Multiple choice

Directions: In this problem, a question is followed by statements marked (I), (II) and (III). Read the statements carefully and determine which of the given statements is/are sufficient/necessary to answer the question. What is the difference between the ages of P and Q? I. Ten years ago, age of R was double that of Q. II. P is 5 years younger than R. III. Present ratio of ages of Q and R is 3 : 4.

  1. All three statements

  2. Only statements I and II

  3. Only statements II and III

  4. Only statement II and either statement I or statement III

  5. None of the statements
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A Correct answer
Explanation

We need the difference between P and Q. I: R-10 = 2(Q-10). II: P = R-5. III: Q/R = 3/4. With these, we can express P, Q, and R in terms of one variable and solve for the difference P-Q.

AI explanation

Let the present ages of P, Q and R be p, q and r. Statement I gives the equation r - 10 = 2(q - 10), which simplifies to r - 2q = -10. Statement II provides the equation p = r - 5, and statement III establishes the ratio q/r = 3/4. Using statements I and III, you can solve for the exact values of q and r. Once r is known, you can use the equation from statement II to find p, making all three statements necessary to find the difference between p and q.

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