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2016 Math Kangaroo

Problem 11

Problem 11 · 2016 Math Kangaroo Hard
Algebra & Patterns substitution

a, b, c, d are positive whole numbers for which \(a + 2 = b - 2 = c \times 2 = d \div 2\) holds true. Which of the four numbers a, b, c and d is biggest?

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Answer: Dd
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Hint 1 of 2
Set the common value equal to k and write each of a, b, c, d in terms of k.
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Hint 2 of 2
Compare a = k-2, b = k+2, c = k/2, d = 2k.
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Approach: express all four through the common value
  1. Let a+2 = b-2 = 2c = d/2 = k.
  2. Then a = k-2, b = k+2, c = k/2, d = 2k.
  3. For positive whole numbers 2k exceeds the others, so d is biggest.
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