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# If n is an integer, is (29 - n)/n an integer?

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Math Expert
Joined: 02 Sep 2009
Posts: 50730
If n is an integer, is (29 - n)/n an integer?  [#permalink]

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10 Dec 2017, 00:06
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Difficulty:

35% (medium)

Question Stats:

54% (01:28) correct 46% (01:36) wrong based on 33 sessions

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If n is an integer, is (29 - n)/n an integer?

(1) n is prime.
(2) n is an odd factor of 116.

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Joined: 25 Feb 2013
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If n is an integer, is (29 - n)/n an integer?  [#permalink]

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10 Dec 2017, 05:34
Bunuel wrote:
If n is an integer, is (29 - n)/n an integer?

(1) n is prime.
(2) n is an odd factor of 116.

$$\frac{(29-n)}{n}=\frac{29}{n}-\frac{n}{n}=\frac{29}{n}-1$$

so we need to know whether $$n=29$$ or $$1$$

Statement 1: $$n$$ can be any prime number. Insufficient

Statement 2: factors of $$116 = 1*2*2*29$$. as $$1$$ & $$29$$ are the only odd factors so $$n=1$$ or $$29$$. Sufficient

Option B
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Re: If n is an integer, is (29 - n)/n an integer?  [#permalink]

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10 Dec 2017, 05:54
Bunuel wrote:
If n is an integer, is (29 - n)/n an integer?

(1) n is prime.
(2) n is an odd factor of 116.

(1) n is prime. If n = 2, $$\frac{(29 - 2)}{2}$$ = not integer. If n = 29, $$\frac{(29 - 29)}{29}$$ = integer, not suf.

(2) n is an odd factor of 116. The prime factors of 116 are $$2^2*29$$, and 116 has 6 factors of which only {1,29} are odd.

If n = 1, $$\frac{(29 - 1)}{1}$$ = integer, and if n = 29, $$\frac{(29 - 29)}{29}$$ = integer, sufficient.

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If n is an integer, is (29 - n)/n an integer?  [#permalink]

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10 Dec 2017, 06:44
Bunuel wrote:
If n is an integer, is (29 - n)/n an integer?

(1) n is prime.
(2) n is an odd factor of 116.

Actually we need to find out whether 29/n is an integer.

1. n can be any prime number - so A is insufficient.
2. The odd factors of 116 are 1 & 29- hence the required expression comes out to be an integer in each case.

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If n is an integer, is (29 - n)/n an integer? &nbs [#permalink] 10 Dec 2017, 06:44
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