Difference between revisions of "2010 AMC 12B Problems/Problem 6"
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{{duplicate|[[2010 AMC 12B Problems|2010 AMC 12B #6]] and [[2010 AMC 10B Problems|2010 AMC 10B #12]]}} | {{duplicate|[[2010 AMC 12B Problems|2010 AMC 12B #6]] and [[2010 AMC 10B Problems|2010 AMC 10B #12]]}} | ||
| − | == Problem | + | == Problem == |
At the beginning of the school year, <math>50\%</math> of all students in Mr. Well's class answered "Yes" to the question "Do you love math", and <math>50\%</math> answered "No." At the end of the school year, <math>70\%</math> answered "Yes" and <math>30\%</math> answered "No." Altogether, <math>x\%</math> of the students gave a different answer at the beginning and end of the school year. What is the difference between the maximum and the minimum possible values of <math>x</math>? | At the beginning of the school year, <math>50\%</math> of all students in Mr. Well's class answered "Yes" to the question "Do you love math", and <math>50\%</math> answered "No." At the end of the school year, <math>70\%</math> answered "Yes" and <math>30\%</math> answered "No." Altogether, <math>x\%</math> of the students gave a different answer at the beginning and end of the school year. What is the difference between the maximum and the minimum possible values of <math>x</math>? | ||
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== Solution == | == Solution == | ||
| − | Clearly, the minimum possible value would be <math>70 - 50 = 20\%</math>. The maximum possible value would be <math>30 + 50 = 80\%</math>. The difference is <math>80 - 20 = \boxed{ | + | Clearly, the minimum possible value would be <math>70 - 50 = 20\%</math>. The maximum possible value would be <math>30 + 50 = 80\%</math>. The difference is <math>80 - 20 = \boxed{\textbf{(D) }60}</math>. |
==Video Solution== | ==Video Solution== | ||
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== See also == | == See also == | ||
{{AMC12 box|year=2010|num-b=5|num-a=7|ab=B}} | {{AMC12 box|year=2010|num-b=5|num-a=7|ab=B}} | ||
| + | {{AMC10 box|year=2010|num-b=11|num-a=13|ab=B}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 15:58, 6 July 2023
- The following problem is from both the 2010 AMC 12B #6 and 2010 AMC 10B #12, so both problems redirect to this page.
Contents
Problem
At the beginning of the school year, 
of all students in Mr. Well's class answered "Yes" to the question "Do you love math", and answered "No." At the end of the school year, 
answered "Yes" and 
answered "No." Altogether, 
of the students gave a different answer at the beginning and end of the school year. What is the difference between the maximum and the minimum possible values of 
?
Solution
Clearly, the minimum possible value would be 
. The maximum possible value would be 
. The difference is 
.
Video Solution
https://youtu.be/vYXz4wStBUU?t=160
~IceMatrix
See also
| 2010 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 5 |
Followed by Problem 7 |
| 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 AMC 12 Problems and Solutions | |
| 2010 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 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 AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
