Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient to answer the question and then mark the option accordingly. Weights of four friends A, B, C and D are in arithmetic progression. What is their average weight? (1) The weight of B is 54 kg and that of C is 56 kg. (2) The average weight of A and D is 52 kg.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statements (1) and (2) together are sufficient, but neither statement alone is sufficient.

  4. Each statement alone is sufficient.

  5. Statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In an arithmetic progression with 4 terms, the average is (A+D)/2 or (B+C)/2. Statement (1) gives B and C, so average = (54+56)/2 = 55. Statement (2) gives (A+D)/2 = 52, which is the average of the 4 terms. Both are sufficient.

AI explanation

The average of any arithmetic progression equals the average of its two middle terms. Statement (1) provides the middle terms B and C as 54 kg and 56 kg, yielding an average of (54 + 56) / 2 = 55 kg. Statement (2) gives the average of the first and last terms A and D as 52 kg, which is also the overall average of the progression since the sum of equidistant terms is constant. Therefore, each statement alone provides enough data to find the average weight.

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