are 49*4=a*b
as 49 and 4 are perfect squares so,
49+4=53
so option 7 is correct