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# Is a*b*c divisible by 24? (1) a,b, and c are consecutive

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Is a*b*c divisible by 24? (1) a,b, and c are consecutive [#permalink]  28 May 2012, 05:06
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Is a*b*c divisible by 24?

(1) a, b, and c are consecutive even integers
(2) a*b is divisible by 12

This problem is from GMATClub Quant tests.
I am confused in this problem. Since 0 is also an EVEN number so statement 1 cannot be true. Am i right?
[Reveal] Spoiler: OA

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Last edited by Bunuel on 29 May 2012, 00:39, edited 1 time in total.
Edited the question and added the OA
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Re: GMATClub number problem confusion [#permalink]  28 May 2012, 07:45

Even if one of the even integers a, b, c is 0, the product a*b*c = 0 is divisible by 24.

0/24 = 0 => integer. So a * b * c is divisible by 24.
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Re: GMATClub number problem confusion [#permalink]  28 May 2012, 08:42
Oops! here is the catch which you pointed out. 0 is divisible by 24. Now I got it.
Yes the answer is A. Thanks a lot for the explanation.
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Re: Is a*b*c divisible by 24? (1) a,b, and c are consecutive [#permalink]  29 May 2012, 00:40
dexerash wrote:
Is a*b*c divisible by 24?

(1) a, b, and c are consecutive even integers
(2) a*b is divisible by 12

This problem is from GMATClub Quant tests.
I am confused in this problem. Since 0 is also an EVEN number so statement 1 cannot be true. Am i right?

Note that an integer a is a multiple of an integer b (integer a is a divisible by an integer b) means that \frac{a}{b}=integer: so, as 0 divided by any integer (except zero itself) yields an integer then zero is a multiple of every integer (except zero itself).

Also on GMAT when we are told that a is divisible by b (or which is the same: "a is multiple of b", or "b is a factor of a"), we can say that:
1. a is an integer;
2. b is an integer;
3. \frac{a}{b}=integer.

BACK TO THE ORIGINAL QUESTION:
Is a*b*c divisible by 24?

(1) a, b, and c are consecutive even integers --> a=2k-2, b=2k and c=2k+2 for some integer k --> abc=(2k-2)2k(2k+2)=8(k-1)k(k+1), now (k-1), k, (k+1) are 3 consecutive integers, which means that one of them must be a multiple of 3, thus abc is divisible by both 8 and 3, so by 24. Sufficient.

Or even without the formulas: the product of 3 consecutive even integers will have 2*2*2=8 as a factor, plus out of 3 consecutive even integers one must be a multiple of 3, thus abc is divisible by both 8 and 3, so by 24.

(2) a*b is divisible by 12, clearly insufficient as no info about c (if ab=12 and c=1 answer will be NO but if ab=24 and c=any integer then the answer will be YES).

Hope it's clear.
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Re: Is a*b*c divisible by 24? (1) a,b, and c are consecutive   [#permalink] 29 May 2012, 00:40
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