1993 AMC 8 Problem 24

Below is the professionally curated solution for Problem 24 of the 1993 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1993 AMC 8 solutions, or check the answer key.

Difficulty rating: 1140

24.

What number is directly above $142$ in this array of numbers?

$\begin{array}{ccccccccc} & & & & 1 & & & & \\ & & & 2 & 3 & 4 & & & \\ & & 5 & 6 & 7 & 8 & 9 & & \\ & 10 & 11 & 12 & \cdots & & & & \end{array}$

$99$

$119$

$120$

$121$

$122$

Each row ends at a perfect square, so the row containing $142$ ends at $144 = 12^2,$ and the row above it ends at $121 = 11^2.$

Since the rows are aligned at their right edges, $121$ sits directly above $143,$ and therefore $120$ sits directly above $142.$

Thus, the correct answer is C .