Multiple choice

Directions: The item given below consists of a question and two statements, numbered I and II. You have to decide whether the data provided in the statement is sufficient to answer the question. Read both the statements and choose the correct option. What is the present age of M? I. The ratio of age of M to the age of N is 3 : 4. Ten years ago, the age of M was half of N. II. The difference between the age of M and N is 10. Ten years from now, the ratio of the age of M to that of N will become 4 : 5.

  1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. The data either in statement I alone or in statement II alone is sufficient to answer the question.

  4. The data in both statement I and II together is necessary to answer the question.

  5. The data even in both statements I and II together is not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I: M/N = 3/4 and (M-10)/(N-10) = 1/2. This is a system of two equations with two variables, sufficient to solve for M. Statement II: |M-N| = 10 and (M+10)/(N+10) = 4/5. This is also a system of two equations, sufficient to solve for M.

AI explanation

Statement I gives a ratio of 3 to 4, meaning the present ages of M and N are 3x and 4x. The equation for 10 years ago is 3x - 10 = 0.5 * (4x - 10), which yields 3x - 10 = 2x - 5, making x = 5 and M's age 15. Statement II states the difference is 10 and the ratio 10 years from now will be 4 to 5, which provides another solvable equation for M's present age. Each statement independently provides enough data to answer the question.

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