If a and b are positive integers, a>b and (a+b)²- (a-b)²>29, then the smallest value of a is · ABC26GN0190
Subject: General Aptitude · Chapter: Number System
If $a$ and $b$ are positive integers, $a>b$ and $(a+b)^{2}-$ $(a-b)^{2}>29$, then the smallest value of $a$ is
(a)3
(b)4
(c)6
(d)7
Answer
Answer (as printed): B
Explanation
Since $(a+b)^{2}-(a-b)^{2}=4 a b$, so the given expression should be a multiple of 4 . So, the least value of $4 a b$ is 32 and so the least value of $a b$ is 8. Hence, the smallest value of $a$ is 4 and that of $b$ is 2 . Hence, $a=4$.
Explanation as extracted from the printed page; notation may be imperfect.