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m is a multiple of 13. Is mn a multiple of 195?

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Thu Jan 09, 2020 9:28 pm
BTGmoderatorDC wrote:m is a multiple of 13. Is mn a multiple of 195?

(1) n has every factor that 45 has.

(2) m is divisible by 18.

OA A

Source: Princeton Review
We know that 195 = 13*15. Since m is a multiple of 13, co-prime to 15, if n is a multiple of 15, we can conclude that mn is a multiple of 195.

Let's take each statement one by one.

(1) n has every factor that 45 has.

Since 15 is a factor of 45, n has every factor that 15 has. Sufficient.

(2) m is divisible by 18.

Note that 195 = 13*3*5. Given that m is a multiple of 13 and 18, we can't be sure that m or n is also a multiple of 5. Note that 3 as a factor of 18 will be rendered but not 5. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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by swerve » Fri Jan 10, 2020 11:22 am
BTGmoderatorDC wrote:m is a multiple of 13. Is mn a multiple of 195?

(1) n has every factor that 45 has.

(2) m is divisible by 18.




OA A

Source: Princeton Review
Prime factors of \(195 = 3 \cdot 5 \cdot 13 \)
m is a multiple of 13 \(\Longrightarrow\) 13 is a prime factor of m

From (1): known factors of \(n = 3 \cdot 3 \cdot 5\)
\(\Rightarrow\) known factors of \(mn = 3\cdot 3 \cdot 5 \cdot 13 \Rightarrow\) minimum prime factors of \(195 \Rightarrow\) Sufficient. \(\Large{\color{green}\checkmark}\)

From (2): known factors of \(m = 2\cdot 3 \cdot 3 \cdot 13 \)
Since no information about \(5 \Rightarrow\) Insufficient. \(\Large{\color{red}\chi}\)

Therefore, the correct answer is A
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