Problem 14 · 2015 Math Kangaroo
Hard
Algebra & Patterns
substitution
We know the following about five positive whole numbers a, b, c, d, e. All the numbers are different, b = c : e, d = a + b and a = e − d. Which of the numbers a, b, c, d, e is the largest?
Show answer
Answer: C — c
Show hints
Hint 1 of 2
Express everything in terms of the smaller quantities, then see which is built up the most.
Still stuck? Show hint 2 →
Hint 2 of 2
c is a product, while the others are sums or differences.
Show solution
Approach: rewrite each in terms of a and b
- From a = e−d and d = a+b, we get e = 2a+b, so e and d are modest sums.
- b = c÷e means c = b·e, a product of two positive whole numbers larger than 1.
- A product of such factors beats the sums, so c is the largest (C).
Mark:
· log in to save