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


If n is an integer, is n+1

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

2 Explanations


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


Gravatar Mike McGarry, Magoosh Tutor

Dec 28, 2013 • Comment

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