Problem 9 · 1996 AJHSME
Medium
Algebra & Patterns
reciprocal
If 5 times a number is 2, then 100 times the reciprocal of the number is
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Answer: D — 250.
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Hint 1 of 2
'5 times the number is 2' pins the number down. Find it first, then remember the reciprocal just flips the fraction upside down.
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Hint 2 of 2
5 × number = 2 means the number is 2/5; flipping gives the reciprocal 5/2. Then it's one multiplication.
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Approach: find the number, then flip and scale
- From 5 × number = 2, the number is 2/5. The reciprocal flips it: 5/2.
- 100 × (5/2) = 250. So the answer is 250.
- Sanity-check: 5/2 = 2.5, and 100 × 2.5 = 250 — a sensible result, and the tempting trap 100 × (2/5) = 40 (choice B) is what you'd get if you forgot to flip.
Another way — scale the given relation directly:
- 100 × reciprocal = 100 ÷ number. The given says 5 × number = 2, so number = 2 ÷ 5.
- Then 100 ÷ (2 ÷ 5) = 100 × 5 ÷ 2 = 500 ÷ 2 = 250 — no need to write a separate reciprocal step.
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