2023 AMC 8 Problem 18 - Math Gold Medalist

Lor

2023 AMC 8

Problem 18

Greta Grasshopper sits on a long line of lily pads in a pond. From any lily pad, Greta can jump $5$ pads to the right or $3$ pads to the left. What is the fewest number of jumps Greta must make to reach the lily pad located $2023$ pads to the right of her starting point?

$\textbf{(A)}\ 405 \qquad \textbf{(B)}\ 407 \qquad \textbf{(C)}\ 409 \qquad \textbf{(D)}\ 411 \qquad \textbf{(E)}\ 413$

Related Ideas

Starting From a Special Case

Hint

In each step we have +5 or -3 and the order is not important

Special Case:

+5+5+…+5=2025 -> 2025 – 2023 = 2 is not multiple of 3

+5+5+…+5=2030 -> 2030 – 2023 = 7 is not multiple of 3

+5+5+…+5=2035 -> 2035 – 2023 = 12 is multiple of 3