If a&b are >0 integers such that a/b=2.86... CAT explanation

[bruno]

Hi,

I just did this question in my last CAT

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

The explanation says this at the end

[...]
The question asks about a. We know that a must be divisible by 13

I do not understand this at all. Why a?!

Isn't the question

which of the following must be a divisor of a?

?

If we look for a divisor of a, how come we are looking for a? Isn't b a divisor of a? So why aren't we looking for b?

Thanks in advance for the clarification

[RonPurewal]

No.
"a" and "b" are integers, and you're looking for factors (= "divisors") of the integer a.
I.e., once you figure out what kinds of numbers "a" can be, "b" becomes completely irrelevant.

Here a/b = 2.86 = 286/100 = 143/50, so "a" and "b" are multiples of 143 and 50, respectively.
Once you figure that out, the party line is "a is a multiple of 143", and there's no reason to care about b anymore.