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Math Expert V
Joined: 02 Sep 2009
Posts: 58340
If n is a positive integer, is 150/n an integer? (1) n < 7 (2) n is a  [#permalink]

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Difficulty:   15% (low)

Question Stats: 85% (00:58) correct 15% (00:50) wrong based on 96 sessions

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If n is a positive integer, is 150/n an integer?

(1) n < 7

(2) n is a prime number

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Intern  B
Joined: 21 May 2018
Posts: 2
If n is a positive integer, is 150/n an integer? (1) n < 7 (2) n is a  [#permalink]

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If n is a positive integer, is 150/n an integer?

(1) n < 7

(2) n is a prime number

Given n is an integer > 0. And we need to find out if it divides 150=5*5*3*2. So, essentially all we have to do is find out if n has these prime factors so we will be able to cancel them out.

(1) n < 7
Therefore, n = 1,2,3,4,5,6.
Except for n=4 all other values divides 150. This statement is not sufficient.

(2) n is a prime
n = 2 divides 150 whereas n = 7 does not. So this statement is also not sufficient.

(1) & (2) together limits n to three values.
Now n = 2,3,5 all of which divides 150.

Hence, the correct option is (C).
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Re: If n is a positive integer, is 150/n an integer? (1) n < 7 (2) n is a  [#permalink]

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Bunuel wrote:
If n is a positive integer, is 150/n an integer?

(1) n < 7

(2) n is a prime number

Question: Is 150/n an Integer?

This will be true only if n is a factor of 150 i.e.e question becomes

Question: Is n a factor of 150?

Factors of 150 are {1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150}

Statement 1: n < 7
n may be 1, 2, 3, 5 or 6 which are factors of 150 and
n may be 4 as well which is NOT a factor of 150 hence
NOT SUFFICIENT

Statement 2: n is a prime number
n may be 2 or 3 which are factors of 150 and n may be 7 as well which is NOT a factor of 150 hence
NOT SUFFICIENT

Combining the two statements
n may only be 2 or 3 or 5 (Prime numbers less than 7) which are all factors of 150 hence
SUFFICIENT

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If n is a positive integer, is 150/n an integer? (1) n < 7 (2) n is a

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