1996 AMC 12 Problem 1

Attempt Problem 1 of the 1996 AMC 12 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 1996 AMC 12 solutions, or check the answer key.

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

1.

The addition below is incorrect. What is the largest digit that can be changed to make the addition correct? 641852+9732456 \begin{array}{r} 641\\ 852\\ {}+973\\ \hline 2456 \end{array}
44
55
66
77
88
Answer: D
Concepts:additionplace value
Small hint:
Compare the displayed sum with the actual sum of the three addends
Big hint:
The correction must lower the total by one unit in a particular place
Solution:
The three addends total 641+852+973=2466,641+852+973=2466, which is 1010 too large. Changing the tens digit 77 in 973973 to 66 lowers the sum by 1010 and gives 2456.2456. No larger listed digit can make that change, so the correct answer is D.
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