Difference between revisions of "1993 AJHSME Problems/Problem 5"

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?

$[asy] unitsize(36); draw(circle((0,0),1),gray); fill((0,0)--arc((0,0),(0,-1),(1,0))--cycle,gray); fill((0,0)--arc((0,0),(1,0),(0,1))--cycle,black); [/asy]$

$[asy] unitsize(4); fill((1,0)--(1,15)--(5,15)--(5,0)--cycle,gray); fill((6,0)--(6,15)--(10,15)--(10,0)--cycle,black); draw((11,0)--(11,20)--(15,20)--(15,0)); fill((26,0)--(26,15)--(30,15)--(30,0)--cycle,gray); fill((31,0)--(31,15)--(35,15)--(35,0)--cycle,black); draw((36,0)--(36,15)--(40,15)--(40,0)); fill((51,0)--(51,10)--(55,10)--(55,0)--cycle,gray); fill((56,0)--(56,10)--(60,10)--(60,0)--cycle,black); draw((61,0)--(61,20)--(65,20)--(65,0)); fill((76,0)--(76,10)--(80,10)--(80,0)--cycle,gray); fill((81,0)--(81,15)--(85,15)--(85,0)--cycle,black); draw((86,0)--(86,20)--(90,20)--(90,0)); fill((101,0)--(101,15)--(105,15)--(105,0)--cycle,gray); fill((106,0)--(106,10)--(110,10)--(110,0)--cycle,black); draw((111,0)--(111,20)--(115,20)--(115,0)); for(int a = 0; a < 5; ++a) { draw((25*a,21)--(25*a,0)--(25*a+16,0)); } label("(A)",(8,21),N); label("(B)",(33,21),N); label("(C)",(58,21),N); label("(D)",(83,21),N); label("(E)",(108,21),N); [/asy]$

Solution

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 $A, B, D, E$ . The final answer is now $\boxed{C}$ .

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
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Difference between revisions of "1993 AJHSME Problems/Problem 5"

Revision as of 21:29, 22 December 2012

Problem 5

Solution

See Also

@@ Line 1: / Line 1: @@
+== 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==
 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}}