Multiple choice

What are the present ages of A and B? Consider statements A, B, and C to determine which statement(s) are necessary/sufficient to answer the question. Statement A: Four years hence the ratio of their ages will be 4 : 7 Statement B: B is 6 years older than A. Statement C: The sum of their ages is 14 years.

  1. Any two of them are sufficient.

  2. A and B together are sufficient

  3. B and C together are sufficient

  4. A and C together are sufficient

  5. All statements are required.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

With A and B together: (A+4)/(B+4) = 4/7 and B = A+6 gives A=4, B=10. With B and C: B=A+6 and A+B=14 gives A=4, B=10. With A and C: (A+4)/(B+4)=4/7 and A+B=14 gives A=4, B=10. Each pair of statements forms a solvable system yielding the same unique solution.

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