2014 AMC 8 Problem 1

Attempt Problem 1 of the 2014 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 2014 AMC 8 solutions, or check the answer key.

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

1.

Harry and Terry are each told to calculate 8−(2+5).8-(2+5). Harry gets the correct answer. Terry ignores the parentheses and calculates 8−2+5.8-2+5. If Harry’s answer is HH and Terry’s answer is T,T, what is H−T?H-T?
−10 -10
−6 -6
0 0
6 6
10 10
Answer: A
Concepts:order of operations
Small hint:
Compute inside the parentheses first for Harry.
Big hint:
Compare Harry’s result with Terry’s left-to-right calculation.
Solution:
Harry calculates it correctly as follows: 8−(2+5)=8−7=1.\begin{align*} 8 - (2 + 5) &= 8 - 7 \\ &= 1. \end{align*} Terry calculates it incorrectly as follows: 8−2+5=6+5=11.\begin{align*} 8 - 2 + 5 &= 6 + 5 \\ &= 11. \end{align*} Therefore: H−T=1−11=−10.\begin{align*} H - T &= 1 - 11 \\ &= -10. \end{align*}
Thus, A is the correct answer.
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