Problem 9 · 1992 AJHSME
Hard
Fractions, Decimals & Percents
read-graphratio
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Answer: B — 160.
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Hint 1 of 3
The numbers up the side are missing — but the picture still tells you something. How do the two bar HEIGHTS compare? (Look at the line drawn partway up the F bar.)
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Hint 2 of 3
Even with no scale, a bar graph still shows ratios: if one bar is twice as tall as another, those groups are in a 2 : 1 ratio. Turn the ratio into "equal parts" of the whole.
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Hint 3 of 3
Total people = female parts + male parts. Find the size of one part, then take the males' share.
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Approach: missing scale is fine — read the height ratio, then divide the total into parts
- The line across the F bar marks exactly the M bar's height, showing the female bar is twice the male bar. So females : males = 2 : 1.
- That's 2 parts + 1 part = 3 equal parts making up the whole town of 480. One part = 480 ÷ 3 = 160.
- Males are 1 part, so there are 160 males.
- Why this transfers: a bar graph without numbers is useless for amounts but perfect for ratios — comparing heights still works. Convert any ratio a : b into (a+b) equal parts of the total and you can split the whole.
- Sanity check: 160 males + 320 females = 480, and 320 is indeed double 160. Fits the picture.
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