1995 AMC 8 Problem 22

Below is the professionally curated solution for Problem 22 of the 1995 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1995 AMC 8 solutions, or check the answer key.

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Concepts:prime factorization factor

Difficulty rating: 1170

22.

The number $6545$ can be written as a product of a pair of positive two-digit numbers. What is the sum of this pair of numbers?

$162$

$172$

$173$

$174$

$222$

Solution:

The prime factorization is $6545 = 5 \times 7 \times 11 \times 17.$ To split into two two-digit factors, pair the primes: $5 \times 17 = 85$ and $7 \times 11 = 77.$

These are the only two-digit pair, and their sum is $85 + 77 = 162.$

Thus, the correct answer is A .

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