Averages Quiz Set 008

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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?

 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.


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Creative Commons License
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.

Posted by Parveen(Hoven),
Aptitude Trainer


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