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If m is an integer, is m/102 an integer?

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If m is an integer, is m/102 an integer?

Post Sun Oct 08, 2017 11:11 am
If m is an integer, is m/102 an integer?

(1) 99 is a factor of 165m.
(2) 34 is a factor of 7m

The OA is C.

I don't know how to solve this DS question. Experts, may you explain this to me?

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Post Sun Oct 08, 2017 10:57 pm
Vincen wrote:
If m is an integer, is m/102 an integer?

(1) 99 is a factor of 165m.
(2) 34 is a factor of 7m

The OA is C.

I don't know how to solve this DS question. Experts, may you explain this to me?
m is an integer if m is a factor of 102.

Let's do prime factorization of 102.

Prime factors of 102 are 2, 3, and 17.

If m is a factor of 2, 3 and 17, the answer is Yes, else No.

(1) 99 is a factor of 165m.

Since 99 is a factor of 165m, it means that (165m)/99 is an integer; (165m)/99 = (3*5*11*m)/(3^2*11) = 5m/3 .

This implies that m is a factor of 3; however, this is not sufficient. If m is also a factor of 2 and 17, the answer is Yes, else No. Insufficient.

(2) 34 is a factor of 7m.

Since 34 is a factor of 7m, it means that (7m)/34 is an integer; (7m)/34 = (7m)/(2*17) .

This implies that m is a factor of 2 and 17; however, this is not sufficient. If m is also a factor of 3, the answer is Yes, else No. Insufficient.

(1) and (2)

From (1), we know that m is a factor of 3 and from (2), we know that m is a factor of 2 and 17, thus m is a factor of 2, 3, and 17. Sufficient.

The correct answer: C

Hope this helps!

-Jay

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