If n is an integer such that 1/6

Question

If n is an integer such that  \frac{1}{6} < \frac{1}{(n-1)} < \frac{1}{3} , what is the value of n?

(1)  (n - 6)(n - 7) = 0

(2)  (n - 5)(n - 3) ≠ 0

SaquibHGMATWhiz · Answer

Question Stem Analysis:

The expression is,  \frac{1}{6} < \frac{1}{(n-1)} < \frac{1}{3} 
 Since 'n' is an integer we can infer that the values n - 1 can take is either 4 or 5 and thus n can be 5 or 6.
So we need to find whether n is 5 or 6.

Statement 1

We have, (n−6)(n−7)=0
 This suggests n can be 6 or 7.
ISo, 'n' cannot be 7 as we already know n is 5 or 6.

Hence, this is sufficient.

We eliminate options B, C, and E.

Statement 2

We have, (n−5)(n−3)≠0
 This suggests n is neither 5 nor 3.
Since we know n is either 5 or 6 so we can say it must be 6.

This statement is also sufficient. So eliminate options A.

The answer is D.

Bunuel · Answer

Anyone else want to try ?

ankitgoswami · Answer

1/6 < 1/(n-1) < 1/3 so 6 > n-1 > 3 7 > n > 4 N is an integer so n can take two values - 5,6 Statement A (n−6)(n−7)=0 n = 6 or 7 it can't be 7 as it violates the question stem Sufficient Statement B (n−5)(n−3)≠0 From the question stem, we have that n = 5 or 6 This statement says n ≠ 5 So n=6 Sufficient Ans is D

SaquibHGMATWhiz · Answer

Misinterpreted the question as 'yes'-'no' type. This was a good hint

. Edited the solution now.

chetan2u · Answer

As all terms are positive, we can cross multiply them without changing the sign \frac{1}{6} < \frac{1}{(n-1)} < \frac{1}{3} 3>n-1>6…………4>n>7 So we have to find whether n is 5 or 6. (1) (n - 6)(n - 7) = 0 n can be 6 or 7. Only possible value is 6. Sufficient (2) (n - 5)(n - 3) ≠ 0 n cannot be 3 or 5, but n is either 5 or 6. Thus, n is 6. Sufficient D

dkhosa · Answer

how do you know n is positive? Question only says it is an integer? if it is negative then n<-7 and n>-4 are also possible. in that case answer should be A.

chetan2u · Answer

If n<-7, then n can be -8 = 1/(n-1)=1/(-8-1)=1/-9.
Is 1/6<1/-9<1/3 correct?

Bunuel · Answer

Official Solution:

If  n  is an integer such that  \frac{1}{6} < \frac{1}{n-1} < \frac{1}{3} , what is the value of  n ? 
 
Given that  n  is an integer, for the inequality  \frac{1}{6} < \frac{1}{n-1} < \frac{1}{3}  to hold true,  \frac{1}{n-1}  must be either  \frac{1}{5}  or  \frac{1}{4} . Hence,  n  must be either 6 or 5. The question essentially asks: if  n  is either 6 or 5, what is the value of  n ? 
 
(1)  (n - 6)(n - 7) = 0 .
 
This statement implies that  n  is either  6  or  7 . Therefore,  n  cannot be 5, and it must be 6. Sufficient.
 
(2)  (n - 5)(n - 3) ≠ 0 .
 
This statement implies that  n  is neither  5  nor  3 . Since  n  is not 5, it must be 6. Sufficient

Answer: D

Bunuel · Answer

Practice harder version of this question  HERE .

If n is an integer such that 1/6 < 1/(n-1) < 1/3, what is the value of

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