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2020 Math Kangaroo

Problem 1

Problem 1 · 2020 Math Kangaroo Easy
Number Theory primesprime-test

Which of the following additions does not give a prime number?

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Answer: E — 5 + 7
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Hint 1 of 2
Work out each sum first, then ask which total has a factor other than 1 and itself.
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Hint 2 of 2
A number is prime only if nothing besides 1 and itself divides it — check the five totals.
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Approach: add each pair, then test the five sums for primality
  1. The sums are 13, 11, 17, 7 and 12.
  2. 13, 11, 17 and 7 are all prime (no smaller divisor works).
  3. 5 + 7 = 12 = 2 × 6, which is composite.
  4. So the sum that is not prime is choice E.
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