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01 Nov 2020, 00:45
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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85% (01:23) correct
15%
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If positive integers x and y are not both odd, which of the following can never 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
01 Nov 2020, 04:00
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If positive integers x and y are not both odd, which of the following can never be even?
As both x and y cannot be odd then either both are even or one of them is odd and the other is even.
Looking at the answer choices,
(A) xy (Will always be even, as either x or y is even, therefore the product has to be even.) Not our answer.
(B) x + y (This can be either even or odd, if x and y are both even then the sum is even, if one is even and the other number is odd then the sum is odd.) Not our answer.
(C) x - y (This can again be either odd or even, if x and y are both even then then difference is even, if one is even and the other is odd then the difference between them is also odd.) Not our answer.
(D) x + y - 1 (This can be either even or odd, if x and y are both even then the sum is even but if you subtract one then the result is odd, if one is even and the other number is odd then the sum is odd, if you subtract one then the result is even.) Not our answer.
(E) 2(x + y) - 1 (This will always be odd because whatever the nature of the sum of x+y be whether odd or even, multiplying it by 2 will make it even and subtracting 1 from it will make it odd.) This is our answer.
The OA is E.
If you like my explanation do give kudos
As both x and y cannot be odd then either both are even or one of them is odd and the other is even.
Looking at the answer choices,
(A) xy (Will always be even, as either x or y is even, therefore the product has to be even.) Not our answer.
(B) x + y (This can be either even or odd, if x and y are both even then the sum is even, if one is even and the other number is odd then the sum is odd.) Not our answer.
(C) x - y (This can again be either odd or even, if x and y are both even then then difference is even, if one is even and the other is odd then the difference between them is also odd.) Not our answer.
(D) x + y - 1 (This can be either even or odd, if x and y are both even then the sum is even but if you subtract one then the result is odd, if one is even and the other number is odd then the sum is odd, if you subtract one then the result is even.) Not our answer.
(E) 2(x + y) - 1 (This will always be odd because whatever the nature of the sum of x+y be whether odd or even, multiplying it by 2 will make it even and subtracting 1 from it will make it odd.) This is our answer.
The OA is E.
If you like my explanation do give kudos
01 Nov 2020, 04:06
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Bunuel
If positive integers x and y are not both odd, which of the following can never 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
From the wording, what I understand is that both the integers are not odd simultaneously. So one is even and the other is odd or both are Even.
Eliminate using the Options
Option 1: xy = Even * Even = Even. Option 1 can be even.
Option 2: x + y = Even + Even = Even. Option 2 can be even.
Option 3: x - y = Even - Even = Even. Option 3 can be even
Option 4: x + y - 1 = Even + Odd - 1 = Odd - 1 = Even. Option 4 can be even
Option 5: 2(x + y) - 1. Since x + y is multiplied by an even number, it's product will always be even. Therefore Even - 1 will always be odd and we will never get an even number.
Option E
Arun Kumar
