shridhar786 wrote:
If n ≠ 0 and n ≠ 1, is \(\frac{1}{n(n-1)}> 1\) ?
(1) n is an integer
(2) n < 1
Given: n ≠ 0 and n ≠ 1 Target question: Is \(\frac{1}{n(n-1)}> 1\) ? Statement 1: n is an integer We already know that n ≠ 0 and n ≠ 1
So, there are two possible cases when it comes to the value of n:
Case a: n ≥ 2. This means n ≥ 2 and (n - 1) ≥ 1, which means n(n-1) ≥ 2, which means the answer to the target question is
NO, it's not the case that \(\frac{1}{n(n-1)}> 1\)Case b: n ≤ -1. This means n ≤ -1 and (n - 1) ≤ -2, which means n(n-1) ≥ 2, which means the answer to the target question is
NO, it's not the case that \(\frac{1}{n(n-1)}> 1\)Since both possible cases yield the
same answer to the target question, statement 1 is SUFFICIENT
Statement 2: n < 1There are several values of n that satisfy statement 2. Here are two:
Case a: n =0.5 This means \(\frac{1}{n(n-1)}=\frac{1}{0.5(0.5-1)}=\frac{1}{-0.25}=-4\). So, the answer to the target question is
NO, it's not the case that \(\frac{1}{n(n-1)}> 1\) Case b: n =-0.5 This means \(\frac{1}{n(n-1)}=\frac{1}{-0.5(-0.5-1)}=\frac{1}{0.75}=\frac{4}{3}\). So, the answer to the target question is
YES, it's the case that \(\frac{1}{n(n-1)}> 1\) Since we can’t answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent