Difference between revisions of "2014 AMC 8 Problems/Problem 1"

Revision as of 14:06, 25 August 2025

Problem

Harry and Terry are each told to calculate $8-(2+5)$ . Harry gets the correct answer. Terry ignores the parentheses and calculates $8-2+5$ . If Harry's answer is $H$ and Terry's answer is $T$ , what is $H-T$ ?

$\textbf{(A) }-10\qquad\textbf{(B) }-6\qquad\textbf{(C) }0\qquad\textbf{(D) }6\qquad \textbf{(E) }10$

Solution

We have $H=8-7=1$ and $T=8-2+5=11$ . Clearly $1-11=-10$ , so our answer is $\boxed{\textbf{(A)}-10}$ .

Solution 2

We use PEMDAS, 8-(2+5) is the same as 8-7 which is 1, 8-2+5 is the same as 6+5 because 8-2 comes first, and the sum is 11. H-T is 1-11 which is $\boxed{\textbf{(A)}-10}$ .

Solution 3

Harry, who calculates it correctly, gets 8 - 7 = 1. Terry, who calculates it without parenthesis gets 8 - 2 + 5 which is 6 + 5 = 11 1 - 11 = -10 -JasonDaGoat

Video Solution (CREATIVE THINKING)

https://youtu.be/dljBE3_G85E

~Education, the Study of Everything

Video Solution

https://youtu.be/6TRHPxBveh0

~savannahsolver

2014 AMC 8 (Problems • Answer Key • Resources)
Preceded by First Problem	Followed by Problem 2
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.

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