Difference between revisions of "1993 AJHSME Problems/Problem 5"
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| + | == Problem == | ||
| + | |||
| + | Which one of the following bar graphs could represent the data from the circle graph? | ||
| + | |||
| + | <asy> | ||
| + | unitsize(36); | ||
| + | draw(circle((0,0),1),gray); | ||
| + | fill((0,0)--arc((0,0),(0,-1),(1,0))--cycle,gray); | ||
| + | fill((0,0)--arc((0,0),(1,0),(0,1))--cycle,black); | ||
| + | </asy> | ||
| + | |||
| + | <asy> | ||
| + | unitsize(4); | ||
| + | |||
| + | fill((1,0)--(1,15)--(5,15)--(5,0)--cycle,gray); | ||
| + | fill((6,0)--(6,15)--(10,15)--(10,0)--cycle,black); | ||
| + | draw((11,0)--(11,20)--(15,20)--(15,0)); | ||
| + | |||
| + | fill((26,0)--(26,15)--(30,15)--(30,0)--cycle,gray); | ||
| + | fill((31,0)--(31,15)--(35,15)--(35,0)--cycle,black); | ||
| + | draw((36,0)--(36,15)--(40,15)--(40,0)); | ||
| + | |||
| + | fill((51,0)--(51,10)--(55,10)--(55,0)--cycle,gray); | ||
| + | fill((56,0)--(56,10)--(60,10)--(60,0)--cycle,black); | ||
| + | draw((61,0)--(61,20)--(65,20)--(65,0)); | ||
| + | |||
| + | fill((76,0)--(76,10)--(80,10)--(80,0)--cycle,gray); | ||
| + | fill((81,0)--(81,15)--(85,15)--(85,0)--cycle,black); | ||
| + | draw((86,0)--(86,20)--(90,20)--(90,0)); | ||
| + | |||
| + | fill((101,0)--(101,15)--(105,15)--(105,0)--cycle,gray); | ||
| + | fill((106,0)--(106,10)--(110,10)--(110,0)--cycle,black); | ||
| + | draw((111,0)--(111,20)--(115,20)--(115,0)); | ||
| + | |||
| + | for(int a = 0; a < 5; ++a) | ||
| + | { | ||
| + | draw((25*a,21)--(25*a,0)--(25*a+16,0)); | ||
| + | } | ||
| + | |||
| + | label("(A)",(8,21),N); | ||
| + | label("(B)",(33,21),N); | ||
| + | label("(C)",(58,21),N); | ||
| + | label("(D)",(83,21),N); | ||
| + | label("(E)",(108,21),N); | ||
| + | </asy> | ||
| + | |||
==Solution== | ==Solution== | ||
Since the white portion of the graph is twice as much as the black and gray, its bar in the bar graph will need to be twice as much as the black and gray. Note that the black and gray portions are equal. This cancels choices <math>A, B, D, E</math>. The final answer is now <math>\boxed{C}</math>. | Since the white portion of the graph is twice as much as the black and gray, its bar in the bar graph will need to be twice as much as the black and gray. Note that the black and gray portions are equal. This cancels choices <math>A, B, D, E</math>. The final answer is now <math>\boxed{C}</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{AJHSME box|year=1993|num-b=4|num-a=6}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 23:10, 4 July 2013
Problem
Which one of the following bar graphs could represent the data from the circle graph?
![[asy] unitsize(36); draw(circle((0,0),1),gray); fill((0,0)--arc((0,0),(0,-1),(1,0))--cycle,gray); fill((0,0)--arc((0,0),(1,0),(0,1))--cycle,black); [/asy]](http://latex.artofproblemsolving.com/b/4/8/b480e466979a91180c302aa9c41642901ab83158.png)
![[asy] unitsize(4); fill((1,0)--(1,15)--(5,15)--(5,0)--cycle,gray); fill((6,0)--(6,15)--(10,15)--(10,0)--cycle,black); draw((11,0)--(11,20)--(15,20)--(15,0)); fill((26,0)--(26,15)--(30,15)--(30,0)--cycle,gray); fill((31,0)--(31,15)--(35,15)--(35,0)--cycle,black); draw((36,0)--(36,15)--(40,15)--(40,0)); fill((51,0)--(51,10)--(55,10)--(55,0)--cycle,gray); fill((56,0)--(56,10)--(60,10)--(60,0)--cycle,black); draw((61,0)--(61,20)--(65,20)--(65,0)); fill((76,0)--(76,10)--(80,10)--(80,0)--cycle,gray); fill((81,0)--(81,15)--(85,15)--(85,0)--cycle,black); draw((86,0)--(86,20)--(90,20)--(90,0)); fill((101,0)--(101,15)--(105,15)--(105,0)--cycle,gray); fill((106,0)--(106,10)--(110,10)--(110,0)--cycle,black); draw((111,0)--(111,20)--(115,20)--(115,0)); for(int a = 0; a < 5; ++a) { draw((25*a,21)--(25*a,0)--(25*a+16,0)); } label("(A)",(8,21),N); label("(B)",(33,21),N); label("(C)",(58,21),N); label("(D)",(83,21),N); label("(E)",(108,21),N); [/asy]](http://latex.artofproblemsolving.com/6/a/6/6a6150208e92b19052587795c996686bcd1a5a50.png)
Solution
Since the white portion of the graph is twice as much as the black and gray, its bar in the bar graph will need to be twice as much as the black and gray. Note that the black and gray portions are equal. This cancels choices 
. The final answer is now 
.
See Also
| 1993 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 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. 
