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

1. 10 2. 13 3. 18 4. 26 5. 50

\frac{a}{b}=2.86=\frac{286}{100}=\frac{143}{50} --> b=\frac{50a}{143}=\frac{50a}{11*13}, for b to be an integer a must have all the factors of 143 (50 has none of them). Hence a must be divisible by both 11 and 13.

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

1. 10 2. 13 3. 18 4. 26 5. 50

\frac{a}{b}=2.86=\frac{286}{100}=\frac{143}{50} --> b=\frac{50a}{143}=\frac{50a}{11*13}, for b to be an integer a must have all the factors of 143 (50 has none of them). Hence a must be divisible by both 11 and 13.

Answer: B.

Hi Bunuel,

I'm trying to follow MGMAT's method: we know that a/b = 2.86 2.86 => 2 and 86/100 or 43/50 and we know that r/b = 43/50 hence 50r = 43b from that we conclude that b must be a multiple of 50 and 43 a multiple of r. What am I doing wrong?

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