1997 AMC 8 Problem 2

Below is the professionally curated solution for Problem 2 of the 1997 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1997 AMC 8 solutions, or check the answer key.

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Concepts:optimization

Difficulty rating: 450

2.

Ahn chooses a two-digit integer, subtracts it from 200,200, and doubles the result. What is the largest number Ahn can get?

200200

202202

220220

380380

398398

Solution:

To get the largest number, we would want to subtract the smallest number possible from 200.200.

The smallest two-digit number is 10.10. Having Ahn choose this number will give us 2(20010)=2190=380 2 (200 - 10) = 2 \cdot 190 = 380 as the final result.

Thus, D is the correct answer.

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