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.

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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 82+5.8-2+5. If Harry's answer is HH and Terry’s answer is T,T, what is HT?H-T?

10 -10

6 -6

0 0

6 6

10 10

Answer: A
Concepts:order of operations
Difficulty rating: 370
Solution:

Harry calculates it correctly as follows: 8(2+5)=87=1.\begin{align*} 8 - (2 + 5) &= 8 - 7 \\ &= 1. \end{align*} Terry calculates it incorrectly as follows: 82+5=6+5=11.\begin{align*} 8 - 2 + 5 &= 6 + 5 \\ &= 11. \end{align*} Therefore: HT=111=10.\begin{align*} H - T &= 1 - 11 \\ &= -10. \end{align*}

Thus, A is the correct answer.

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