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# If a and b are integers, and m is an even integer, is ab/4

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If a and b are integers, and m is an even integer, is ab/4 [#permalink]  19 Dec 2012, 22:45
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Question Stats:

55% (02:43) correct 45% (02:00) wrong based on 68 sessions
If a and b are integers, and m is an even integer, is ab/4 an integer?

(1) a+b is even.

(2) m/(ab) is an odd integer.

Source: HULT
[Reveal] Spoiler: OA
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Re: If a and b are integers, and m is an even integer, is ab/4 [#permalink]  19 Dec 2012, 23:33
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Amateur wrote:
If a and b are integers, and m is an even integer, is ab/4 an integer?

(1) a+b is even.

(2) m/(ab) is an odd integer.

Source: HULT

1) Obviously Insufficient. If a+b =2, answer is no, If a+b = 4, answer is yes. We have no info about ab.

2) We are given ab is even. If ab =2, answer is no, if ab=4, answer is yes. Insufficient.

1 & 2 together, ab is even and a+b is even. So, a & b have to be even. Product of two even numbers is always divisible by 4.

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Re: If a and b are integers, and m is an even integer, is ab/4 [#permalink]  19 Dec 2012, 23:34
Amateur wrote:
If a and b are integers, and m is an even integer, is ab/4 an integer?

(1) a+b is even.

(2) m/(ab) is an odd integer.

Source: HULT

Hi,

Question basically asks if ab is a multiple of 4 or not

From St 1, a is even, b is even or a is odd, b is odd. So not sufficient alone

From St 2 we get that m is even integer and m/ab is odd integer. Therefore we can say that m is odd multiple of ab and ab is even integer.

Therefore there will be 3 cases

1. a is even, b is even and thus ab is even
2. a is odd, b is even and thus ab is even
3. a is even, b is odd and thus ab is even

Thus st2 alone is not sufficient

Combining both statements we get a+b is even and ab is even. For both these conditions to be true a, b have to be even and hence ans should be C
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Last edited by WoundedTiger on 16 Jan 2014, 02:25, edited 1 time in total.
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Re: If a and b are integers, and m is an even integer, is ab/4 [#permalink]  20 Dec 2012, 01:29
Expert's post
If a and b are integers, and m is an even integer, is ab/4 an integer?

(1) a+b is even. This implies that either both a and b are odd or both even. Now, if a=b=1 the answer is NO but if a=b=2 the answer is YES. Not sufficient.

(2) m/(ab) is an odd integer. Since given that m=even, then we have that $$\frac{even}{ab}=odd$$ --> $$ab*odd=even$$ --> $$ab=even$$ --> at least one of the unknowns is even. Not sufficient.

(1)+(2) Since from (2) we have that at least one from a and b is even then from (1) it follows that both a and b must be even. The product of two even numbers is divisible by 4. Sufficient.

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Re: If a and b are integers, and m is an even integer, is ab/4 [#permalink]  30 Sep 2014, 11:56
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Re: If a and b are integers, and m is an even integer, is ab/4   [#permalink] 30 Sep 2014, 11:56
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