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# If n is an integer divisible by 6 but not by 4, then which of the foll

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Math Expert
Joined: 02 Sep 2009
Posts: 58423
If n is an integer divisible by 6 but not by 4, then which of the foll  [#permalink]

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24 Feb 2019, 23:58
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64% (00:53) correct 36% (01:03) wrong based on 58 sessions

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If n is an integer divisible by 6 but not by 4, then which of the following CANNOT be an integer?

A. $$\frac{n}{2}$$

B. $$\frac{n}{3}$$

C. $$\frac{n}{6}$$

D. $$\frac{n}{10}$$

E. $$\frac{n}{12}$$

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Re: If n is an integer divisible by 6 but not by 4, then which of the foll  [#permalink]

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25 Feb 2019, 00:41
Bunuel wrote:
If n is an integer divisible by 6 but not by 4, then which of the following CANNOT be an integer?

A. $$\frac{n}{2}$$

B. $$\frac{n}{3}$$

C. $$\frac{n}{6}$$

D. $$\frac{n}{10}$$

E. $$\frac{n}{12}$$

n is divisible by 6 NOT by 4.

n = 6, 18, 30, 42, 54.

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Re: If n is an integer divisible by 6 but not by 4, then which of the foll  [#permalink]

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25 Feb 2019, 01:13
Bunuel wrote:
If n is an integer divisible by 6 but not by 4, then which of the following CANNOT be an integer?

A. $$\frac{n}{2}$$

B. $$\frac{n}{3}$$

C. $$\frac{n}{6}$$

D. $$\frac{n}{10}$$

E. $$\frac{n}{12}$$

okay

n is an integer divisible by 6 but not by 4, means that all other factor of n other than 6 is odd, so there is a single 2 in n

for an integer to be divisible by 4, it has to have at least 2 "2s"

so here in option E, 12 has 2 "2s" and hence, 12 cannot divide n as it has only 1 "2"

so, I think "E" can be the answer

thanks
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Re: If n is an integer divisible by 6 but not by 4, then which of the foll  [#permalink]

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25 Feb 2019, 01:24
Bunuel wrote:
If n is an integer divisible by 6 but not by 4, then which of the following CANNOT be an integer?

A. $$\frac{n}{2}$$

B. $$\frac{n}{3}$$

C. $$\frac{n}{6}$$

D. $$\frac{n}{10}$$

E. $$\frac{n}{12}$$

let n = 30
so all are correct
except
$$\frac{n}{12}$$
IMO E
Re: If n is an integer divisible by 6 but not by 4, then which of the foll   [#permalink] 25 Feb 2019, 01:24
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