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1993 AJHSME Problems/Problem 2

Revision as of 15:28, 1 April 2010 by YottaByte (talk | contribs) (Created page with '== Problem == When the fraction <math>\dfrac{49}{84}</math> is expressed in simplest form, then the sum of the numerator and the denominator will be <math>\text{(A)}\ 11 \qquad…')
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Problem

When the fraction $\dfrac{49}{84}$ is expressed in simplest form, then the sum of the numerator and the denominator will be

$\text{(A)}\ 11 \qquad \text{(B)}\ 17 \qquad \text{(C)}\ 19 \qquad \text{(D)}\ 33 \qquad \text{(E)}\ 133$

Solution

The fraction is already in simplest form. The prime factorization of $49$ is $7^2$ and for $84$ it is $2*37$, so the greatest common factor is 1.

Then we add $49+84$ and get $133 \Rightarrow E$.

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