Is the integer $$n$$ even?

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Is the integer $$n$$ even?

by Vincen » Sat Dec 04, 2021 7:42 am

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Is the integer $$n$$ even?

(1) $$n - 5$$ is an odd integer.
(2) $$\dfrac{n}5$$ is an even integer.

Source: GMAT Paper Tests

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Re: Is the integer $$n$$ even?

by [email protected] » Sun Dec 05, 2021 6:29 am

00:00

A

B

C

D

E

Global Stats

Vincen wrote:
Sat Dec 04, 2021 7:42 am
Is the integer $$n$$ even?

(1) $$n - 5$$ is an odd integer.
(2) $$\dfrac{n}5$$ is an even integer.

Source: GMAT Paper Tests
Some important rules:
1. ODD - ODD = EVEN
2. EVEN - ODD = ODD
3. ODD - EVEN = ODD
4. EVEN - EVEN = EVEN

5. (ODD)(ODD) = ODD
6. (ODD)(EVEN) = EVEN
7. (EVEN)(EVEN) = EVEN

Target question: Is integer n even?

Statement 1: n – 5 is an odd integer
Since 5 is ODD, statement 1 is saying: n - ODD = ODD
From rule #2 above, we can conclude that n is EVEN
So, the answer to the target question is "YES, n IS even"
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n/5 is an even integer.
First multiply both sides by 5 to get: n = (5)(some EVEN integer)
Since 5 is ODD, we statement 2 is saying: n = (ODD)(EVEN)
From rule #6 above, we can conclude that n is EVEN
So, the answer to the target question is "YES, n IS even"
Since we can answer the target question with certainty, statement 2 is SUFFICIENT