1987 AJHSME Problems/Problem 11

Problem

The sum $2\frac17+3\frac12+5\frac{1}{19}$ is between

$\text{(A)}\ 10\text{ and }10\frac12 \qquad \text{(B)}\ 10\frac12 \text{ and } 11 \qquad \text{(C)}\ 11\text{ and }11\frac12 \qquad \text{(D)}\ 11\frac12 \text{ and }12 \qquad \text{(E)}\ 12\text{ and }12\frac12$

Solution

Since $\frac{1}{7}<\frac14$ and $\frac{1}{19}<\frac14$ , $2\frac17+3\frac12+5\frac{1}{19}<2\frac14+3\frac12+5\frac14 =11$

Clearly, $2\frac17+3\frac12+5\frac{1}{19}>2+3\frac12+5=10\frac12$

Thus, the sum is between $10\frac12$ and $11$ .

$\boxed{\text{B}}$

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1987 AJHSME Problems/Problem 11

Problem

Solution

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