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

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by BTGmoderatorDC » Tue Jun 09, 2020 8:08 pm

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Answers

A

B

C

D

E

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Difficulty—

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
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Source: — Data Sufficiency |

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

by Jay@ManhattanReview » Wed Jun 10, 2020 1:13 am
BTGmoderatorDC wrote: ↑
Tue Jun 09, 2020 8:08 pm
 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 see that 195/13 = 15. So for mn to be a multiple of 195, m, n or both must be a multiple of 15.

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.

This information does not assure us that m is a factor of 15, too. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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Re: m is a multiple of 13. Is mn a multiple of 195?

by swerve » Wed Jun 10, 2020 4:28 am
BTGmoderatorDC wrote: ↑
Tue Jun 09, 2020 8:08 pm
 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 x 5 x 13
m is a multiple of 13 ---> 13 is a prime factor of m
From (1): known factors of n = 3 x 3 x 5
--> known factors of mn = 3x3x5x13 --> minimum prime factors of 195 --> Sufficient
From (2): known factors of m = 2x3x3x13
Since no information about 5 --> Insufficient
Therefore, A
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