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

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

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New post 15 Aug 2016, 23:22
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A
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E

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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
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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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New post 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)

--> Answer is E.
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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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New post 16 Aug 2016, 08:09
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HieuNguyenVN - 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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New post 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

thus answer none of these
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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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New post 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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Re: If U is an odd number and V and W are different integers, which of the  [#permalink]

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New post 02 Oct 2019, 08:36
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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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New post 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.

Answer: E
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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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