1992 AMC 8 Problem 7 — Solution | LIVE by Po-Shen Loh

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1992 AMC 8 Problem 7

Attempt Problem 7 of the 1992 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 1992 AMC 8 solutions, or check the answer key.

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

7.

The digit-sum of $998$ is $9 + 9 + 8 = 26.$ How many $3$ -digit whole numbers, whose digit-sum is $26$ , are even?

$1$

$2$

$3$

$4$

$5$

Answer: A

Concepts:digits parity

Difficulty rating: 900

Solution:

A digit-sum of $26$ with three digits requires the digits $9, 9, 8.$ The $3$ -digit numbers using them are $899, 989,$ and $998.$

Of these, only $998$ is even, so there is exactly $1$ such number.

Thus, the correct answer is A .

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