1993 AJHSME Problems/Problem 5: Difference between revisions
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== Problem 5 == | |||
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}} | |||
Revision as of 21:29, 22 December 2012
Problem 5
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 | ||
