2014 AMC 8 Problems/Problem 1: Difference between revisions
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==Problem== | ==Problem== | ||
Harry and Terry are each told to calculate <math>8-(2+5)</math>. Harry gets the correct answer. Terry ignores the parentheses and calculates <math>8-2+5</math>. If Harry's answer is <math>H</math> and Terry's answer is <math>T</math>, what is <math>H-T</math>? | Harry and Terry are each told to calculate <math>8-(2+5)</math>. Harry gets the correct answer. Terry ignores the parentheses and calculates <math>8-2+5</math>. If Harry's answer is <math>H</math> and Terry's answer is <math>T</math>, what is <math>H-T</math>? | ||
<math>\textbf{(A) }-10\qquad\textbf{(B) }-6\qquad\textbf{(C) }0\qquad\textbf{(D) }6\qquad \textbf{(E) }10</math> | <math>\textbf{(A) }-10\qquad\textbf{(B) }-6\qquad\textbf{(C) }0\qquad\textbf{(D) }6\qquad \textbf{(E) }10</math> | ||
==Solution== | ==Solution== | ||
We have <math>H=8-7=1</math> and <math>T=8-2+5=11</math>. Clearly <math>1-11=\boxed{-10}</math>, | We have <math>H=8-7=1</math> and <math>T=8-2+5=11</math>. Clearly <math>1-11=-10</math> | ||
, so our answer is <math>\boxed{\textbf{(A)}-10}</math>. | |||
==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 <math>\boxed{\textbf{(A)}-10}</math>. | |||
==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 | |||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2014| | {{AMC8 box|year=2014|before=First Problem|num-a=2}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 13:06, 25 August 2025
Problem
Harry and Terry are each told to calculate 
. Harry gets the correct answer. Terry ignores the parentheses and calculates 
. If Harry's answer is 
and Terry's answer is 
, what is 
?
Solution
We have 
and 
. Clearly 
, so our answer is 
.
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 .
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)
~Education, the Study of Everything
Video Solution
~savannahsolver
See Also
| 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. Error creating thumbnail: File missing
