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# If U is an odd number and V and W are different integers, which of the

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Intern
Joined: 14 Aug 2016
Posts: 4
If U is an odd number and V and W are different integers, which of the  [#permalink]

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15 Aug 2016, 23:22
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If U is an odd number and V and W are different integers, which of the following must be even?

a. UV+UW
b. U+VW
c. UVW
d. U+V+W
e. None of these
Intern
Joined: 21 Nov 2014
Posts: 31
Location: Viet Nam
GMAT 1: 760 Q50 V44
Re: If U is an odd number and V and W are different integers, which of the  [#permalink]

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16 Aug 2016, 01:13
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The answer is E. None of the above must be even.

Just plug in some numbers and you will see.
Let U = 3.

a. UV + UW
If V = 1 and W = 2 -> UV + UW = 3*1 + 3*2 = 9 (Odd)
b. U + VW
If V = 1 and W = 2 -> U+VW = 3 + 1*2 = 5 (Odd)
c. UVW
If V = 1 and W = 5 -> UVW = 1*3*5 = 15 (Odd)
d. U + V + W
If V = 1 and W = 5 -> U + V + W = 1 + 3 + 5 = 9 (Odd)

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Intern
Joined: 14 Aug 2016
Posts: 4
Re: If U is an odd number and V and W are different integers, which of the  [#permalink]

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16 Aug 2016, 08:09
1
HieuNguyenVN - Thank You!
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Joined: 29 Jun 2016
Posts: 41
Re: If U is an odd number and V and W are different integers, which of the  [#permalink]

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17 Aug 2016, 21:31
u is odd and v,w are itegers
We know
o*o=o
e*o=e

A. U(V+W) => o*(e or o)=> V+W can be odd or even as noting is mentioned=> cannot say
B. U+VW =>o+(0 or e) => cannot say
c. UVW =>o*(e or o) =. cannot say
D. U+V+W=>o+(e or o)=>cannot say

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Re: If U is an odd number and V and W are different integers, which of the  [#permalink]

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02 Oct 2019, 08:27
Can any of the forum moderators/Bunuel add an OA to this question as this is from 2016. Thanks!

I go with E too. Below is my reasoning.

1. As there is no information about V and W apart from them being integers, $$V$$ and $$W$$ can be either made odd or even to disprove and eliminate the options
2. For an answer choice to be true, we need to ensure that the outcome is even for all possible odd/even combinations

A. $$UV + UW$$
Say, $$V$$ is even and $$W$$ is odd then - $$UV + UW$$ = $$odd*even + odd*odd$$ = $$even + odd$$ = $$odd$$

B. $$U + VW$$
Say, $$V$$ and $$W$$ are both even then - $$odd + even*even$$ = $$odd + even = odd$$

C. $$UVW$$
Say, $$V$$ and $$W$$ are odd, then as U is also odd the product will be odd

D. $$U + V + W$$
Say, $$V$$ is even and $$W$$ is even then - $$odd + even + even$$ = $$odd$$

This leaves us with the last option. Ans. E
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Posts: 58446
Re: If U is an odd number and V and W are different integers, which of the  [#permalink]

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02 Oct 2019, 08:36
Pritishd wrote:
Can any of the forum moderators/Bunuel add an OA to this question as this is from 2016. Thanks!

_______________
Done. Thank you.
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Re: If U is an odd number and V and W are different integers, which of the  [#permalink]

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05 Oct 2019, 16:56
ash42 wrote:
If U is an odd number and V and W are different integers, which of the following must be even?

a. UV+UW
b. U+VW
c. UVW
d. U+V+W
e. None of these

Although we know that U is odd, in order to be able to determine which answer choice must be even, we need information about V and W.

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Re: If U is an odd number and V and W are different integers, which of the   [#permalink] 05 Oct 2019, 16:56
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