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If N is a positive integer and N2 is divisible by 12, then which of th
[#permalink]
07 Jul 2023, 05:24

Expert Reply

Question Stats:

If N is a positive integer and \(N^2\) is divisible by 12, then which of the following must be an integer?

A. N/8

B. N/6

C. 3N/5

D. 2N/3

E. 4N/3

Post A Detailed Correct Solution For The Above Questions And Get Kudos.

Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos

\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge

\(\Longrightarrow\) GRE NUMBER PROPERTIES

A. N/8

B. N/6

C. 3N/5

D. 2N/3

E. 4N/3

Post A Detailed Correct Solution For The Above Questions And Get Kudos.

Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos

\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge

\(\Longrightarrow\) GRE NUMBER PROPERTIES

Intern

Joined: **12 May 2023 **

Posts: **20**

Given Kudos: **65 **

Re: If N is a positive integer and N2 is divisible by 12, then which of th
[#permalink]
20 Jul 2023, 01:31

1

is there an error in the question? is it N/2 or is it N2?

Re: If N is a positive integer and N2 is divisible by 12, then which of th
[#permalink]
20 Jul 2023, 01:36

Expert Reply

Fixed. The Latex code did not show up properly

Thanks

Thanks

Intern

Joined: **12 May 2023 **

Posts: **20**

Given Kudos: **65 **

Re: If N is a positive integer and N2 is divisible by 12, then which of th
[#permalink]
28 Jul 2023, 02:13

Can you explain how option D) and E) also be an answer. What I did was:

12 = 2^2 and 3^1

so N^2 must content atleast 2^2 and 3^1. So, N must contain atleast 2^1 and 3^1 therefore N/6 satisfies the requirement.

12 = 2^2 and 3^1

so N^2 must content atleast 2^2 and 3^1. So, N must contain atleast 2^1 and 3^1 therefore N/6 satisfies the requirement.

Re: If N is a positive integer and N2 is divisible by 12, then which of th
[#permalink]
16 Sep 2023, 15:20

Expert Reply

OE

As ๐ is a positive integer and ๐^2 is divisible by 12, hence it can be written as

N^2/12=I (I is an integer)

๐๐, \(๐^2 = 12๐ผ = 2 ร 2 ร 3 ร ๐ผ\)

๐๐, \(๐ =\sqrt{ 2*2*3*I}=2 \sqrt{3*I}\)

Now, the fact important to notice here is under the root is I because the root must be also an integer to have N= integer

the minimum value of \(\sqrt{3*I}\) is I=3

therefore the minimum value of N is 6

D) 2N/3=2*6/3=12/3=4 It is an integer

E) 4N/3=6*4/3=8 It is an integer

As ๐ is a positive integer and ๐^2 is divisible by 12, hence it can be written as

N^2/12=I (I is an integer)

๐๐, \(๐^2 = 12๐ผ = 2 ร 2 ร 3 ร ๐ผ\)

๐๐, \(๐ =\sqrt{ 2*2*3*I}=2 \sqrt{3*I}\)

Now, the fact important to notice here is under the root is I because the root must be also an integer to have N= integer

the minimum value of \(\sqrt{3*I}\) is I=3

therefore the minimum value of N is 6

D) 2N/3=2*6/3=12/3=4 It is an integer

E) 4N/3=6*4/3=8 It is an integer

Re: If N is a positive integer and N2 is divisible by 12, then which of th
[#permalink]
13 Apr 2024, 15:27

1

As N^2 is divisible by 12.

assume N =12

Therefore N^2 is divisible by 12.

looking at the options put N =12

Answer = B,D,E

assume N =12

Therefore N^2 is divisible by 12.

looking at the options put N =12

Answer = B,D,E

gmatclubot

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