Question

Three consecutive positive integers are raised to the first, second and third powers respectively and then added. The sum so obtained is a perfect square whose square root equals the total of the three original integers. Which of the following best describes the minimum value, say m, of these three integers?(CAT 2008)

• A. 1<=m<=3
• B. 4<=m<=6
• C. 7
• D. 10
• E. 13<=m<=15

Answer 1

The correct option is A 1<=m<=3

Ans: a
It's an easy question. Trial with some numbers will give you the solution
$1<=m<=3$
$3^1+4^2+5^3=144={12}^2=(3+4+5{)}^2.$