The Gateway to Computer Science Excellence
0 votes

Given that $a$ and $b$ are integers and $a+a^2 b^3$ is odd, which of the following statements is correct?

  1. $a$ and $b$ are both odd
  2. $a$ and $b$ are both even
  3. $a$ is even and $b$ is odd
  4. $a$ is odd and $b$ is even
in Numerical Ability by Veteran (431k points)
recategorized by | 105 views
Migrated from GO Mechanical 7 months ago by Arjun

1 Answer

+1 vote
Best answer
Given that $a$ and $b$ are integers.

And $a+a^{2}b^{3}$ is odd

So, $a(1+ab^{3})$ is also odd.

We now that only odd$\times$ odd is odd. (even $\times$ even = even, odd $\times$ even = even)
Therefore $a$ is odd and  $(1+ab^{3})$ is odd

So, $ab^{3}=$ even        $\{\because 1+x \text{ is odd}\implies x \text{ is } odd-1\implies x \text{ is even}\}$

Since $a$ is odd and $ab^{3}$ is even, $b$ must be even.

Therefore, $a$ is odd and $b$ is even.

Hence, the correct answer is (D).
by Veteran (59.2k points)
selected by

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
50,737 questions
57,356 answers
105,252 users