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# Gmatprep DS: the positive integer k has exactly two positive

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Gmatprep DS: the positive integer k has exactly two positive [#permalink]  27 Feb 2008, 20:33
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Gmatprep DS: the positive integer k has exactly two positive prime factors, 3 and 7. If K has a total of 6 positive factors, including 1 and k, what is the value of K?

1) 3^2 is a factor of k

2) 7^2 is NOT a factor of k

I searched thru 6-7 pages using keywords, but I did not find this question asked, I think this could be a newly added question in the gmatprep software.

somewhat of a tricky wording question, especially when time is running short. oa is d.

correction: oa is D.
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Last edited by gmatnub on 28 Feb 2008, 13:21, edited 1 time in total.
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Re: Gmatprep DS: the positive integer k has exactly two [#permalink]  27 Feb 2008, 21:34
Based on stem, the 6 factors of k are 1,3,7,21, x and k . where 7 < x < k.

If statement (1) is used, the factors are, 1, 3, 7, 9, 21, k. k = 63. sufficient
Since stem says 3,7 are the only prime factors, x has to be 3^2 since x cannot be 7^2. - sufficient

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Re: Gmatprep DS: the positive integer k has exactly two [#permalink]  28 Feb 2008, 07:19
gmatnub wrote:
Gmatprep DS: the positive integer k has exactly two positive prime factors, 3 and 7. If K has a total of 6 positive factors, including 1 and k, what is the value of K?

1) 3^2 is a factor of k

2) 7^2 is NOT a factor of k

I searched thru 6-7 pages using keywords, but I did not find this question asked, I think this could be a newly added question in the gmatprep software.

somewhat of a tricky wording question, especially when time is running short. oa is a.

K has 6 factors: 1,3,7,21,X,K (different factors) Essentially we need to find X then we will know K.

1: X must be 9. b/c K has two 3's as factors.

2: if 7^2 is not a factor of K then X cannot be 49. Since we only have 3 and 7 as prime factors, 3 must be the other factor and X would be 9.

I get D

Im not sure why OA is A... =(
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Re: Gmatprep DS: the positive integer k has exactly two [#permalink]  28 Feb 2008, 07:29
gmatnub wrote:
Gmatprep DS: the positive integer k has exactly two positive prime factors, 3 and 7. If K has a total of 6 positive factors, including 1 and k, what is the value of K?

1) 3^2 is a factor of k

2) 7^2 is NOT a factor of k

I searched thru 6-7 pages using keywords, but I did not find this question asked, I think this could be a newly added question in the gmatprep software.

somewhat of a tricky wording question, especially when time is running short. oa is a.

To me it would be D as well, being that they are both true since #2 has "NOT" in it.

hmmm...
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Re: Gmatprep DS: the positive integer k has exactly two [#permalink]  28 Feb 2008, 13:23
sorry guys, oa is d.

i flagged it for review, but i assumed that i got it wrong.
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Re: Gmatprep DS: the positive integer k has exactly two [#permalink]  16 Feb 2009, 22:55
Good question. I have a different way of solving this.

Let P1 = Power of first factor
Let P2 = Power of second factor
The number of factors can be found using the equation (P1 + 1)(P2 + 1). This is a rule, I didn't come up with this.
Therefore here we have:
2*3 or 3*2, both equal 6.

statement 1: says that 3*2 is out, therefore sufficient
statement 2: says that 3*2 is out, therefore sufficient.

note that we cannot use 6*1, because then we have a 7^0 or a 3^0, which is not the case here.

What do you think?
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Re: Gmatprep DS: the positive integer k has exactly two [#permalink]  19 Feb 2009, 11:07
x1050us wrote:
Based on stem, the 6 factors of k are 1,3,7,21, x and k . where 7 < x < k.

If statement (1) is used, the factors are, 1, 3, 7, 9, 21, k. k = 63. sufficient
Since stem says 3,7 are the only prime factors, x has to be 3^2 since x cannot be 7^2. - sufficient

I don't understand why k=63, why can't it be 27 (due to 3 x 9)??
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Re: Gmatprep DS: the positive integer k has exactly two [#permalink]  19 Feb 2009, 12:11
DaveGG wrote:
x1050us wrote:
Based on stem, the 6 factors of k are 1,3,7,21, x and k . where 7 < x < k.

If statement (1) is used, the factors are, 1, 3, 7, 9, 21, k. k = 63. sufficient
Since stem says 3,7 are the only prime factors, x has to be 3^2 since x cannot be 7^2. - sufficient

I don't understand why k=63, why can't it be 27 (due to 3 x 9)??

In that case, k would have 3^3 as factor. If so, the k would have more than 6 factors as under: 1, 3, 7, 9, 21, 27, 42, 63, and 189

gmatnub wrote:
Gmatprep DS: the positive integer k has exactly two positive prime factors, 3 and 7. If K has a total of 6 positive factors, including 1 and k, what is the value of K?

1) 3^2 is a factor of k
2) 7^2 is NOT a factor of k

We need one more either 3 or 7 to have 6 +ve factors of k.

a: 3^2 makes 6 +ve factors.
b. if there is no 7^2 as a factor of k, then it also makes sure that 3^3 is a factor of k.
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Re: Gmatprep DS: the positive integer k has exactly two   [#permalink] 19 Feb 2009, 12:11
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