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# If N is an integer, is 36/N an integer?

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If N is an integer, is 36/N an integer?  [#permalink]

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26 Mar 2018, 23:15
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45% (medium)

Question Stats:

81% (01:00) correct 19% (00:29) wrong based on 30 sessions

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If N is an integer, is 36/N an integer?

(1) N is a multiple of 9.
(2) 9 < N < 27

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Re: If N is an integer, is 36/N an integer?  [#permalink]

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27 Mar 2018, 00:22
Bunuel wrote:
If N is an integer, is 36/N an integer?

(1) N is a multiple of 9.
(2) 9 < N < 27

we are looking for whether 36/N is an integer or not.

1. N is multiple of 9. so, N could be 9 , 18, 27, 36, 54
substituting the value of N won't give us integer all tym.

2. 9<N<27. it describes the range of N . no. of value is available here but but not all value provide us integer. if we consider N=18, we will get an integer value.
not sufficient.

(1+2) is sufficient. 1st statement tells us that N is a multiple of 9 and 2nd one specifies the value of N which will be 18 in this case. thus, the correct answer will be C.
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If N is an integer, is 36/N an integer?  [#permalink]

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27 Mar 2018, 00:23
Bunuel wrote:
If N is an integer, is 36/N an integer?

(1) N is a multiple of 9.
(2) 9 < N < 27

1. If N is a multiple of 9, 36/N can or cannot be an integer.
If N = 9, 18, or 36 - 36/N is an integer. Else it is not an integer (Insufficient)

2. In this range 9 < N < 27, is N = 10, 36/N is not an integer.
But 36/18 is an integer. Hence, this statement alone isn't enough (Insufficient)

On combining the information from both the statements,
N can take only one value 18 and 36/N is an integer (Sufficient - Option C)
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Re: If N is an integer, is 36/N an integer?  [#permalink]

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27 Mar 2018, 05:32
Bunuel wrote:
If N is an integer, is 36/N an integer?

(1) N is a multiple of 9.
(2) 9 < N < 27

Question: Is N a factor of 36?

St 1: If N = 9, answer to the question is YES

If N = 27, answer to the question is NO

Insufficient

St 2: If N = 18, answer to the question is YES

If N = 15, answer to the question is NO

Insufficient

Combining we get N = 18, answer to the question is YES only. Sufficient

(C)
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Re: If N is an integer, is 36/N an integer?   [#permalink] 27 Mar 2018, 05:32
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