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### 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?

### 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?

This Blog Post/Article "Averages Quiz Set 008" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2019-08-18.