Average - Aptitude MCQ Questions and Solutions with Explanations

41

The sum of the three consecutive even numbers is 44 more than the average of these numbers. Which of the following is the third largest of these numbers?

A) 16 B) 18 C) 24 D) Cannot be determined E) None of these

Discuss

Answer & Solution

Answer: Option C

Solution:

Let the numbers be x, x + 2 and x + 4
Then,
⇒ (x + x + 2 + x + 4) - $$\frac{(x + x + 2 + x + 4)}{3}$$ = 44
⇒ (3x + 6) - $$\frac{(3x + 6)}{3}$$ = 44
⇒ 2 (3x + 6) = 132
⇒ 6x = 120
⇒ x = 20
∴ Largest number = x + 4 = 24

42

The average of five consecutive odd numbers is 95. What is the fourth number in the descending order?

A) 91 B) 95 C) 97 D) 99 E) None of these

Discuss

Answer & Solution

Answer: Option E

Solution:

Let the numbers be x, x + 2, x + 4, x + 6 and x + 8
Then,
$$ \Rightarrow \frac{{x + \left( {x + 2} \right) + \left( {x + 4} \right) + \left( {x + 6} \right) + \left( {x + 8} \right)}}{5} $$ $$= 95$$
$$\eqalign{ & \Rightarrow 5x + 20 = 475 \cr & \Rightarrow 5x = 455 \cr & \Rightarrow x = 91 \cr} $$
So, the numbers are 91, 93, 95, 97 and 99
Clearly, the fourth number in the descending order is 93

43

The average of two numbers is 6.5 and square root of their product is 6. What are the numbers?

A) 11 and 2 B) 8 and 5 C) 9 and 4 D) 10 and 3

Discuss

Answer & Solution

Answer: Option C

Solution:

Let the two numbers be x and y
Then,
x + y = 6.5 × 2 = 13 and
$$\sqrt {{\text{xy}}} $$ = 6 or xy = 36
⇒ (x - y)² = (x + y)² - 4xy
⇒ (x - y)² = (13)² - 4 × 36
⇒ (x - y)² = 169 - 144
⇒ (x - y)² = 25
⇒ (x - y) = 5
Solving x + y = 13 and x - y = 5
We get : x = 9 , y = 4

44

A, B, C and D are four consecutive even numbers respectively and their average is 65. What is the product of A and D?

A) 3968 B) 4092 C) 4216 D) 4352 E) None of these

Discuss

Answer & Solution

Answer: Option C

Solution:

Let x, x + 2, x + 4 and x + 6 represent numbers A, B, C and D respectively.
Then,
$$\eqalign{ & \Rightarrow \frac{{x + \left( {x + 2} \right) + \left( {x + 4} \right) + \left( {x + 6} \right)}}{4} = 65 \cr & \Rightarrow 4x + 12 = 260 \cr & \Rightarrow 4x = 248 \cr & \Rightarrow x = 62 \cr} $$
So, A = 62, B = 64, C = 66, D = 68
∴ A × D = 62 × 68 = 4216

45

The arithmetic mean of the series 1, 2, 4, 8, 16, . . . . . . , 2ⁿ is -

A) $$\frac{{{2^n} - 1}}{{n + 1}}$$ B) $$\frac{{{2^n} + 1}}{{n}}$$ C) $$\frac{{{2^n} - 1}}{{n}}$$ D) $$\frac{{{2^{n + 1}} - 1}}{{n + 1}}$$

Discuss

Answer & Solution

Answer: Option D

Solution:

The given series is a G.P. with first term, a = 1 and common ratio, r = 2,
It has (n + 1) terms.
∴ Sum of the terms of the series
= $$\frac{{{2^{n + 1}} - 1}}{{2 - 1}}$$
= 2^{n + 1} $$ - $$ 1
Arithmetic mean = $$\frac{{{2^{n + 1}} - 1}}{{n + 1}}$$

46

The following table shows the number of working hours and the number of employees employed in a small scale industry

No. of working hours	No. of employees
3 - 5	7
5 - 7	10
7 - 9	18
9 - 11	57
11 - 13	14
13 - 15	8

The average number of working hours of an employee is

A) 8.5 B) 9.5 C) 10.5 D) None of these

Discuss

Answer & Solution

Answer: Option B

Solution:

We have :

Mean working hours	4	6	8	10	12	14
No. of employees	7	10	18	57	14	8

Sum of working hours of all the employees
= (4 × 7 + 6 × 10 + 8 × 18 + 10 × 57 + 12 × 14 + 14 × 8)
= (28 + 60 + 144 + 570 + 168 + 112)
= 1082
Total number of employees
= (7 + 10 + 18 + 57 + 14 + 8)
= 114
∴ Average number of working hours
= $$\left( {\frac{{1082}}{{114}}} \right)$$
= 9.49 $$ \approx $$ 9.5

47

In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Arun and he thinks that Arun’s weight is greater is that 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Arun?

A) 67 kg B) 68 kg C) 69 kg D) Data inadequate E) None of these

Discuss

Answer & Solution

Answer: Option A

Solution:

Let Arun's weight be X kg.
According to Arun, 65 < X < 72
According to Arun's brother, 60 < X < 70
According to Arun's mother, X ≯ 68 i.e. X $$ \leqslant $$68
The values satisfying all the above conditions are 66, 67 and 68
∴ Required average
$$\eqalign{ & = \left( {\frac{{66 + 67 + 68}}{3}} \right){\text{ kg}} \cr & = \left( {\frac{{201}}{3}} \right){\text{ kg}} \cr & = 67{\text{ kg}} \cr} $$

48

The mean of the first ten even natural number is-

A) 0 B) 10 C) 11 D) 12

Discuss

Answer & Solution

Answer: Option C

Solution:

Required mean
$$\eqalign{ & = \left( {\frac{{2 + 4 + 6 + ..... + 20}}{{10}}} \right) \cr & = \frac{{2\left( {1 + 2 + ..... + 10} \right)}}{{10}} \cr} $$
$$ = \left( {\frac{1}{5} \times \frac{{10 \times 11}}{2}} \right)$$ $$\left[ {\because 1 + 2 + 3 + ... + n = \frac{{n\left( {n + 1} \right)}}{2}} \right]$$
$$ = 11$$

49

The average of the first nine prime numbers is-

A) 9 B) 11 C) $$11\frac{1}{9}$$ D) $$11\frac{2}{9}$$

Discuss

Answer & Solution

Answer: Option C

Solution:

Average
$$ = \left( {\frac{{2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23}}{9}} \right)$$
$$\eqalign{ & = \frac{{100}}{9} \cr & = 11\frac{1}{9} \cr} $$

50

The arithmetic mean of first 11 natural numbers is

A) 5 B) 5.5 C) 6.0 D) 6.5

Discuss

Answer & Solution

Answer: Option C

Solution:

Required mean
$$\eqalign{ & = \left( {\frac{{1 + 2 + ..... + 11}}{{11}}} \right) \cr & = \left( {\frac{1}{{11}} \times \frac{{11 \times 12}}{2}} \right) \cr & = 6 \cr} $$
$$\left[ {\because 1 + 2 + ..... + n = \frac{{n\left( {n + 1} \right)}}{2}} \right]$$