Difference between revisions of "2011 AMC 8 Problems/Problem 11"
(Created page with "Average the differences between the two times. 10, -10, 20, 30, -20 The sum is 30. Divide by 5 = 6.") |
|||
| (5 intermediate revisions by one other user not shown) | |||
| Line 1: | Line 1: | ||
| − | 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 01:59, 5 July 2013
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?
![[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]](http://latex.artofproblemsolving.com/3/f/8/3f89cfb6f42754e61437502705cb54a5f518690d.png)
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. 
