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}  and  (n - 5)(n - 3) 
eq 0 , what is the value of  n ?

A. 2
B. 3
C. 4
D. 5
E. 6

Bunuel · Accepted Answer

Official Solution:

If  n  is an integer such that  \frac{1}{6} < \frac{1}{n-1} < \frac{1}{3}  and  (n - 5)(n - 3) 
eq 0 , what is the value of  n ?

A. 2
B. 3
C. 4
D. 5
E. 6

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.

From  (n - 5)(n - 3) 
eq 0 , we can deduce that  n  cannot be  5  or  3 . Therefore, since  n  is not 5, it must be 6.

Answer: E

gmatophobia · Answer

\frac{1}{6} < \frac{1}{n-1} < \frac{1}{3}

Taking the reciprocal of the equation

3 < n - 1 < 6

Adding 1 throughout the inequality

3+1 < n - 1 + 1 < 6 + 1

4 < n < 7

Hence, possible values of n = {5, 6}

(n - 5)(n - 3) 
eq 0

Inference:  n
eq 5  and  n
eq 3

Therefore only possible value of n = 6

Option E

sayan640 · Answer

E should be the answer.
Out of all the options given , n can only be 2 or 4 or 6 , given n not equals 3 or 5. ( Given (n-5)*(n-3) not equals 0 )
Only n = 6 satisfies as 1/5 = 20% falls between 16.66% and 33%.

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mooh · Answer

(n−5)(n−3)≠0  already eliminates options B and D

Going ahead to key in the value of n, option A i.e.  2 
1/6 < 1/(2 - 1) < 1/3 
1/6 < 1  but  1< 1/3 
Option A is  Wrong

Key in the value of n in option C i.e.  4 
1/6 < 1/(4 - 1) < 1/3 
1/6 < 1 /3  but  1/3 is not < 1/3 
Option C is  Wrong

Key in the value of n in option C i.e.  6 
1/6 < 1/(6 - 1) < 1/3 
1/6 < 1 /5  and  1/5 is < 1/3 
Option E is  Correct

VivekSri · Answer

If n is an integer such that 1/6 < 1/(n - 1) < 1/3 and (n - 5)(n - 3)

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