Problem 20 · 2019 Math Kangaroo
Hard
Number Theory
place-valuedigit-sum
The sum of the seven digits of a seven-digit phone number aaabbbb is a two-digit number ab. How big is the value of the sum a + b?
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Answer: C — 10
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Hint 1 of 2
The seven digits are three a's and four b's, summing to the two-digit number “ab”.
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Hint 2 of 2
Set 3a + 4b = 10a + b and solve for the digits.
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Approach: turn the digit-sum condition into an equation
- Digit sum = 3a + 4b; the two-digit value “ab” = 10a + b.
- So 3a + 4b = 10a + b, giving 3b = 7a, hence a = 3, b = 7.
- Then a + b = 10.
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