Problem 2 · 1992 AJHSME
Easy
Fractions, Decimals & Percents
compare-fractions
Which of the following is not equal to 54?
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Answer: D — 1 1/5.
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Hint 1 of 3
5/4 is one whole plus a quarter. Which choices are secretly just a quarter dressed up — and which one hides a different-sized piece?
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Hint 2 of 3
When choices look different but might be equal, convert them all to ONE common form (a decimal, or a fraction over the same bottom number) so they line up for comparison.
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Hint 3 of 3
A bigger denominator means a smaller slice: 1/5 is less than 1/4, so don't be fooled into reading 1 1/5 as 1.25.
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Approach: rewrite every choice in one common form so the odd one out stands out
- 5/4 = 1 + 1/4 = 1.25. Now test each: 10/8 = 1.25 (just doubled top and bottom); 1 1/4 = 1.25; 1 3/12 = 1 + 1/4 = 1.25 (3/12 reduces to 1/4); 1 10/40 = 1 + 1/4 = 1.25 (10/40 reduces to 1/4).
- That leaves 1 1/5. Since 1/5 = 0.2, this is 1.2, NOT 1.25 — so 1 1/5 is the one not equal.
- Trap to remember: a fifth feels "close" to a quarter, but cutting something into 5 pieces gives smaller pieces than cutting into 4. The trickster choice swaps the denominator from 4 to 5 hoping you won't notice the slice shrank.
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