m is an integer if m is a factor of 102.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?
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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