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# Can n/196 be an integer?

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Intern
Joined: 03 Jul 2018
Posts: 2
Can n/196 be an integer?  [#permalink]

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Updated on: 03 Jul 2018, 10:26
2
00:00

Difficulty:

85% (hard)

Question Stats:

21% (01:42) correct 79% (02:05) wrong based on 36 sessions

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Can n/196 be an integer?

(1) n is a multiple of 24 but not 16

(2) n is a multiple of 8 but not 48

Originally posted by Newman2019 on 03 Jul 2018, 09:13.
Last edited by Bunuel on 03 Jul 2018, 10:26, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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Joined: 02 Sep 2009
Posts: 51035
Can n/196 be an integer?  [#permalink]

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03 Jul 2018, 09:27
2
Can n/196 be an integer?

Notice that the question asks whether $$\frac{n}{196} = \frac{n}{2^2*7^2}$$ CAN be an integer, not whether it IS an integer. n/196 could be an integer if n has 2 in the power of at least 2 and 7 in the power of at least 2.

(1) n is a multiple of 24 but not 16.

Since the question asks whether n/196 CAN be an integer, then we are only interested in the numbers n is NOT divisible by, to check whether this discards this possibility. We are told that n is NOT divisible by 2^4. No problem. We needed 2 in the power of at least 2. So, for example, if n = 24*7^2, then n will be divisible by 196. So, n/196 CAN be an integer. Sufficient.

(2) n is a multiple of 8 but not 48

Again, since the question asks whether n/196 CAN be an integer, then we are only interested in the numbers n is NOT divisible by, to check whether this discards this possibility. We are told that n is NOT divisible by 2^4*3. No problem. We needed 2 in the power of at least 2 and are not concerned about 3 at all. So, for example, if n = 8*7^2, then n will be divisible by 196. So, n/196 CAN be an integer. Sufficient.

Hope it's clear.
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Re: Can n/196 be an integer?  [#permalink]

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03 Jul 2018, 22:04
Is n/196 an integer?

then the correct choice would be E.

Correct me if I am wrong.
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Re: Can n/196 be an integer?  [#permalink]

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03 Jul 2018, 22:07
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arun6765 wrote:
Is n/196 an integer?

then the correct choice would be E.

Correct me if I am wrong.

Yes, because in that case we would not be able to get a definite YES or NO.
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Re: Can n/196 be an integer? &nbs [#permalink] 03 Jul 2018, 22:07
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# Can n/196 be an integer?

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