Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labeled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. What is the father's current age? (i) Three years ago, the father's age was four times his son's age. (ii) Four years from now, the father's age will be 3 years less than three times his son's age.

  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.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement (1) gives F - 3 = 4(S - 3), which is one equation with two variables. Statement (2) gives F + 4 = 3(S + 4) - 3, another equation with two variables. Together, they form a system of two linear equations that can be solved for F and S.

AI explanation

Statement one yields the equation F - 3 = 4(S - 3), which simplifies to F = 4S - 9, but it cannot be solved alone because it contains two variables. Statement two yields the equation F + 4 = 3(S + 4) - 3, which simplifies to F = 3S + 5, which also cannot be solved alone. Setting the equations equal gives 4S - 9 = 3S + 5, meaning S = 14, and substituting S back into the first equation gives F = 47. Both statements together are sufficient to find the father's current age.

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