MathDB

1

Part of 2022 AMC 10

Problems(2)

Finitely Nested Fractions

Source: 2022 AMC 10A #1 / 2022 AMC 12A #1

11/11/2022
What is the value of 3+13+13+13?3 + \frac{1}{3+\frac{1}{3+\frac{1}{3}}}? <spanclass=′latex−bold′>(A)</span>3110<spanclass=′latex−bold′>(B)</span>4915<spanclass=′latex−bold′>(C)</span>3310<spanclass=′latex−bold′>(D)</span>10933<spanclass=′latex−bold′>(E)</span>154<span class='latex-bold'>(A) </span> \frac{31}{10} \qquad <span class='latex-bold'>(B) </span> \frac{49}{15} \qquad <span class='latex-bold'>(C) </span> \frac{33}{10} \qquad <span class='latex-bold'>(D) </span> \frac{109}{33} \qquad <span class='latex-bold'>(E) </span> \frac{15}{4}
2022 AMC2022 AMC 10a2022 AMC 12AAMC 10AMC 12AMCFractions
Absolute computation

Source: 2022 AMC 10B#1/AMC 12B #1

11/17/2022
Define x⋄yx\diamond y to be ∣x−y∣|x-y| for all real numbers xx and yy. What is the value of (1⋄(2⋄3))−((1⋄2)⋄3)?(1\diamond(2\diamond3))-((1\diamond2)\diamond3)?
<spanclass=′latex−bold′>(A)</span> −2<spanclass=′latex−bold′>(B)</span> −1<spanclass=′latex−bold′>(C)</span> 0<spanclass=′latex−bold′>(D)</span> 1<spanclass=′latex−bold′>(E)</span> 2 <span class='latex-bold'>(A)</span>\ -2 \qquad <span class='latex-bold'>(B)</span>\ -1 \qquad <span class='latex-bold'>(C)</span>\ 0 \qquad <span class='latex-bold'>(D)</span>\ 1 \qquad <span class='latex-bold'>(E)</span>\ 2
AMCAMC 10AMC 122022 AMC2022 AMC 10B2022 AMC 12B