factor of m

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kushal.adhia: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Thu Aug 12, 2010 11:47 pm; Location: chennai, india; Thanked: 2 times

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

Kushal

Quote

Source: Beat The GMAT — Data Sufficiency | Mon Nov 01, 2010 10:42 am

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pm; Location: Milpitas, CA; Thanked: 447 times; Followed by:88 members

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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