Difference between revisions of "2011 AMC 8 Problems/Problem 11"
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− | Average the differences between | + | ==Problem== |
− | 10, -10, 20, 30, -20 | + | The graph shows the number of minutes studied by both Asha (black bar) and Sasha (grey bar) in one week. On the average, how many more minutes per day did Sasha study than Asha? |
− | + | ||
+ | <asy> | ||
+ | size(300); | ||
+ | real i; | ||
+ | defaultpen(linewidth(0.8)); | ||
+ | draw((0,140)--origin--(220,0)); | ||
+ | for(i=1;i<13;i=i+1) { | ||
+ | draw((0,10*i)--(220,10*i)); | ||
+ | } | ||
+ | label("$0$",origin,W); | ||
+ | label("$20$",(0,20),W); | ||
+ | label("$40$",(0,40),W); | ||
+ | label("$60$",(0,60),W); | ||
+ | label("$80$",(0,80),W); | ||
+ | label("$100$",(0,100),W); | ||
+ | label("$120$",(0,120),W); | ||
+ | path MonD=(20,0)--(20,60)--(30,60)--(30,0)--cycle,MonL=(30,0)--(30,70)--(40,70)--(40,0)--cycle,TuesD=(60,0)--(60,90)--(70,90)--(70,0)--cycle,TuesL=(70,0)--(70,80)--(80,80)--(80,0)--cycle,WedD=(100,0)--(100,100)--(110,100)--(110,0)--cycle,WedL=(110,0)--(110,120)--(120,120)--(120,0)--cycle,ThurD=(140,0)--(140,80)--(150,80)--(150,0)--cycle,ThurL=(150,0)--(150,110)--(160,110)--(160,0)--cycle,FriD=(180,0)--(180,70)--(190,70)--(190,0)--cycle,FriL=(190,0)--(190,50)--(200,50)--(200,0)--cycle; | ||
+ | fill(MonD,grey); | ||
+ | fill(MonL,lightgrey); | ||
+ | fill(TuesD,grey); | ||
+ | fill(TuesL,lightgrey); | ||
+ | fill(WedD,grey); | ||
+ | fill(WedL,lightgrey); | ||
+ | fill(ThurD,grey); | ||
+ | fill(ThurL,lightgrey); | ||
+ | fill(FriD,grey); | ||
+ | fill(FriL,lightgrey); | ||
+ | draw(MonD^^MonL^^TuesD^^TuesL^^WedD^^WedL^^ThurD^^ThurL^^FriD^^FriL); | ||
+ | label("M",(30,-5),S); | ||
+ | label("Tu",(70,-5),S); | ||
+ | label("W",(110,-5),S); | ||
+ | label("Th",(150,-5),S); | ||
+ | label("F",(190,-5),S); | ||
+ | label("M",(-25,85),W); | ||
+ | label("I",(-27,75),W); | ||
+ | label("N",(-25,65),W); | ||
+ | label("U",(-25,55),W); | ||
+ | label("T",(-25,45),W); | ||
+ | label("E",(-25,35),W); | ||
+ | label("S",(-26,25),W);</asy> | ||
+ | |||
+ | <math> \textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 12 </math> | ||
+ | |||
+ | ==Solution== | ||
+ | Average the differences between each day. We get <math>10, -10,\text{ } 20,\text{ } 30,-20</math>. We find the average of this list to get <math>\boxed{\textbf{(A)}\ 6}</math> | ||
+ | |||
+ | ==See Also== | ||
+ | {{AMC8 box|year=2011|num-b=10|num-a=12}} | ||
+ | {{MAA Notice}} |
Revision as of 13:42, 25 January 2021
Problem
The graph shows the number of minutes studied by both Asha (black bar) and Sasha (grey bar) in one week. On the average, how many more minutes per day did Sasha study than Asha?
Solution
Average the differences between each day. We get . We find the average of this list to get
See Also
2011 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.