Do You Make These 3 Mistakes in GMAT Even-Odd Questions? – Part 1/3:
If is a positive integer, is odd?
1) is even
2) is even
As soon as you read the above problem, did you start thinking of the algebraic formula you can use to solve it? If yes, then you just fell in to the number #1 pitfall that stops many students from becoming an even odd champion. That’s true! Even though Even-Odd numbers is deemed to be among the easier concepts on GMAT Quant, many students are not able to solve 700+ level questions from it. Read on to find why that is the case.
In our efforts to help students ace this concept, we closely studied the mistakes that students make in Even-Odd questions.
Our research ground comprised of the doubts students ask in our internal forums, the mistakes made by 1000+ students in our recurring Number Properties Live Session, and most recently, the 5000+ attempts made on The E-GMAT Number Properties Knockout.
Our analysis shows that following are the three main pitfalls in which students tend to fall while solving Even-Odd questions:
- Getting intimidated by complex expressions
- Wasting time on unimportant terms
- Getting stumped in division
In this article series, we will explain each of the above 3 pitfalls with examples, discuss why it is important to avoid that pitfall, tell you how to avoid it, and finally, give you 700+ level practice questions.
Sounds good? Right then … let’s focus on Pitfall #1, which is theme of this article.
Pitfall # 1 Getting intimidated by seemingly complex expressions
What do we mean?
A few Even-Odd questions may have scary-looking expressions. For example, consider the expression given above:
If is a positive integer, is odd?
Did you too feel a bit nervous reading this question? Well, that is the first pitfall that you have to guard against. Because, if you let yourself become nervous, you will:
i) Either randomly guess the question
ii) Or panic; panic clouds our ability to think rationally, increasing our chances of making an error.
- For example, in your panic, you may scramble to remember and apply the formula for on the terms of this expression, only to realize that you’ve actually complicated the question.
So, as you can see, getting intimidated by complex expressions is indeed a dangerous pitfall.
What can you do to avoid this pitfall?
The next time you face such a question and notice your heartbeat increasing, take a deep breath and tell yourself,
“Since this is a GMAT question, it can be simplified elegantly.”
This is true! The beauty of official GMAT questions is that no matter how complex they look, they can always be simplified to a couple of cases.
Example: Let’s think through the question we posed above and see how it can be simplified.
The given expression is
You’re probably familiar with the property that the power of a number doesn’t impact the even-odd nature of the number.
- , where is a positive integer = Even
i) will have the same even-odd nature as . Similarly, will have the same even-odd nature as
ii) will have the same even-odd nature as itself.
So, using this property, we’ve done the first level of simplification: now, we only have to determine the even-odd nature of this, simpler expression:
The simpler expression above is a product of 2 terms: and
When will the product of 2 terms be odd? Only if both the 2 terms are themselves odd. If even one of these terms is even, the product will be even.
So, to answer the question, we need to know: is each of the 2 terms odd?
So, from the earlier situation of dealing with the product as a whole, we are now dealing with individual terms only: and
Getting to the answer
Now, can either be Even or Odd.
Case 1: is odd
In this case,
Since both the terms are Even, the answer in this case will be NO, the given expression in not odd.
Case 2: is even
In this case,
Since both the terms are odd, the answer in this case will be YES, the given expression is odd.
So, as you can see, using this step-wise approach, we’ve been able to simplify the question to this:
- Don’t get intimidated by complex expressions in Even-Odd questions.
- Have the confidence that all Even-Odd questions in the GMAT can be easily simplified.
- Use the properties of Even-Odd combinations to simplify scary-looking expressions.
- Avoid the impulse to search for algebraic formulae to apply on such expressions.
You’ll know that you’ve learnt this lesson well if your heart doesn’t skip a beat at the first look of the following question:
If , where and are positive integers, is divisible by 2?
2. is Even
Post your responses for the above question here.
Try the Even-Odd concept file in the Quant Free-Trial by registering for free on e-GMAT.