There are 21 consecutive odd numbers. If the average of the first 19 numbers is X, then what is the average of the last 2 numbers?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. X + 21.
The first 19 odd numbers are a, (a + 2), (a + 4), .....,(a + 36)
We know that,
Average = Sum of observations/Number of observations
For the first 19 numbers
X = Sum of first 19 numbers/19
⇒ Sum = 19X
The last two numbers are (a + 38) and (a + 40)
Average = ((a + 38) + (a + 40))/2
⇒ (2a + 78)/2 = (a + 39)
Now,
The sum of the sequence = a, (a + 2), (a + 4), .....,(a + 36)
Sum = Number of terms/2 × (FIrst term + Last term)
⇒ 19X = 19/2 × (a + (a + 36))
⇒ 19X = 19/2 × (2a + 36)
⇒ 19X = 19 × (a + 18)
⇒ X = a + 18
⇒ a = X - 18
The average of the last two numbers = (a + 39) = (X - 18) + 39 = X + 21