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The expression ab+a is odd when the a and b are integers. Which of the

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Bunuel
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The expression ab+a is odd when the a and b are integers. Which of the [#permalink] New post   26 May 2016, 12:19
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The expression ab+a is odd when the a and b are integers. Which of the following expressions must be even?

(A) a
(B) b
(C) a + b
(D) ab - a
(E) a + b^2
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BrentGMATPrepNow
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Re: The expression ab+a is odd when the a and b are integers. Which of the [#permalink] New post   15 Feb 2019, 10:48
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Bunuel wrote:
The expression ab+a is odd when the a and b are integers. Which of the following expressions must be even?

(A) a
(B) b
(C) a + b
(D) ab - a
(E) a + b²


GIVEN: ab+a is odd
Factor to get: a(b+1) is ODD

This means a and b+1 must be ODD, which means b must be EVEN
So, we already know that a is odd and b is even

So, a quick approach will be to take each answer choice and replace a with 1 (odd) and replace b with 0 (even)
We get:

(A) 1 = ODD (ELIMINATE)
(B) 0 = EVEN. keep
(C) 1 + 0 = 1, which is ODD (ELIMINATE)
(D) (1)(0) - 1 = -1, which is ODD (ELIMINATE)
(E) 1 + 0² = 1, which is ODD (ELIMINATE)

Answer: B

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Brent
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Re: The expression ab+a is odd when the a and b are integers. Which of the [#permalink] New post   27 May 2016, 14:33
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Given : ab + a is always odd. the expression can be simplified as :

ab + a = a(b+1) = odd. Only a multiplication of an odd to another odd number will yield an odd. => odd * odd = odd.

Thus, a= odd, and b+1 = odd => b = even. Hence B.
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Re: The expression ab+a is odd when the a and b are integers. Which of the [#permalink] New post   26 May 2016, 14:48
Bunuel wrote:
The expression ab+a is odd when the a and b are integers. Which of the following expressions must be even?

(A) a
(B) b
(C) a + b
(D) ab - a
(E) a + b^2



ab+a is odd

a and b are integers

If a were even "ab+a" would be even despite any value of b.

B can't be odd, so "b" must be even.

Ans : B
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The expression ab+a is odd when the a and b are integers. Which of the [#permalink] New post   27 May 2016, 22:05
Bunuel wrote:
The expression ab+a is odd when the a and b are integers. Which of the following expressions must be even?

(A) a
(B) b
(C) a + b
(D) ab - a
(E) a + b^2


a b ab a ab+a
e o e e e
o e e o o (2nd line)
e e e e e
o o 0 0 e

Only the 2nd line gives us an odd value so "a" has to be odd and "b" has to be even

Testing all the options with these inputs will give us option B as the answer.
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Re: The expression ab+a is odd when the a and b are integers. Which of the [#permalink] New post   31 May 2016, 13:51
A very quick solution:

ab + a = a (b + 1)
For the above equation to be odd, both a and (b+1) must be odd
If b+1 must be odd, b must be even

Answer: B
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Re: The expression ab+a is odd when the a and b are integers. Which of the [#permalink] New post   30 Jun 2021, 05:55
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Re: The expression ab+a is odd when the a and b are integers. Which of the [#permalink]
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