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# The positive integer k has exactly two positive prime factors, 3 and 7

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Senior Manager
Joined: 14 Dec 2017
Posts: 389
Re: The positive integer k has exactly two positive prime factors, 3 and 7  [#permalink]

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11 Jun 2018, 23:34
gmatnub wrote:
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

Given $$K = 3^x * 7^y$$ & $$(x+1)(y+1) = 6$$

Hence x can take 2 values to give integer values of y
$$x = 2$$, we get $$y = 1$$ & hence $$K = 3^2 * 7$$
$$x = 1$$, we get $$y = 2$$ & hence $$K = 3 * 7^2$$

Statement 1:
$$3^2$$ is a factor of $$K$$
Hence $$y = 1$$ & $$K = 3^2 * 7$$

Statement 1 alone is Sufficient.

Statement 2:
$$7^2$$ is NOT a factor of $$K$$
Hence $$x = 2$$ & $$y = 1$$
$$K = 3^2 * 7$$

Statement 2 alone is Sufficient.

Thanks,
GyM
Re: The positive integer k has exactly two positive prime factors, 3 and 7 &nbs [#permalink] 11 Jun 2018, 23:34

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