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If n is a positive integer, is n/18 an integer? 12 Mar 2016, 10:04
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A
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25% (medium)

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67% (01:00) correct 33% (01:11) wrong based on 95 sessions

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If n is a positive integer, is n/18 an integer?

(1) 5n/18 is an integer.

(2) 3n/18 is an integer.
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A
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If n is a positive integer, is n/18 an integer? 12 Mar 2016, 10:35
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shapla
If n is a positive integer, is n/18 an integer?

(1) 5n/18 is an integer.

(2) 3n/18 is an integer.
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Hi,
If n is the multiple of 18 ,ans is yes..

Let's see the statements
1) 5n/18 is integer
Since 5 and 18 are coprimes, n must be a multiple of 18..
Suff

2) 3n/18 is an integer.
Since 3 and18 are not coprimes, n may or may not be multiple of 18..
Insuff.

Ans A
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If n is a positive integer, is n/18 an integer? 12 Mar 2016, 10:45
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Option 1 is not alone enough and the answer is C.Please refer to similar questions for explanation
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If n is a positive integer, is n/18 an integer? 14 May 2020, 11:45
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Manhattan OE:

(1) SUFFICIENT: We are told that 5n/18 is an integer. This allows us to determine that n/18 is an integer—in order for 5n to be divisible by 18, 5n must contain all the prime factors of 18 (3, 3, and 2). Since 5 does not contain any of these prime factors, n must contain ALL of them. Therefore, n has 3, 3, and 2 as prime factors, so n is divisible by 18, and n/18 is an integer.

(2) INSUFFICIENT: We are told that 3n/18 is an integer. This does not allow us to determine that n/18 is an integer—in order for 3n to be divisible by 18, 3n must contain all the prime factors of 18 (3, 3, and 2). However, 3 contains one of those prime factors (3), so n might only contain a 3 and a 2. Therefore, we cannot determine whether n has 3, 3, and 2 as prime factors, so n might not be divisible by 18 and n/18 might not be an integer. (For example, n could equal 6, or it could equal 18.)

The correct answer is A.
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If n is a positive integer, is n/18 an integer? 22 Jun 2024, 19:48
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