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

HieuNguyenVN - Thank You!

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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Done. Thank you.

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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