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Source: 2022 AMC 10B #5

November 17, 2022
AMCAMC 102022 AMC2022 AMC 10BFractions

Problem Statement

What is the value of (1+13)(1+15)(1+17)(1−132)(1−152)(1−172)?\frac{(1+\frac{1}{3})(1+\frac{1}{5})(1+\frac{1}{7})}{\sqrt{(1-\frac{1}{3^2})(1-\frac{1}{5^2})(1-\frac{1}{7^2})}}?
<spanclass=′latex−bold′>(A)</span>3<spanclass=′latex−bold′>(B)</span>2<spanclass=′latex−bold′>(C)</span>15<spanclass=′latex−bold′>(D)</span>4<spanclass=′latex−bold′>(E)</span>105<span class='latex-bold'>(A) </span>\sqrt{3} \qquad <span class='latex-bold'>(B) </span>2 \qquad <span class='latex-bold'>(C) </span>\sqrt{15} \qquad <span class='latex-bold'>(D) </span>4 \qquad <span class='latex-bold'>(E) </span>\sqrt{105}
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