Problem 7 · 2021 Math Kangaroo
Easy
Algebra & Patterns
Number Theory
place-valuesubstitution
A student correctly added the two two-digit numbers on the left of the board (AB + CD) and got the answer 137. What answer will he get if he adds the two four-digit numbers on the right of the board (ADCB + CBAD)?
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Answer: B — 13 837
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Hint 1 of 2
Write the right-hand sum ADCB + CBAD in terms of the totals A+C and B+D.
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Hint 2 of 2
The left-hand fact AB + CD = 137 already pins down 10(A+C) + (B+D).
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Approach: express the big sum using A+C and B+D
- From AB + CD = 137 we get 10(A+C) + (B+D) = 137, so A+C = 13 and B+D = 7.
- ADCB + CBAD = 1010(A+C) + 101(B+D).
- = 1010·13 + 101·7 = 13130 + 707 = 13837.
- So the answer is B.
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