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Which of the following statement are correct? A. The average of first twenty multiples of 8 is 84 B. There are 25 prime numbers between 100 to 200. C. Average of ten positive numbers is X. If each number is increased by 10%, then new average increases by 11%. Choose the correct answer from the options given below

Which of the following statement are correct? A. The average of first twenty multiples of 8 is 84 B. There are 25 prime numbers between 100 to 200. C. Average of ten positive numbers is X. If each number is increased by 10%, then new average increases by 11%. Choose the correct answer from the options given below Correct Answer A only

Calculation:

Statement A: The average of first twenty multiples of 8 is 84

First twenty multiples of 8 are:

⇒ 8 × 1, 8 × 2, 8 × 3,...........8 × 20

So, AP = 8 + 16 + 24, +..............+ 160

Required average = 8(1 + 2 + 3 + ............+ 20)/20

AP: Sum of first n numbers = n/2

Required average of AP = (8 + 160)/2 = 84

Hence, statement A is correct.

Statement B. There are 25 prime numbers between 100 to 200.

Prime numbers from 100 to 200 are:

101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 173, 179, 181, 191, 193, 197, 199.

There are 21 prime numbers between 100 to 200

Hence, statement B is incorrect.

Statement C. Average of ten positive numbers is X. If each number is increased by 10%, then new average increases by 11%.

Let the ten positive numbers be m1, m2, m3, ............ m10

Now, average of ten positive numbers is X.

⇒ X = (m1 + m2 + m3 +............+ m10)/10

If each number is increased by 10% then, new average Y is,

⇒ Y = (1.1m1 + 1.1m2 + 1.1m3 +............+ 1.1m10)/10  

⇒ Y = 1.1 × (m1 + m2 + m3 +............+ m10)/10

⇒ Y = 1.1 × m

New average Y is increased by 10%

Hence, statement C is incorrect.

∴ Only statement A is correct.

Additional Information

  •  A prime number has exactly two factors and is a positive integer. If 'p' is a prime number, then 1 and p themselves are only necessary factors. Any number that does not obey this is called a composite number.

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