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nandanarpan11
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If n is a positive integer, is √n/3 an integer? 1) √(n/3) is an integ Updated on: 14 Jun 2021, 02:22
Originally posted by nandanarpan11 on 14 Jun 2021, 00:12.
Last edited by Bunuel on 14 Jun 2021, 02:22, edited 1 time in total.
Renamed the topic.
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55% (hard)

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58% (01:47) correct 42% (02:07) wrong based on 233 sessions

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If n is a positive integer, is √n/3 an integer?

1) √(n/3) is an integer

2) √(14n) is not an integer
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A
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If n is a positive integer, is √n/3 an integer? 1) √(n/3) is an integ 14 Jun 2021, 03:20
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nandanarpan11
If n is a positive integer, is √n/3 an integer?

1) √(n/3) is an integer

2) √(14n) is not an integer
Show more

S1:
√(n/3) = k, k is an integer
n/3 = k^2
n = 3*k^2
√(3*k^2)/3
= k*√3/3 which is not an integer
Sufficient

S2: Insuff
we have no idea if √n is a multiple of 3


Answer is A
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If n is a positive integer, is √n/3 an integer? 1) √(n/3) is an integ 14 Jun 2021, 04:12
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Nice one!

Similar question:
https://gmatclub.com/forum/if-n-is-a-po ... fl=similar
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If n is a positive integer, is √n/3 an integer? 1) √(n/3) is an integ 14 Jun 2021, 04:57
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Interesting question. Breaking up Statement (2) into Root 14 and Root N may be helpful. You get to see that ROOT 14 will always make the value a non-integer... but that ROOT N may or may not give an integer.

Keeping in mind that the question is simply asking if ROOT N is divisible by 3 can be helpful.
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If n is a positive integer, is √n/3 an integer? 1) √(n/3) is an integ 06 Mar 2025, 11:51
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How do you know that k*√3/3 is not an integer, you dont have information about k

sherxon
nandanarpan11
If n is a positive integer, is √n/3 an integer?

1) √(n/3) is an integer

2) √(14n) is not an integer

S1:
√(n/3) = k, k is an integer
n/3 = k^2
n = 3*k^2
√(3*k^2)/3
= k*√3/3 which is not an integer
Sufficient

S2: Insuff
we have no idea if √n is a multiple of 3


Answer is A
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If n is a positive integer, is √n/3 an integer? 1) √(n/3) is an integ 06 Mar 2025, 11:57
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leodifolco
How do you know that k*√3/3 is not an integer, you dont have information about k

sherxon
nandanarpan11
If n is a positive integer, is √n/3 an integer?

1) √(n/3) is an integer

2) √(14n) is not an integer

S1:
√(n/3) = k, k is an integer
n/3 = k^2
n = 3*k^2
√(3*k^2)/3
= k*√3/3 which is not an integer
Sufficient

S2: Insuff
we have no idea if √n is a multiple of 3


Answer is A
Show more

k is a positive integer. A positive integer multiplied by the irrational number (√3/3) cannot be an integer.
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If n is a positive integer, is √n/3 an integer? 1) √(n/3) is an integ 10 Mar 2025, 02:53
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I am sorry maybe I am bugging, but what if k=3 or a multiple of 3?

Bunuel
leodifolco
How do you know that k*√3/3 is not an integer, you dont have information about k

sherxon
nandanarpan11If n is a positive integer, is √n/3 an integer?

1) √(n/3) is an integer

2) √(14n) is not an integer

S1:
√(n/3) = k, k is an integer
n/3 = k^2
n = 3*k^2
√(3*k^2)/3
= k*√3/3 which is not an integer
Sufficient

S2: Insuff
we have no idea if √n is a multiple of 3


Answer is A

k is a positive integer. A positive integer multiplied by the irrational number (√3/3) cannot be an integer.
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If k = 3, then k * √3/3 = 3 * √3/3 = √3, which is not an integer.
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If n is a positive integer, is √n/3 an integer? 1) √(n/3) is an integ 12 Mar 2025, 06:29
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Let's take an example:

Let n=48

S1: \sqrt{n/3} in an integer

i.e. \sqrt{16} -> 4 Satisfied

Now how is \sqrt{n}/3 an integer?

Quote:
nandanarpan11
If n is a positive integer, is √n/3 an integer?

1) √(n/3) is an integer

2) √(14n) is not an integer

S1:
√(n/3) = k, k is an integer
n/3 = k^2
n = 3*k^2
√(3*k^2)/3
= k*√3/3 which is not an integer
Sufficient

S2: Insuff
we have no idea if √n is a multiple of 3


Answer is A
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