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Does the integer k have at least three different positive

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Source: — Data Sufficiency |
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by swerve » Fri Oct 04, 2019 3:22 am
BTGmoderatorDC wrote:Does the integer k have at least three different positive prime factors?

(1) k/15 is an integer.
(2) k/10 is an integer.

OA C

Source: Official Guide
Statement 1.

\(K\) is multiple of 15

\(K =5 \cdot 3 \cdot\) some integer \(C\)

Insufficient - \(C\) could be 1 or many other values. \(\Large{\color{red}\chi}\)

Statement 2

\(K\) is a multiple of 10

\(K = 5 \cdot 2 \cdot\) some integer \(C\)

Insufficient - \(C\) could be 2 or 1 or many other values. \(\Large{\color{red}\chi}\)

Statements 1 & 2 combined

Knowing that K is multiple of 15 and 10 just find the LCM and then draw a conclusion

\(LCM(15,10) = 5 \cdot 3 \cdot 2\) \(\Large{\color{green}\checkmark}\)

The correct answer is C
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