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The expression ab+a is odd when the a and b are integers. Which of the
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07 Jul 2021, 08:28
07 Jul 2021, 08:28
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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
(A) a
(B) b
(C) a + b
(D) ab - a
(E) a + b^2
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Re: The expression ab+a is odd when the a and b are integers. Which of the
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07 Jul 2021, 10:22
07 Jul 2021, 10:22
1
Carcass 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
(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
Cheers,
Brent
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Status:Founder & Quant Trainer
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Posts: 1546
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Re: The expression ab+a is odd when the a and b are integers. Which of the
[#permalink]
07 Jul 2021, 10:28
07 Jul 2021, 10:28
Carcass 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) a
(B) b
(C) a + b
(D) ab - a
(E) a + b^2
ab + a = a(b + 1) = odd
i.e. a = odd and (b + 1) = odd
Since, b + 1 = odd
i.e. b + odd = odd
b = even
Straight answer B
