Multiple choice

Directions: The question below is followed by two statements A and B. You are to determine whether the data given in the statements is sufficient for answering the question. (You should use the data and your knowledge of mathematics to choose the possible answer.) The ages of Shruti and Aditi are in the ratio 14 : 11. What is the age of Shruti? (A) After 6 years, the ratio of Shruti's and Aditi's ages will be 17 : 14. (B) The ages of Aditi and Tulika are in the ratio 11 : 6.

  1. Statement (A) alone is sufficient to answer the question, but statement (B) alone is not sufficient.

  2. Statement (B) alone is sufficient to answer the question, but statement (A) alone is not sufficient.

  3. Both statements (A) and (B) together are needed to answer the question.

  4. Either statement (A) alone or statement (B) alone is sufficient to answer the question.

  5. Statements (A) and (B) together are not sufficient.
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A Correct answer
Explanation

Let Shruti's age be 14x and Aditi's be 11x. Statement A: (14x+6)/(11x+6) = 17/14. This is one equation with one variable x, so it is sufficient to find x and thus Shruti's age. Statement B: Aditi and Tulika ratio does not involve Shruti's age directly or provide a fixed value, so it is insufficient.

AI explanation

Let the present ages of Shruti and Aditi be 14x and 11x respectively. Statement A provides the equation (14x + 6) divided by (11x + 6) equals 17 divided by 14. Cross-multiplying yields 196x + 84 = 187x + 102, which simplifies to 9x = 18, giving a unique solution for their ages. Statement B only introduces a new person, Tulika, without providing any numerical value, so statement A alone is sufficient to answer the question.

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