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

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Bunuel
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If n is an integer such that 1/6 < 1/(n-1) < 1/3, what is the value of [#permalink] New post   06 Sep 2022, 06:38
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A
B
C
D
E

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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) \((n - 5)(n - 3) ≠ 0\)

 


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SaquibHGMATWhiz
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Re: If n is an integer such that 1/6 < 1/(n-1) < 1/3, what is the value of [#permalink] New post   Updated on: 08 Sep 2022, 04:23
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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.

Originally posted by SaquibHGMATWhiz on 07 Sep 2022, 05:50.
Last edited by SaquibHGMATWhiz on 08 Sep 2022, 04:23, edited 1 time in total.
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Re: If n is an integer such that 1/6 < 1/(n-1) < 1/3, what is the value of [#permalink] New post   07 Sep 2022, 06:32
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:think: Anyone else want to try ? :angel:
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ankitgoswami
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Re: If n is an integer such that 1/6 < 1/(n-1) < 1/3, what is the value of [#permalink] New post   07 Sep 2022, 08:09
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Bunuel wrote:
:think: Anyone else want to try ? :angel:


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
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Re: If n is an integer such that 1/6 < 1/(n-1) < 1/3, what is the value of [#permalink] New post   08 Sep 2022, 04:24
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Bunuel wrote:
:think: Anyone else want to try ? :angel:


Misinterpreted the question as 'yes'-'no' type.

This was a good hint :). Edited the solution now.
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Re: If n is an integer such that 1/6 < 1/(n-1) < 1/3, what is the value of [#permalink] New post   08 Sep 2022, 04:45
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Bunuel wrote:
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) \((n - 5)(n - 3) ≠ 0\)

 


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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


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Re: If n is an integer such that 1/6 < 1/(n-1) < 1/3, what is the value of [#permalink] New post   12 Sep 2022, 12:44
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.
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Re: If n is an integer such that 1/6 < 1/(n-1) < 1/3, what is the value of [#permalink] New post   12 Sep 2022, 19:39
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dkhosa wrote:
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.


If n<-7, then n can be -8 = 1/(n-1)=1/(-8-1)=1/-9.
Is 1/6<1/-9<1/3 correct?
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Re: If n is an integer such that 1/6 < 1/(n-1) < 1/3, what is the value of [#permalink] New post   26 Apr 2023, 04:13
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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
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Re: If n is an integer such that 1/6 < 1/(n-1) < 1/3, what is the value of [#permalink] New post   26 Apr 2023, 04:39
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Bunuel wrote:
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) \((n - 5)(n - 3) ≠ 0\)

 


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Re: If n is an integer such that 1/6 < 1/(n-1) < 1/3, what is the value of [#permalink]
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