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

Question

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

HieuNguyenVN · Answer

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.

ash42 · Answer

HieuNguyenVN  - Thank You!

ShravyaAlladi · Answer

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

Pritishd · Answer

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

Bunuel · Answer

_______________
Done. Thank you.

ScottTargetTestPrep · Answer

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

bumpbot · Answer

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

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