1988 AMC 8 Problem 14 — Solution | LIVE by Po-Shen Loh

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1988 AMC 8 Problem 14

Attempt Problem 14 of the 1988 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1988 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

14.

If $\diamond$ and $\triangle$ are whole numbers and $\diamond \times \triangle = 36,$ the largest possible value of $\diamond + \triangle$ is

$12$

$13$

$15$

$20$

$37$

Answer: E

Concepts:factor optimization

Difficulty rating: 730

Solution:

The factor pairs of $36$ are $1 \times 36,$ $2 \times 18,$ $3 \times 12,$ $4 \times 9,$ and $6 \times 6.$

The sum is largest for the most spread-out pair, $1 + 36 = 37.$

Thus, the correct answer is E .

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