gayathri wrote:
If \(\sqrt{n}\) is a positive integer, what is the value of n?
(1) \(1 < \sqrt{n} < 5\)
(2) 10 < n < 24
Target question: What is the value of n? Given: √n = a positive integer This tells us that n is a PERFECT SQUARE
So, some possible values of n are:
1, 4, 9, 16, 25, 36, 49, ...etc Statement 1: 1 < √n < 5 There are several values of n that satisfy statement 1. Here are two:
Case a: n = 4, in which case 1 < √4 < 5. In this case, the answer to the target question is
n = 4Case b: n = 9, in which case 1 < √9 < 5. In this case, the answer to the target question is
n = 9Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 10 < n < 24We already know that some possible values of n are:
1, 4, 9, 16, 25, 36, 49, ...etcAmong those possible values,
16 is the ONLY value that satisfies the condition that 10 < n < 24
So, the answer to the target question is
n = 16Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent