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2018 Math Kangaroo

Problem 8

Problem 8 · 2018 Math Kangaroo Hard
Number Theory cryptarithmplace-value

In the correct addition shown, some digits were replaced by the letters P, Q, R and S. What is the value of P + Q + R + S?

Figure for Math Kangaroo 2018 Problem 8
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Answer: B — 15
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Hint 1 of 2
Work column by column, watching for a carry.
Still stuck? Show hint 2 →
Hint 2 of 2
The units column 5 + S ends in 4, and the tens column 4 + R ends in 5.
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Approach: solve the addition column by column
  1. Units: 5 + S ends in 4, so S = 9 with a carry of 1.
  2. Tens: 4 + R + 1 (carry) ends in 5, so R = 0 with a carry of 1.
  3. Hundreds: P + Q + 1 (carry) = 6, so P + Q = 5.
  4. Thus P + Q + R + S = 5 + 0 + 9 = 15.
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