1994 AMC 8 Problem 10 — Solution | LIVE by Po-Shen Loh

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1994 AMC 8 Problem 10

Attempt Problem 10 of the 1994 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 1994 AMC 8 solutions, or check the answer key.

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

10.

For how many positive integer values of $N$ $(N \gt 0)$ is the expression

$\frac{36}{N+2}$

an integer?

$7$

$8$

$9$

$10$

$12$

Answer: A

Concepts:divisibility factor

Difficulty rating: 860

Solution:

The expression is an integer when $N+2$ divides $36.$ The divisors of $36$ are $1, 2, 3, 4, 6, 9, 12, 18, 36.$

Because $N \gt 0,$ we need $N + 2 \gt 2,$ leaving the divisors $3, 4, 6, 9, 12, 18, 36$ : that is $7$ values.

Thus, the correct answer is A .

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