Source: Official Guide for the GMAT 13th Ed. Data Sufficiency; #7 Official Guide for the GMAT 2015 14th Ed. Data Sufficiency; #7

1

If n is an integer, is n+1

If n is an integer, is n+1 odd?

2 Explanations

1

Kalifa Howard

I don't understand how statement one proves n+1 is odd. For example if n=3 3+1 = 4 therefore even and 3+2 is odd. Can you explain further using examples?

Jan 10, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Happy to explain further :)

Statement 1 states that n+2 is even, and as we evaluate Statement 1, any value of n we choose must meet that requirement. For example, we cannot choose n=3 because this value does not satisfy statement 1:

n = 3
n+2 = 3+2 = 5 (NOT EVEN!)

Since when n=3, n+2 is not even, n cannot equal 3.

And we'll see a similar outcome for any odd number: since EVEN + ODD = ODD, n+2 will be odd for any odd integer we choose for n.

With that in mind, n must be even for the statement n+2 is EVEN to be true, since EVEN + EVEN = EVEN. For example,

n=2: 2+2 = 4 (EVEN)
n=4: 4+2 = 6 (EVEN)
n=18: 18+2 = 20 (EVEN)

We've therefore concluded that considering only Statement 1, n must be even. Now, let's return to the original question: "Is n+1 odd?"

Can we answer that question? Since n must be even, we have the situation

EVEN + 1 = ?

And since 1 is an odd number, we have the sum of an even and odd number. This sum will always be ODD. We can therefore definitively answer the question "Is n+1 odd?" with the answer, "Yes."

I hope this helps :)

Jan 13, 2016 • Reply

1

Gravatar Mike McGarry, Magoosh Tutor

Dec 28, 2013 • Comment

Add Your Explanation

You must have a Magoosh account in order to leave an explanation.

Learn More About Magoosh

Official GMAT Material

Official Guide for GMAT Review 2016

Official Guide for the GMAT 2015 14th Ed.

Official Guide for the GMAT 13th Ed.

Nova's GRE Prep

Official Guide for the GMAT 12th Ed.

Revised GRE PDF 2nd Ed.


Section 6.3 Data Sufficiency

Section 6.3 Data Sufficiency

Improve Your Score

Magoosh GMAT is an affordable online course for studying the GMAT.

Learn More About Magoosh

Share Post

Email

Facebook