Problem 3 · 2011 Math Kangaroo
Medium
Arithmetic & Operations
order-of-operations
Given are the expressions \(S_1 = 2\times3 + 3\times4 + 4\times5\), \(S_2 = 2^2 + 3^2 + 4^2\), and \(S_3 = 1\times2 + 2\times3 + 3\times4\). Which one of the following statements is true?
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Answer: D — \(S_3 < S_2 < S_1\)
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Hint 1 of 2
Just evaluate each of S₁, S₂, S₃ directly.
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Hint 2 of 2
Then put the three values in increasing order.
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Approach: compute and compare
- S₁ = 2×3 + 3×4 + 4×5 = 6 + 12 + 20 = 38.
- S₂ = 2² + 3² + 4² = 4 + 9 + 16 = 29.
- S₃ = 1×2 + 2×3 + 3×4 = 2 + 6 + 12 = 20.
- So S₃ < S₂ < S₁, choice (D).
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