Problem 29 · 2025 Math Kangaroo
Stretch
Algebra & Patterns
sum-constraintsubstitution
The letters p, q, r, s and t stand for five consecutive positive integers, but not necessarily in that order. It is given that p + q = 69 and s + t = 72. Which number does r stand for?
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Answer: C — 34
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Hint 1 of 2
Five consecutive integers add up to 5 times the middle one.
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Hint 2 of 2
Add p+q and s+t, then compare with the total of all five to isolate r.
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Approach: use the total of the five consecutive integers
- Adding the two given sums, \((p+q)+(s+t)=69+72=141\), accounts for every letter except \(r\).
- The five consecutive integers must be 33, 34, 35, 36, 37 (their two largest add to 72 and two others add to 69), and together they total 175.
- So \(r=175-141=\) 34, which is (C).
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