# Averages Quiz Set 008

### Question 1

There is a sequence of 64 consecutive odd numbers. The average of first 29 of them is 137. What is the average of all the 64 numbers?

A

172.

B

173.

C

171.

D

170.

Soln.
Ans: a

The consecutive odd numbers form an AP with a common difference of 2. If the first term is a, then the average of first n terms of this AP is \${a + (a + (n-1) × 2)}/2\$ which is = a + n-1. We are given the average of first 29 terms as 137. So a + 29 - 1 = 137, which gives a = 109. The average of first 64 terms would be a + 64 - 1 = 109 + 64 - 1 = 172.

### Question 2

Average marks of class of 8 students is 80. What will be the average if each student is given 8 as grace marks?

A

88.

B

89.

C

87.

D

86.

Soln.
Ans: a

Let the total score of the class before grace marks be x. Then, by average formula \$80 = x/8\$, which gives x = \$80 × 8 = 640\$. When grace marks = 8 are added for each of the 8 students, the new total becomes \$640 + 8 × 8 = 704\$, the new average becomes \$704/8 = 88\$. TIP: As a shortcut, the new average = old average + grace marks.

### Question 3

What is the increase in the average of 17 numbers if the number 11 is replaced by 232?

A

13.

B

14.

C

12.

D

15.

Soln.
Ans: a

If a number r is replaced by a number R, the increase/decrease of average is determined according to the formula \$(R - r)/n\$. So in our case we have R = 232, r = 11, n = 17. So increase = \$(232 - 11)/17\$ = 13.

### Question 4

There is a sequence of 79 consecutive odd numbers. The average of first 22 of them is 72. What is the average of all the 79 numbers?

A

129.

B

130.

C

128.

D

127.

Soln.
Ans: a

The consecutive odd numbers form an AP with a common difference of 2. If the first term is a, then the average of first n terms of this AP is \${a + (a + (n-1) × 2)}/2\$ which is = a + n-1. We are given the average of first 22 terms as 72. So a + 22 - 1 = 72, which gives a = 51. The average of first 79 terms would be a + 79 - 1 = 51 + 79 - 1 = 129.

### Question 5

The sales(in rupees) of a karyana store for five consecutive days is 1308, 2706, 2280, 2898, 2796. What should be the sale on the sixth day so that the overall average sale is 2684?

A

Rs.4116.

B

Rs.4122.

C

Rs.4110.

D

Rs.4128.

Soln.
Ans: a

The total sale on first five days is 1308 + 2706 + 2280 + 2898 + 2796 = 11988. Let the sale on 6th day be x. The average for 6 days is: 2684 = \${11988 + x}/6\$ which gives x = \$6 × 2684 - 11988\$ = Rs. 4116. 