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Is J divisible by 24?

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Is J divisible by 24? [#permalink]

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Is J divisible by 24?

(1) J is divisible by both 12 and 20.
(2) J is divisible by 8.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 29 Aug 2012, 02:32, edited 1 time in total.
Edited the question and added the OA.
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Re: Is J divisible by 24? [#permalink]

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Is J divisible by 24?

(1) J is divisible by both 12 and 20 --> J is divisible by the least common multiple of 12 and 20, so by 60. Now, if J=60, then the answer is NO but if J=120, then the answer is YES. Not sufficient.

(2) J is divisible by 8. If J=8, then the answer is NO but if J=24, then the answer is YES. Not sufficient.

(1)+(2) Since from (1) J is divisible by 3 and from (2) J is divisible by 8, then it's divisible by the least common multiple of 3 and 8, so by 24. Sufficient.

Answer: C.

Hope it's clear.
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Re: Is J divisible by 24? [#permalink]

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Re: Is J divisible by 24? [#permalink]

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Re: Is J divisible by 24? [#permalink]

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Re: Is J divisible by 24? [#permalink]

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conty911 wrote:
Is J divisible by 24?

(1) J is divisible by both 12 and 20.
(2) J is divisible by 8.


We need to determine whether J/24 = integer.

Statement One Alone:

J is divisible by both 12 and 20.

If J is divisible by both 12 and 20, then J is divisible by the LCM of 12 and 20, which is 60. Furthermore, J will be divisible by any factors of 60. However, since 24 is not a factor of 60, J may or may not be divisible by 24. For example, if J = 120, then J is divisible by 24. On the other hand, if J = 60, then J is not divisible by 24. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

J is divisible by 8.

Statement two alone is not sufficient to answer the question. For example, when J = 8, J/24 is NOT an integer, but when J = 24, J/24 IS an integer.

Statements One and Two Together:

From statements one and two, we know that J is divisible by both 8 and 60. Thus, J is divisible by the LCM of 8 and 60, which is 120. Since 24 is a factor of 120, J is also divisible by 24.

Answer: C
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Re: Is J divisible by 24?   [#permalink] 14 Apr 2017, 05:52
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