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

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Posts: 389
Re: The positive integer k has exactly two positive prime factors, 3 and 7  [#permalink]

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New post 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.

Answer D.


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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