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# If K is a factor of positive integer X that has total 8 factors

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If K is a factor of positive integer X that has total 8 factors  [#permalink]

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11 Sep 2018, 06:19
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Difficulty:

45% (medium)

Question Stats:

66% (01:46) correct 34% (02:04) wrong based on 70 sessions

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If K is a factor of positive integer X that has total 8 factors, then how many prime factors does $$K^2X^n$$ have?

A. 2

B. 3

C. $$n^3$$

D. $$(n+1)^3$$

E. cannot be determined.

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If K is a factor of positive integer X that has total 8 factors  [#permalink]

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11 Sep 2018, 08:28
Isn't the answer actually asking for the number of prime factors of x itself? And that should either be 1 2 or 3 and since there isn't 1 as an option it should be either 2 or 3. So it can't be determined
chetan2u

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If K is a factor of positive integer X that has total 8 factors  [#permalink]

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11 Sep 2018, 09:32
workout wrote:
If K is a factor of positive integer X that has total 8 factors, then how many prime factors does $$K^2X^n$$ have?

A. 2

B. 3

C. $$n^3$$

D. $$(n+1)^3$$

E. cannot be determined.

rahulkashyap
yes, it cannot be determined till we do not know what are the number of prime factors of x
1) 8=1*8 so a^7.... just one prime factor.....
2) 8=2*4 so a^1*b^3... so two factors a and b
3) 8=2*2*2 so abc.. 3 factors

so we cannot say for sure if it is 1 or 2 or 3

E
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Re: If K is a factor of positive integer X that has total 8 factors  [#permalink]

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11 Sep 2018, 09:38
chetan2u wrote:
workout wrote:
If K is a factor of positive integer X that has total 8 factors, then how many prime factors does $$K^2X^n$$ have?

A. 2

B. 3

C. $$n^3$$

D. $$(n+1)^3$$

E. cannot be determined.

rahulkashyap
yes, it cannot be determined till we do not know what are the number of prime factors of x

E

If K is a factor, the question basically asks the number of favors of x, correct? Because k cannot have any new prime factors

So it can be 1 (a^7)
2( a^3 b^1)
3(a b c)

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Posts: 7752
Re: If K is a factor of positive integer X that has total 8 factors  [#permalink]

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11 Sep 2018, 09:41
rahulkashyap wrote:
chetan2u wrote:
workout wrote:
If K is a factor of positive integer X that has total 8 factors, then how many prime factors does $$K^2X^n$$ have?

A. 2

B. 3

C. $$n^3$$

D. $$(n+1)^3$$

E. cannot be determined.

rahulkashyap
yes, it cannot be determined till we do not know what are the number of prime factors of x

E

If K is a factor, the question basically asks the number of favors of x, correct? Because k cannot have any new prime factors

So it can be 1 (a^7)
2( a^3 b^1)
3(a b c)

Posted from my mobile device

absolutely correct..
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Re: If K is a factor of positive integer X that has total 8 factors  [#permalink]

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12 Sep 2018, 18:31
workout wrote:
If K is a factor of positive integer X that has total 8 factors, then how many prime factors does $$K^2X^n$$ have?

A. 2

B. 3

C. $$n^3$$

D. $$(n+1)^3$$

E. cannot be determined.

Since X has 8 factors, X could be 2 x 3 x 5 = 30 (notice that (1+1)(1+1)(1+1) = 8). Since K is a factor of X, K^2 will not contribute any new prime factor and thus, K^2*X^n has 3 prime factors (namely 2, 3 and 5) However, if X = 2^3 x 3 = 24 (which also has (3+1)(1+1) = 8 factors), then K^2 * X^n has only two prime factors (namely 2 and 3). Therefore, we can’t determine the number of prime factors in K^2 * X^n.

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Re: If K is a factor of positive integer X that has total 8 factors   [#permalink] 12 Sep 2018, 18:31
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