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# Can n/192 be an integer? (1) n is a multiple of 24 but not 16 (2) n

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Math Expert
Joined: 02 Sep 2009
Posts: 51215
Can n/192 be an integer? (1) n is a multiple of 24 but not 16 (2) n  [#permalink]

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03 Jul 2018, 10:29
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Difficulty:

55% (hard)

Question Stats:

67% (01:25) correct 33% (02:13) wrong based on 27 sessions

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Can n/192 be an integer?

(1) n is a multiple of 24 but not 16

(2) n is a multiple of 8 but not 48

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Math Expert
Joined: 02 Aug 2009
Posts: 7106
Re: Can n/192 be an integer? (1) n is a multiple of 24 but not 16 (2) n  [#permalink]

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03 Jul 2018, 10:40
Can n/192 be an integer?
when will $$\frac{n}{192}$$ be an integer --- when n is a multiple of 192 = $$3*64=3*2^6$$

(1) n is a multiple of 24 but not 16
this means n is not multiple of 2^4, so there will be 2s left in denominator
ans NO n/192 is not an integer
suff

(2) n is a multiple of 8 but not 48
48 = 2^4*3
so n is not a multiple of 2^4*3, so it will surely be not a multiple pf 3*2^6
ans NO
suff

D
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Re: Can n/192 be an integer? (1) n is a multiple of 24 but not 16 (2) n  [#permalink]

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03 Jul 2018, 14:35
Ans: D
we know 192= 2^6 x 3 so for n/192 to be an int n has to have 2^6 and 3 as its factor.

Stat-1) n = multiple of 24 but not 16 means 2^3 is there but not 2^4; so n does not have 2^6 as its factor. so n/192 is not an int (Suff)
Stat-2) n = multiple of 8 but not 48 means 2^3 is there but 2^4 is the max. again n/192 is not an int (Suff)

Both Statement alone are sufficient to ans the question.

Bunuel wrote:
Can n/192 be an integer?

(1) n is a multiple of 24 but not 16

(2) n is a multiple of 8 but not 48

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Re: Can n/192 be an integer? (1) n is a multiple of 24 but not 16 (2) n &nbs [#permalink] 03 Jul 2018, 14:35
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