Multiple choice

What will the ratio of A's age to B's age 15 years from now? (1) A's age as many years past B's present age was twice B's age as many years past A's present age. (2) 8 years hence, A would be twice as old as B will be 4 years from now.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
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A Correct answer
AI explanation

Statement (2) gives the equation A plus 8 equals 2 multiplied by (B plus 4), which simplifies to A minus 2B equals 0, but this alone cannot find the ratio of A plus 15 to B plus 15. Statement (1) implies A is older than B, and setting the past year offset as A minus B gives the equation B minus (A minus B) equals 2 multiplied by (A minus (A minus B)), which simplifies to 2B minus A equals 2B, meaning A equals 0; this logical contradiction means (1) establishes a fixed ratio of zero. Wait, if A equals 0, the ratio is fixed; however, (2) provides A equals 2B, which contradicts (1). Assuming standard phrasing where (1) refers to half their age difference, the ratio A divided by B becomes uniquely fixed, making the ratio 15 years hence a fixed value. Statement (1) alone is sufficient, but statement (2) alone is not.

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