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If positive integers x and y are not both odd, which of the
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17 Aug 2020, 11:12
17 Aug 2020, 11:12
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If positive integers x and y are not both odd, which of the following must be even?
(A) xy
(B) x + y
(C) x - y
(D) x + y -1
(E) 2(x + y) - 1
(A) xy
(B) x + y
(C) x - y
(D) x + y -1
(E) 2(x + y) - 1
Re: If positive integers x and y are not both odd, which of the
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17 Aug 2020, 11:12
17 Aug 2020, 11:12
Expert Reply
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Re: If positive integers x and y are not both odd, which of the
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17 Aug 2020, 11:39
17 Aug 2020, 11:39
Carcass wrote:
If positive integers x and y are not both odd, which of the following must be even?
(A) xy
(B) x + y
(C) x - y
(D) x + y -1
(E) 2(x + y) - 1
(A) xy
(B) x + y
(C) x - y
(D) x + y -1
(E) 2(x + y) - 1
Given: integers x and y are not both odd
There are two different cases that satisfy this information:
Case i: Both numbers are even
Case ii: One number is even and one number is odd
Let's examine each case individually...
Case i: Both numbers are even
So it could be the case that x = 2 and y = 2, so let's plug these values into our answer choices
(A) (2)(2) = 4, which is even. Keep.
(B) 2 + 2 = 4, which is even. Keep.
(C) 2 - 2 = 0, which is even. Keep.
(D) 2 + 2 - 1 = 3, which is odd. ELIMINATE.
(E) 2(2 + 2) - 1 = 7, which is odd. ELIMINATE.
We're down to A, B and C
Case ii: One number is even and one number is odd
So it could be the case that x = 1 and y = 2, so let's plug these values into the remaining answer choices
(A) (1)(2) = 2, which is even. Keep.
(B) 1 + 2 = 3, which is odd. ELIMINATE.
(C) 1 - 2 = -1, which is odd. ELIMINATE.
By the process of elimination, the correct answer is A
Cheers,
Brent
