Do You Make These 3 Mistakes in GMAT Even-Odd Questions? – Part 2/3

by on October 9th, 2015

P2.1 If a and b are integers, is a + 8b even?

I) 2a + b is even

II) a^b is even

While reading the expression a+8b, did you think whether b was even or odd? If you did then you just fell in to the second pitfall that stops many students from becoming even odd champions. Why is that? That’s because you just wasted some time, thinking about an aspect that’s not relevant because in the given expression, the term 8b will be even, irrespective of whether b is even or odd (because, Even*Odd = Even and Even*Even = Even).

This article is a part of a 3-part article series in which we will explore why students fail to master the concept of Even and Odd numbers, despite it being deemed as one of the easier concepts on GMAT Quant. Our first article in the series covered the pitfall faced by many students while solving even odd questions—Getting Intimidated by seemingly complex expressions.

Right then … let’s move on to understanding where exactly you might be going wrong in your approach to solving even odd questions and therefore may be facing timing issues in them.

Pitfall #2: Wasting time on unimportant terms

What do we mean?

As you probably experienced above, you pondered on an aspect that wasn’t even relevant in the first place. If you fall into such pitfalls in the exam, then you’ll be squandering your most precious resource in the GMAT—Time. Minutes frittered away thus may create a time crunch towards the end of the test, and then, coming under the pressure of the seconds ticking away, you may frantically answer questions testing concepts you are most comfortable in, wrongly. So, it is very important to be on strict guard against even a moment spent on unneeded analysis.

Most likely, the reason you faced this problem was not that you didn’t know that the result of an even integer multiplied with any integer will be even. In all likelihood, you faced this problem because your strategy to solving such questions wasn’t in place.

You need to understand how to apply the concepts you know on a regular basis. Before starting with any calculation or applying any formula, you need to first get the maximum out of the given information.

So, in the expression at hand, a + 8b, since you know that 8b will be even, you should focus all your attention on analyzing whether a is even or odd, because that is what will get you to the answer.

What can you do to avoid this pitfall?  

In order to not waste even a second on the unimportant terms, here are a few pointers that you should use to weed out the unimportant terms in an expression:

  • A term of the form Even number*X will always be even.
  • In a term of the form Even number + X, the (Even number) plays no role in the Even-Odd nature of the term.
  • In a term of the form Odd number*X, the (Odd number) plays no role in the Even-Odd nature of the term.


You’ve already seen an example of the first pointer in Question P2.1

Here’s an example that will show all the three pointers in action:

P2.2 If a, b, c, and n are integers, is a + 8b + (2n+1) c even?

I) 2a + 4c is even

II) 3a + c is even

1st Pointer

The term 8b will always be even, irrespective of the value of b.

2nd Pointer

In the given expression, the even term 8b doesn’t impact the even-odd nature of this expression. So, the expression will have the same even-odd nature as the sum a + (2n+1)c.

3rd Pointer

In the term (2n+1)c, (2n+1) is an odd number, and so plays no role in the even-odd nature of this term. So, the term (2n+1)c will have the same even-odd nature as c.

So, the expression a + (2n+1)c will have the same even-odd nature as the expression a + c.


When you see an expression, first use the three pointers to determine the unimportant terms. Do not waste precious time on processing the unimportant terms.

Test Yourself

See how much time you take on this question and if you waste time on any term that doesn’t deserve it:

P2.3 If ab, and n are positive integers such that n = 3a - b^3, is n^2+ 3 divisible by 2?

I) a^2 -4b^3 - 5 = 0

II) 3b^3 - a^2 + 6 = 0

Next Steps

  1. To take your understanding of this concept to the next level, try the e-GMAT Quant Free Trial.
  2. Watch the recording of our Number Properties Free Session to understand how the correct approach can help you solve 700+ level questions with ease.

1 comment

  • For P2.3 is the correct answer D?

    n^2+3=E. if n is even then n=3a-b^3 is E - E = E, therefore A is automatically E. so the question is what's b?

    1) a^2-4b^3-5=0 rearranged is 4b^3=E-E, which is b^3=E, this means b is E. Sufficient

    2) 3b^3-a^2+6=0 rearranged is 3b^3=E-E, which is b^3 = E/3 (since b is an integer) ......b^3 = E, which again means b=Even. Sufficient

    My thought process might be flawed, but this ish is frustrating.

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