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fozzzy
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What is the value of a two-digit positive integer n, where i Updated on: 17 Jun 2013, 02:19
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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E
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Difficulty:

85% (hard)

Question Stats:

44% (01:58) correct 56% (02:17) wrong based on 193 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.
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E
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What is the value of a two-digit positive integer n, where i 17 Jun 2013, 02:11
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fozzzy
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.
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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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What is the value of a two-digit positive integer n, where i 17 Jun 2013, 02:18
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mau5
fozzzy
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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Yes, the answer is E: n could be 60 or 72.
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What is the value of a two-digit positive integer n, where i 17 Jun 2013, 02:23
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Can anyone explain the answer pls. I am finding it difficult.
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What is the value of a two-digit positive integer n, where i 17 Jun 2013, 02:30
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Great Explanation Mau totally missed the case of 60...


samara15000
Can anyone explain the answer pls. I am finding it difficult.
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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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What is the value of a two-digit positive integer n, where i 15 Mar 2016, 10:10
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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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What is the value of a two-digit positive integer n, where i 11 Jul 2023, 04:49
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