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If x is an even integer and y is an odd integer, which of the followin

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Bunuel
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If x is an even integer and y is an odd integer, which of the followin [#permalink] New post  14 Oct 2019, 08:06
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If x is an even integer and y is an odd integer, which of the following is even?

(A) 3x + 4y - 1
(B) 3x + 3y - 2
(C) 4x + 4y + 1
(D) 4x + 3y + 2
(E) 4x + 3y + 1
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BrentGMATPrepNow
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If x is an even integer and y is an odd integer, which of the followin [#permalink] New post  14 Oct 2019, 08:12
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Bunuel wrote:
If x is an even integer and y is an odd integer, which of the following is even?

(A) 3x + 4y - 1
(B) 3x + 3y - 2
(C) 4x + 4y + 1
(D) 4x + 3y + 2
(E) 4x + 3y + 1


Let's test a "nice" even integer for x (say x = 0) and a nice odd integer for y (say y = 1)

We get....
(A) 3(0) + 4(1) - 1 = 3, which is ODD.
(B) 3(0) + 3(1) - 2 = 1, which is ODD.
(C) 4(0) + 4(1) + 1 = 5, which is ODD.
(D) 4(0) + 3(1) + 2 = 5, which is ODD.
(E) 4(0) + 3(1) + 1 = 4, which is EVEN.

Answer: E

Cheers,
Brent
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TheNightKing
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Re: If x is an even integer and y is an odd integer, which of the followin [#permalink] New post  14 Oct 2019, 08:15
Bunuel wrote:
If x is an even integer and y is an odd integer, which of the following is even?

(A) 3x + 4y - 1
(B) 3x + 3y - 2
(C) 4x + 4y + 1
(D) 4x + 3y + 2
(E) 4x + 3y + 1


x=4,y=3
(A) 3x + 4y - 1 = 3(4)+4(3)-1 = 23
(B) 3x + 3y - 2 = 3(4)+3(3)-2 = 19
(C) 4x + 4y + 1 = 4(4)+4(3)+1 = 29
(D) 4x + 3y + 2 = 4(4)+3(3)+2 = 27
(E) 4x + 3y + 1 = 3(4)+3(3)+1 =22

Option E.

You can also think in terms of even and odd, instead of picking number. Whatever works best for you!
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ThatDudeKnows
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Joined: 11 May 2022
Posts: 1097
Re: If x is an even integer and y is an odd integer, which of the followin [#permalink] New post  17 Jul 2022, 10:19
Expert Reply
Bunuel wrote:
If x is an even integer and y is an odd integer, which of the following is even?

(A) 3x + 4y - 1
(B) 3x + 3y - 2
(C) 4x + 4y + 1
(D) 4x + 3y + 2
(E) 4x + 3y + 1


Even times anything is even, so the first part of all of the answer choices are even. We need the second and third parts to either both be odd or both be even.

(A) Even - Odd ... Nope.
(B) Odd - Even ... Nope.
(C) Even + Odd ... Nope.
(D) Odd + Even ... Nope.
(E) Odd + Odd ... Yep!

Answer choice E.
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gmatclubot
Re: If x is an even integer and y is an odd integer, which of the followin [#permalink]
17 Jul 2022, 10:19
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