Find the divisor of a

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Sep 14, 2013 2:21 pm

Hello,

Can you please assist with this? This is from MGMAT:

If a and b are positive integers such that a/b = 2.86, which of the following must be a divisor of a?

OA: 13

Thanks for your help.

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Source: Beat The GMAT — Problem Solving | Sat Sep 14, 2013 2:21 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Sep 14, 2013 3:24 pm

gmattesttaker2 wrote: If a and b are positive integers such that a/b = 2.86, which of the following must be a divisor of a?
A. 10
B. 13
C. 18
D. 26
E. 50

NOTE: We need the answer choices for this one, so I added them.

Given: a/b = 2.86
Rewrite as fraction: a/b = 286/100
Simplify: a/b = 143/50
Cross multiply to get: 50a = 143b

This tells us that 50a is a multiple of 143, which is the same as saying that 50a is divisible by 143.
Since 50 is not divisible by 143, a must be divisible by 143
Since 143 = (11)(13), a must be divisible by 11 and by 13

Check the answer choices . . . the correct answer is B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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