If n is an integer, is n1?

Question

If n is an integer, is  n\geq 1  ?
(1)  n=x^2 
(2)  n>x

GMATinsight · Answer

Question: Is n ≥ 1?

STatement 1 :  n = x^2

i.e. n is definitely non-negative but it may be  greater  than 1 or  equal to  1 or equal to 0  for n is an Integer  hencehence

NOT SUFFICIENT

Statement 2 :  n>x

x is unknown which may be negative or positive both hence

NOT SUFFICIENT

Combining the statements

n >x and n= x^2

I e. n is non zero integer and x^2 will be positive in that case
I.e. n ≥ 1

Sufficient

Answer: Option C

Mo2men · Answer

Hi  GMATinsight

In statement 1, why did you exclude x=0? If x=0, then n=0 and hence answer is NO.

SHoylandBPrep · Answer

Stat (1) 
n must be a non-negative integer. The key is that n could be 0 -- that is the only way the answer could be Yes.

Plug in:
→ n = 0 → Is n ≥ 1? No.
→ n = 4 → Is n ≥ 1? Yes
 Insufficient

Stat (2) 
n can be any integer.
 Insufficient

Stat (1+2) 
We can no longer use n = 0 because then n would not be greater than x. The smallest integer you can use is n = 1 (with x = -1). Therefore, n ≥ 1 must be true.
 Sufficient

(c) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

If n is an integer, is n>1?

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