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# If A and B are integers, is the product AB even?

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Intern
Joined: 19 Dec 2016
Posts: 47
Location: India
WE: Consulting (Computer Software)
If A and B are integers, is the product AB even?  [#permalink]

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25 Jul 2017, 15:31
00:00

Difficulty:

85% (hard)

Question Stats:

38% (03:02) correct 62% (01:24) wrong based on 13 sessions

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If A and B are integers, is the product AB even?

(1) A+B = (10A + 3B)

(2) (66B-2)/A = 13A - B

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Senior Manager
Joined: 13 Oct 2016
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GPA: 3.98
Re: If A and B are integers, is the product AB even?  [#permalink]

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26 Jul 2017, 01:34
GTExl wrote:
If A and B are integers, is the product AB even?

(1) A+B = (10A + 3B)

(2) (66B-2)/A = 13A - B

Hi

(1) Squaring both sides:

$$A^2 + 2AB + B^2 = 10A + 3B$$

$$A^2 = 10A - 2AB - B^2 + 3B$$

$$A^2 = 10A - 2AB - B(B - 3)$$

$$(B - 3)$$ and $$(B - 1)$$ have same parity (even/odd nature) so we can substitute one with nother.

$$A^2 = 10A - 2AB - B(B - 1)$$

or

$$A^2 = even - even - even = even$$

A is even and the product AB is even as well. Sufficient.

(2) $$66B - 2 = A(13A - B)$$

or

$$A(13A - B) = even$$

Either A is even or A and B are both odd. Hence product will be even or odd. Insufficient

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: If A and B are integers, is the product AB even?   [#permalink] 26 Jul 2017, 01:34
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