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2015 Math Kangaroo

Problem 11

Problem 11 · 2015 Math Kangaroo Medium
Arithmetic & Operations grouping

(2015 + 2015) + (2015 − 2015) + (2015 × 2015) + (2015 ÷ 2015) =

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Answer: C — 2016
Show hints
Hint 1 of 2
Work out the four pieces inside the root separately.
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Hint 2 of 2
The total turns into a perfect square.
Show solution
Approach: simplify inside the root to a perfect square
  1. Inside: (2015+2015)=4030, (2015−2015)=0, (2015×2015)=2015², (2015÷2015)=1.
  2. The sum is 2015² + 4030 + 1 = 2015² + 2·2015 + 1 = (2015+1)².
  3. Its square root is 2015+1 = 2016 (C).
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