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## Is n an integer less than 5?

tagged by: Brent@GMATPrepNow

This topic has 1 expert reply and 0 member replies

### Top Member

Vincen Legendary Member
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#### Is n an integer less than 5?

Tue Sep 12, 2017 11:28 am
Is n an integer less than 5?

(1) 5n is a positive integer.
(2) n/5 is a positive integer.

The OA is B.

Why is it B? Is the statement (1) insufficient?

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Tue Sep 12, 2017 12:14 pm
Vincen wrote:
Is n an integer less than 5?

(1) 5n is a positive integer.
(2) n/5 is a positive integer.
Target question: Is n an integer less than 5?

Statement 1: 5n is a positive integer
Let's TEST some values.
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 1. Here, 5n = (5)(1) = 5, and 5 IS a positive integer. In this case, n IS an integer less than 5
Case b: n = 6. Here, 5n = (5)(6) = 30, and 30 IS a positive integer. In this case, n is NOT an integer less than 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n/5 is a positive integer
If n/5 is positive then n is positive
Also, if n/5 is an integer, then we can conclude that n is divisible by 5
If n is a positive number that's divisible by 5, then some possible values of n are: 5, 10, 15, 20, 25, 30,.....
NOTICE that all of the possible values of n are greater than or equal to 5.
In other words, it is NOT POSSIBLE for n to be an integer less than 5
So, the answer to the target question is "No, n is definitely NOT an integer less than 5"
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

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