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To find Divisor

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To find Divisor

by getso » Mon Dec 21, 2009 9:44 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

Can anybody help me here in solving such problems in few simple steps?

Thanks,
Shobha
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by djkvakin » Mon Dec 21, 2009 10:45 am
I used a simple and rather fast crude approach: since both a and b are integers, then a good pair to analyze that would give us 2.86 when b divides a is 286/100.
so now we are reduced to find divisors of 286. 13 fits the bill.

However, we are not done yet. we notice that 26 is a multiple of 13, and also fits the bill. we must deduct which number MUST be a divisor. The logic is fairly simple: when 26 is a divisor, 13 will always be a divisor. and not vice versa. hence i am inclined to answer B. You can test this by multiplying both a and b by 1.5. (429/150=2.86, and 26 is not a divisor of 429, whereas 13 is).


I hope it helps
Last edited by djkvakin on Mon Dec 21, 2009 1:14 pm, edited 1 time in total.
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by November Rain » Mon Dec 21, 2009 11:56 am
Hi

I think it's E.

Could you please confirm to me the OA?
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by getso » Mon Dec 21, 2009 8:58 pm
OA is 13

Thanks djkvakin. your approach is much easier to follow .
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