Problem 9 · 2018 Math Kangaroo
Medium
Number Theory
place-value
Alice subtracts one two-digit number from another two-digit number. Afterwards she paints over two of the digits in the calculation, so it now reads ?3 − 2? = 25 (each ? hides a digit). What is the sum of the two painted-over digits?
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Answer: D — 13
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Hint 1 of 2
Write the two numbers with their hidden digits as unknowns and line up the subtraction.
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Hint 2 of 2
Turn the painted-over subtraction into a place-value equation; only one pair of digits makes it work.
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Approach: rebuild the subtraction one place value at a time
- The calculation is ?3 − 2? = 25, so the answer 25 sits just above 20.
- For the difference to be 25, the first number must be in the 50s: try 53.
- Then 53 − 2? = 25 forces 2? = 28, so the hidden digits are 5 and 8.
- Their sum is 5 + 8 = 13.
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