If a and b are positive integers of Y such that a/b=2.86, which of the following must be a divisor of a? Options.
A) 10
B) B.13
C) 18
D) 26
E) 50
The prompt gives us a couple of facts to work with:   1) A and B are positive INTEGERS   2) A/B = 2.86   We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in).   The simplest place to start is with...   A = 286   B = 100   286/100= 
<gadget id="calculator">286/100</gadget>
<output>143/50 = around 2.86</output>
2.86   These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...   A= 143   B = 50   143/50= 
<gadget id="calculator">143/50</gadget>
<output>143/50 = around 2.86</output>
2.86   There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....   Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.   Final Answer:   B.13
<result>B</result>
If a and b are positive integers of Y such that a/b=2.86, which of the following must be a divisor of a?