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

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Re: If x is an even integer and y is an odd integer, which of the following is even?

by Brent@GMATPrepNow » Thu Jul 23, 2020 6:56 am
BTGModeratorVI wrote: ↑
Thu Jul 23, 2020 6:45 am
 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

Answer: E
Source: GMAT prep
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

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: If x is an even integer and y is an odd integer, which of the following is even?

by gentvenus » Thu Jul 23, 2020 11:30 am
Trial and error:
x = 0
y = 1

(A) 3(0) + 4(1) - 1 = 3
(B) 3(0) + 3(1) - 2 = 1
(C) 4(0) + 4(1) + 1 = 5
(D) 4(0) + 3(1) + 2 = 5
(E) 4(0) + 3(1) + 1 = 4, which is CORRECT.
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Re: If x is an even integer and y is an odd integer, which of the following is even?

by Scott@TargetTestPrep » Sun Jul 26, 2020 8:18 am
BTGModeratorVI wrote: ↑
Thu Jul 23, 2020 6:45 am
 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

Answer: E
Solution:

Since x is even, 3x and 4x are both even. Since y is odd, 3y is odd and 4y is even. Therefore,

4x + 3y + 1 = even + odd + odd = even

Answer: E

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