Multiple choice

Direction: The following question has two statements, (1) and (2). Answer the question using the following options: What is the average of 5 numbers in AP? (1) The first term is 3 and is 2 less than the next term. (2) The third term is 7.

  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 statements are sufficient independently

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

For 5 numbers in AP, the average is the middle term (3rd term). Statement (1): a = 3, a+d = 3+2 = 5, so d=2. The 3rd term is a+2d = 3+4 = 7. The average is 7. Statement (2): 3rd term is 7. The average is 7. Both are sufficient.

AI explanation

The formula for the average of an odd number of terms in an arithmetic progression is the middle term, so the average of 5 numbers is the third term. From statement 1, the first term is 3 and the common difference is 2, making the third term 3 + 2 + 2 = 7, which gives the average directly. Statement 2 explicitly states that the third term is 7, providing the average immediately without needing the other terms. Therefore, both statements independently give the average value.

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