Average Test-2 (Finding average of specified numbers)

Answer: Option D

Explanation

According to the formula,

The average of 1st 'n' odd numbers = n

Here, n=15

∴ Required average =15

Hence, Option D is correct.

Answer: Option D

Explanation

Even number between 21 to 98 = 22, 24, 26, 28, 30,........98.

This is a series of consecutive even numbers

According to the formula,

The average of consecutive numbers=$\frac{\mathrm{First} \mathrm{number}+\mathrm{Last} \mathrm{number}}{2}$

$$\begin{gathered} =\frac{22+98}{2} \\ =\frac{120}{2} \\ =60 \end{gathered}$$

Hence, Option D is correct.

Answer: Option B

Explanation

The first ten indivisible numbers are 2, 3, 5, 7, 11, 13, 17, 19, 29, 29

∴ Required average 

$$\begin{gathered} =\frac{2+3+5+7+11+13+17+19+23+29}{10} \\ =\frac{129}{10}=12.9 \end{gathered}$$

Hence, Option B  is correct.

Answer: Option C

Explanation

According to the formula,

The average of the cubes of 1st 'n' natural numbers =$\frac{\mathrm{n}{\left(\mathrm{n}+1\right)}^2}{4}$ 

where n=5

∴ Required average

$$\begin{gathered} =\frac{5{\left(5+1\right)}^2}{4} \\ =\frac{5\times 36}{4} \end{gathered}$$ 

= 5×9=45

Hence, Option C is correct.

Answer: Option C

Explanation

The series of consecutive numbers are x, (x+1), (x+2), (x+3).... and so on.

According to the formula,

The average of consecutive numbers= $\frac{\mathrm{First} \mathrm{number} +\mathrm{Last} \mathrm{number}}{2}$

Let First number= x

∴ 4th number (last number)=(x+3)

Given, average of 4 consecutive numbers = 20

Now, substitute these values in above formula,

$20=\frac{\mathrm{x}+\left(\mathrm{x}+3\right)}{2}$

⇒ 2x+3=40

⇒ 2x=37

∴ x= 18.5

 7th number = (x+6)

=(18.5+6)= 24.5

Hence, Option C is correct.