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If integers x and y are NEITHER both odd,

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QuantMadeEasy
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If integers x and y are NEITHER both odd, [#permalink] New post   Updated on: 29 Mar 2020, 22:25
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If integers x and y are NEITHER both odd, NOR both even, which of the following must be odd?​

a. 2(x+y)​

b. 2x + y​

c. x+ 2y​

d. xy + 1​

e. \(x^y\)​

https://youtu.be/oRyquKBDSH0
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D

Originally posted by QuantMadeEasy on 11 Feb 2020, 23:03.
Last edited by QuantMadeEasy on 29 Mar 2020, 22:25, edited 1 time in total.
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Re: If integers x and y are NEITHER both odd, [#permalink] New post   12 Feb 2020, 07:23
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kapil1 wrote:
If integers x and y are NEITHER both odd, NOR both even, which of the following must be odd?​

a. 2(x+y)​

b. 2x + y​

c. x+ 2y​

d. xy + 1​

e. \(x^y\)​


We know that one of x or y is even, and the other is odd. So their product xy will certainly be even, and xy + 1 will certainly be odd. So D is correct.

The other choices don't need to be odd: 2(x+y) is always even since it's clearly divisible by 2; 2x + y will be even if y is even; x + 2y will be even if x is even; and x^y will be even if x is even and y is positive (in fact, x^y need not be an integer at all, if y is negative).
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Re: If integers x and y are NEITHER both odd, [#permalink] New post   14 Feb 2020, 14:27
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kapil1 wrote:
If integers x and y are NEITHER both odd, NOR both even, which of the following must be odd?​

a. 2(x+y)​

b. 2x + y​

c. x+ 2y​

d. xy + 1​

e. \(x^y\)​


Since one is odd and the other is even, then xy is even, so xy + 1 is odd.

Answer: D
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Re: If integers x and y are NEITHER both odd, [#permalink] New post   17 Feb 2020, 12:58
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Re: If integers x and y are NEITHER both odd, [#permalink] New post   12 Mar 2021, 03:08
As we know that one is even and one is odd, so their multiplication will surely be even. And we know the property that even + 1 = odd, so search for that in the answers


d. xy + 1​

so (d) is odd​
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Re: If integers x and y are NEITHER both odd, [#permalink]
12 Mar 2021, 03:08
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