As we know that ,

Correct Option: C

As we know that ,

Average of 7 consecutive numbers is 20.
Since the numbers are consecutive, they form an arithmetic series with common difference 1.
Since, 7 is odd, 20 must be the middle number.
We can write the series as below,
17, 18, 19, 20, 21, 22, 23

Correct Option: B

Average of 7 consecutive numbers is 20.
Since the numbers are consecutive, they form an arithmetic series with common difference 1.
Since, 7 is odd, 20 must be the middle number.
We can write the series as below,
17, 18, 19, 20, 21, 22, 23
∴ The largest of these numbers is 23.

Given that , The average of 15 numbers = 7
The average of the first 8 numbers = 6.5
and the average of the last 8 numbers = 8.5
Middle i.e. eighth number = 8 × 6.5 + 8 × 8.5 – 15 × 7

Correct Option: D

Given that , The average of 15 numbers = 7
The average of the first 8 numbers = 6.5
and the average of the last 8 numbers = 8.5
Middle i.e. eighth number = 8 × 6.5 + 8 × 8.5 – 15 × 7
Middle i.e. eighth number = 52 + 68 – 105
Middle i.e. eighth number = 120 – 105 = 15

Here , The average of 8 numbers = 21
When each number is multiplied by 8, the new average gets multiplied by 8.

Correct Option: D

Here , The average of 8 numbers = 21
When each number is multiplied by 8, the new average gets multiplied by 8.
So , New average = 21 × 8 = 168

Given , Sum of 11 numbers = 63 × 11 = 693
Sum of the first 6 numbers = 60 × 6 = 360
and Sum of the last 6 numbers = 65 × 6 = 390
∴ Sixth number = Sum of the first 6 numbers + Sum of the last 6 numbers – Sum of 11 numbers

Correct Option: A

Given , Sum of 11 numbers = 63 × 11 = 693
Sum of the first 6 numbers = 60 × 6 = 360
and Sum of the last 6 numbers = 65 × 6 = 390
∴ Sixth number = Sum of the first 6 numbers + Sum of the last 6 numbers – Sum of 11 numbers
Sixth number = 360 + 390 – 693 = 57