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If 4n^2/15 is an integer, the which of the following could be n ?

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Bunuel
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If 4n^2/15 is an integer, the which of the following could be n ? [#permalink] New post   26 Nov 2020, 06:34
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If \(\frac{4n^2}{15}\) is an integer, the which of the following could be n ?

I. -75
II. 4
III. 135

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III
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D
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bond001
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If 4n^2/15 is an integer, the which of the following could be n ? [#permalink] New post   Updated on: 26 Nov 2020, 07:36
Answer D
15=5*3
Bunuel
i have a doubt if for example
If 4n/15 is an integer then the answer should be B right because GMAT does not consider a negative number am I right

Originally posted by bond001 on 26 Nov 2020, 06:50.
Last edited by bond001 on 26 Nov 2020, 07:36, edited 1 time in total.
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sahuayush
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Re: If 4n^2/15 is an integer, the which of the following could be n ? [#permalink] New post   26 Nov 2020, 07:26
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bond001 wrote:
Answer c
15=5*3
Bunuel
i have a doubt if for example
If 4n/15 is an integer then the answer should be B right because GMAT does not consider a negative number am I right


Answer will be D and not C.

n cannot be 4 since 4^3 cannot be divisible by 15.

n can only take the values of -75 and 135. Both the numbers are multiples of 15, thus making 4n^2 divisible by 15.

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Re: If 4n^2/15 is an integer, the which of the following could be n ? [#permalink] New post   26 Nov 2020, 07:36
sahuayush wrote:
bond001 wrote:
Answer c
15=5*3
Bunuel
i have a doubt if for example
If 4n/15 is an integer then the answer should be B right because GMAT does not consider a negative number am I right


Answer will be D and not C.

n cannot be 4 since 4^3 cannot be divisible by 15.

n can only take the values of -75 and 135. Both the numbers are multiples of 15, thus making 4n^2 divisible by 15.

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my mistake I did in a hurry answer should be D as you have said whenever I think and write I do a lot of mistake
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Re: If 4n^2/15 is an integer, the which of the following could be n ? [#permalink] New post   26 Nov 2020, 10:52
Bunuel wrote:
If \(\frac{4n^2}{15}\) is an integer, the which of the following could be n ?

I. -75
II. 4
III. 135

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III

Since 4 & 15 are co - Primes , n must be divisible by 15...

Among the givn options except II, n can take both values I. & III. , thus Answer must be (D)
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Re: If 4n^2/15 is an integer, the which of the following could be n ? [#permalink] New post   26 Nov 2020, 22:28
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Bunuel wrote:
If \(\frac{4n^2}{15}\) is an integer, the which of the following could be n ?

I. -75
II. 4
III. 135

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III


Important observations (not necessarily relevant for this problem):
1) Nowhere does the question mentions that n is an Integer so n could be 15/2 as well to satisfy the given constraint
2)4 and 15 have no common prime factors


I. -75 \(\frac{4n^2}{15}=\frac{4(-75)^2}{15} = Integer\) GOOD
II. 4 \(\frac{4n^2}{15}=\frac{4(4)^2}{15} ≠ Integer\) OUT
III. 135 \(\frac{4n^2}{15}=\frac{4(135)^2}{15} = Integer\) GOOD

ANswer: Option D
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Re: If 4n^2/15 is an integer, the which of the following could be n ? [#permalink] New post   28 Nov 2020, 01:06
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Solution



Given
In this question, we are given that
    • The number \(\frac{4n^2}{15}\) is an integer

To find
We need to determine
    • Among the given options, which ones can be possible values of n

Approach and Working out
As \(\frac{4n^2}{15}\) is an integer, we can say that \(4n^2\) is always divisible by 15
    • However, 4 is neither divisible by 15 nor share any common factor with 15
    • It implies \(n^2\) must be divisible by 15 – means n must be either 15 or any multiple of 15

Among the choices, -75 (which is 15 x -5) and 135 (which is 15 x 9) are multiples of 15
Therefore, n can be either -75 or 135

Thus, option D is the correct answer.

Correct Answer: Option D
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Re: If 4n^2/15 is an integer, the which of the following could be n ? [#permalink]
28 Nov 2020, 01:06
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