Multiple choice general knowledge math & puzzles

Problems A, B and C were posed in a mathematical contest. 25 competitors solved at least one of the three. Amongst those who did not solve A, twice as many solved B as C. The number solving only A was one more than the number solving A and at least one other. The number solving just A equalled the number solving just B plus the number solving just C. How many solved just C?

  1. 1

  2. 2

  3. 3

  4. 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let a, b, c be numbers solving only A, B, C respectively. Given: b + c = 2(a + b + c + 2), a = (a + b + c + 2) + 1, a = b + c. From the third: a = b + c. From the first: b + c = 2(a + b + c + 2), but since a = b + c, substitute to get relationships. The system gives a = 6, and c = 2.

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