Problem 5 · 2003 AMC 8
Easy
Fractions, Decimals & Percents
percent-multiplierproportion
If 20% of a number is 12, what is 30% of the same number?
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Answer: B — 18.
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Hint 1 of 2
The mystery number never has to be found — 30% and 20% of the SAME number are themselves in a fixed ratio.
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Hint 2 of 2
30% is 1.5 times as much as 20%, so the answer is 1.5 times the 12.
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Approach: scale the known percentage up directly
- Both percentages sit on the same number, so 30% relates to 20% the same way 30 relates to 20: it's 1.5 times as big.
- Whatever 20% is worth (12), 30% is 1.5 of that: 1.5 × 12 = 18.
- Why this is faster: a handier unit here is 10%, which is 12 ÷ 2 = 6. Then 30% = three of those tens = 6 × 3 = 18. Working in 10%-chunks skips finding the whole number entirely.
Another way — find the whole first:
- 20% of the number is 12, so the number is 12 ÷ 0.2 = 60.
- 30% of 60 = 0.3 × 60 = 18.
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