Multiple choice

Passage

Directions: The question below is followed by statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer (a) if the question can be answered by using statement I alone but cannot be answered by statement II alone (b) if the question can be answered by using statement II alone but cannot be answered by statement I alone (c) if both statements I and II together are required to answer the question (d) if the answer can be found by using any of the two statements alone (e) if both the statements together are not sufficient to answer the question

How many times will the father be of his daughter's age after 5 years? I. The ratio of their ages after 4 years will be 2 : 1, respectively. II. The average of their ages is 41.

  1. (a)

  2. (b)

  3. (c)

  4. (d)

  5. (e)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I gives the ratio of ages at a future time, which is insufficient without current ages. Statement II gives the average age, which is also insufficient. Together, let F and D be current ages. (F+4)/(D+4) = 2/1 and (F+D)/2 = 41. This system of two equations with two variables allows solving for F and D, and thus the future ratio.

AI explanation

Statement I provides only the ratio of their ages after 4 years, which gives infinite possible present ages. Statement II provides the average of their present ages, which gives the sum of their ages but not their individual ages. Using both statements, we can find their exact present ages and determine the ratio after 5 years, so both statements together are required.

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