Suppose a, b, c, d and e are five consecutive odd numbers in ascending

Suppose a, b, c, d and e are five consecutive odd numbers in ascending order. Consider the following statements:

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1. Their average is (a+4).
2. Their average is (b+2).
3. Their average is (e-4).

Which of the statements given above is/are correct?

1 only

2 and 3 only

1 and 3 only

1, 2 and 3

Answer is Right!

Answer is Wrong!

This question was previously asked in

UPSC CAPF – 2018

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The correct answer is D) 1, 2 and 3.

Let the five consecutive odd numbers in ascending order be a, a+2, a+4, a+6, and a+8. Thus, b=a+2, c=a+4, d=a+6, e=a+8.
The average of these five numbers is (a + (a+2) + (a+4) + (a+6) + (a+8)) / 5 = (5a + 20) / 5 = a + 4.
Now let’s check the statements:
1. Their average is (a+4). This is correct.
2. Their average is (b+2). Since b = a+2, b+2 = (a+2)+2 = a+4. This is correct.
3. Their average is (e-4). Since e = a+8, e-4 = (a+8)-4 = a+4. This is correct.
All three statements are correct.

For any sequence of consecutive numbers (arithmetic progression), the average is equal to the median. In this case, c is the middle number, and c = a+4. The average is also the average of the first and last term: (a+e)/2 = (a + a+8)/2 = (2a+8)/2 = a+4. Similarly, the average of the second and fourth term: (b+d)/2 = (a+2 + a+6)/2 = (2a+8)/2 = a+4.

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