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# What is the value of a two-digit positive integer n, where i

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What is the value of a two-digit positive integer n, where i  [#permalink]

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Updated on: 17 Jun 2013, 02:19
2
4
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Difficulty:

95% (hard)

Question Stats:

41% (01:57) correct 59% (02:19) wrong based on 177 sessions

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What is the value of a two-digit positive integer n, where is n<=85.

(1) n has 12 factors, inclusive of 1 and n itself
(2) n is a multiple of 3.

Originally posted by fozzzy on 17 Jun 2013, 01:38.
Last edited by Bunuel on 17 Jun 2013, 02:19, edited 1 time in total.
Edited the OA.
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Re: What is the value of a two-digit positive integer n, where i  [#permalink]

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17 Jun 2013, 02:11
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fozzzy wrote:
What is the value of a two-digit positive integer n, where is n<=85.

(1) n has 12 factors, inclusive of 1 and n itself
(2) n is a multiple of 3.

From F.S 1 , for n = $$2^2*3*5$$, the number of factors = 3*2*2 = 12

Again, for n = $$2^3*3^2$$, the number of factors = 4*3 = 12

Insufficient.

F. S 2 is clearly Insufficient.

Both combined together, we can use the above 2 examples only, it is again Insufficient.

E.
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Re: What is the value of a two-digit positive integer n, where i  [#permalink]

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17 Jun 2013, 02:18
mau5 wrote:
fozzzy wrote:
What is the value of a two-digit positive integer n, where is n<=85.

(1) n has 12 factors, inclusive of 1 and n itself
(2) n is a multiple of 3.

From F.S 1 , for n = $$2^2*3*5$$, the number of factors = 3*2*2 = 12

Again, for n = $$2^3*3^2$$, the number of factors = 4*3 = 12

Insufficient.

F. S 2 is clearly Insufficient.

Both combined together, we can use the above 2 examples only, it is again Insufficient.

E.

Yes, the answer is E: n could be 60 or 72.
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Re: What is the value of a two-digit positive integer n, where i  [#permalink]

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17 Jun 2013, 02:23
Can anyone explain the answer pls. I am finding it difficult.
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Re: What is the value of a two-digit positive integer n, where i  [#permalink]

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17 Jun 2013, 02:30
Great Explanation Mau totally missed the case of 60...

samara15000 wrote:
Can anyone explain the answer pls. I am finding it difficult.

Refer to bunuel's post on this thread it explains the concept tested in this question

if-n-has-15-positive-divisors-inclusive-of-1-and-n-then-wh-154437.html
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Re: What is the value of a two-digit positive integer n, where i  [#permalink]

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15 Mar 2016, 10:10
The key to solving these kind of questions is to factorise the number of factors
so the numbers are only 60 or 72
hence E as they are both divisible by 3
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Re: What is the value of a two-digit positive integer n, where i  [#permalink]

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22 Feb 2018, 18:43
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Re: What is the value of a two-digit positive integer n, where i   [#permalink] 22 Feb 2018, 18:43
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