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factor of m

by kushal.adhia » Mon Nov 01, 2010 10:42 am
If m is an integer, is 14 a factor of m ?

(1) 14 is a factor of 15 m.

(2) 14 is a factor of 16 m.



It took me almost 3.5 to 4 mins to figure out this question and yet i got it wrong :(

Some help please

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by Rahul@gurome » Mon Nov 01, 2010 11:27 am
kushal.adhia wrote:If m is an integer, is 14 a factor of m ?
  • (1) 14 is a factor of 15 m.
    (2) 14 is a factor of 16 m.
It took me almost 3.5 to 4 mins to figure out this question and yet i got it wrong :(

Some help please

Kushal
Given: m is an integer.

Statement 1: 14 is a factor of 15m.
Now, 14 = 2*7 and 15m = (3*5)*m
As 15 doesn't contain 2 or 7 and 14 is a factor of 15m, 2 and 7 must be prime factors of m. Thus 14 is a factor of m.

Sufficient.

Statement 2: 14 is a factor of 16m.
Now, 14 = 2*7 and 16m = (2*2*2*2)*m
Now 16 contains 2 (four times) but doesn't contain 7. Thus m must contain 7 as prime factor to make 16m divisible by 14. But m may or may not contain 2 as prime factor. Thus 14 may or may not be a factor of m.

Not sufficient.

The correct answer is A.
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by pradeepkaushal9518 » Tue Nov 02, 2010 12:51 am
i think the question was easy
A SMALL TOWN GUY