Multiple choice

Direction: The following question has two statements, (1) and (2). Answer the question using the following options: What is the average age of the four brothers, if their ages are in arithmetic progression? (1) The average age of the eldest and the youngest brothers is 21 years. (2) The second brother is 24 years old and the third brother is 18 years old.

  1. if statement (1) alone is sufficient but statement (2) alone is not

  2. if statement (2) alone is sufficient but statement (1) alone is not

  3. if both (1) and (2) together are sufficient but none of them alone is sufficient

  4. if both independently are sufficient

  5. if both statements (1) and (2) together are not sufficient
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D Correct answer
Explanation

In an AP, the average of the four terms is the average of the two middle terms or the average of the first and last terms. Statement (1) gives the average of the first and last, which is the average of the four. Statement (2) gives the two middle terms, allowing calculation of their average.

AI explanation

In an arithmetic progression, the average of all terms equals the average of the first and last terms, and also equals the average of the two middle terms. Statement 1 gives the average of the youngest and eldest brothers as 21, which means the average of all four brothers is 21. Statement 2 gives the ages of the second and third brothers as 24 and 18, and the average of these two middle brothers is (24 + 18) / 2 = 21. Because both statements independently yield the same average of 21 years, both independently are sufficient.

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