Question

If m, n, o, p and q are the integers then \[m\left( {n + o} \right)\left( {p - q} \right)\] must be even then which of the following is even?
A.\[m + n\]
B.\[n + p\]
C.\[m\]
D.\[p\]

Answer 1

Hint: This question is very simple to answer. If one of the factors of the product is even then the whole sum is even. So any one of the factors can be even.

Complete step-by-step answer:
Given that m, n, o, p and q are the integers.
\[m\left( {n + o} \right)\left( {p - q} \right)\] is the product that is performed between combinations of these integers.
We have no idea which integer is even and which one is odd.
But we know that in the case of a product if one of the numbers is even then it affects the whole operation as their product becomes even.
So one of the terms either\[m\], \[n + o\] or \[p - q\] can be even. So let’s check from the options.
From A, B, C and D only option C holds the value of one of these terms that is \[m\].
So the correct option is C.

Note: Other options have the integers but they don’t have the terms given in the product above. So we eliminated them. Remember this is applicable only in case of product because sum or difference of combination of even and odd leads to either even or odd number as the answer.