Problem 25 · 2025 Math Kangaroo
Stretch
Fractions, Decimals & Percents
percent-multiplierestimate-and-pick
John writes a two-digit number on the board. If he erases the ones digit, the value of the number is reduced by p%. Which of the following numbers is closest to the largest possible value of p?
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Answer: D — 95
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Hint 1 of 2
Write the number as 10a + b and the erased value as a; the drop is (9a + b)/(10a + b).
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Hint 2 of 2
To make the percentage drop largest, make a small and b large—try a = 1, b = 9.
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Approach: maximise the fractional drop
- Reduction p = (9a + b)/(10a + b)·100 = (1 − a/(10a + b))·100.
- Smallest a, largest b: a = 1, b = 9 gives p = 18/19·100 ≈ 94.7%.
- Closest listed value is 95.
Mark:
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