Multiple choice

Directions: In this problem, you have to find out which of the following statements is/are redundant for determining the answer of the given question or can be dispensed with. What will be the sum of the ages of mother and the daughter after 12 years? I. The mother's present age is 5/3 of the daughter's present age. II. After 5 years, the ratio of the mother's age to the daughter's age will become 8 : 5. III. The difference between the present ages of the mother and the daughter was equal to the daughter's age 10 years ago.

  1. Either I or II

  2. Either II or III

  3. Either I or III

  4. Any one of the three

  5. Any two of the three
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let M and D be present ages. I: M = 5/3 D. II: (M+5)/(D+5) = 8/5. III: M - D = D - 10. Each statement provides a unique linear relationship between M and D. Since we have two variables, any two of these three statements are sufficient to solve for M and D, meaning any one of them is redundant.

AI explanation

Using the substitution method for simultaneous equations, we find the specific ages. Statement I gives M = 5S / 3, statement II gives (M + 5) / (S + 5) = 8 / 5, and statement III gives M - S = S - 10. Solving any two of these three equations yields the exact present ages of the mother as 40 years and the daughter as 24 years, making the required sum 12 years from now equal to 76 years. Therefore, any two statements are sufficient to determine the answer, meaning any one of the three can be dispensed with.

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