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Manhattan GMAT CAT Question

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by mdavidm_531 » Tue Jul 12, 2011 3:36 am
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

I am not convinced with MGMAT explanation for this one. Will appreciate any sort of help.

Best,
Dave
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Source: — Problem Solving |

by Frankenstein » Tue Jul 12, 2011 3:50 am
Hi,
a/b = 286/100 = 143/50
So, a = 143k and b = 50k where k is a positive integer
a= 11*13*k
11 and 13 must be divisors of 'a' irrespective of k.

Hence, B
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by GMATGuruNY » Tue Jul 12, 2011 4:01 am
mdavidm_531 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

I am not convinced with MGMAT explanation for this one. Will appreciate any sort of help.

Best,
Dave
a/b = 2.86 = 286/100 = 143/50.
143/50 cannot be reduced any further.
Thus, the smallest possible integer values that will yield a quotient of 2.86 are a=143 and b=50.
Since 143 = 11*13, both 11 and 13 must be divisors of a.

The correct answer is B.
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