Average – Part 1

In Quantitative Aptitude, Quants & Reasoning, Quiz
May 9, 2016

a) Average = Sum of observations / Number of observations

b) Suppose a man covers a certain distance at x kmph and an equal distance at y kmph.
Then, the average speed druing the whole journey is 2xy / (x + y) kmph.

1) Find the average of first 40 natural numbers.
a) 20.5
b) 18
c) 19.5
d) 19

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Answer a) 20.5
Sum of first n natural numbers = n(n+1)/2
So, sum of first 40 natural numbers = 40*41/2 = 820
Required average = 820/40 =20.5

2) Find the average of all the numbers between 6 and 34 which are divisible by 5
a) 18
b) 20
c) 24
d) 30

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Answer b) 20
Multiples of 5 between 6 and 34 are 10,15,20,25,30
Average = (10+15+20+25+30)/5 =5(10+30)/2*5 = 40/2 =20

3) The average of 2,7,6 and x is 5 and the average of 18,1,6,x and y is 10. What is the value of y?
a) 5
b) 10
c) 20
d) 30

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Answer c) 20
( 2+7+6+x)/4 = 5 or 15+x =20 or x = 5
Also (18+1+6+x+y)/5 = 10, 25+5+y = 50, y =20

4) The average of 7 consecutive numbers is 20. The largest of these numbers is
a) 20
b) 22
c) 23
d) 24

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Answer c) 23
Let the first number be x, Then the last number is ( x+6)
Average = [x+(x+1)+(x+2)+(x+3)+(x+3)+(x+4)+(x+5)+(x+6)]/7 = 20
7x + 21 = 20*7 = 140, 7x =119, x = 17
The largest number =x+6 =17+6 = 23

5) In the first 10 over of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
a) 6.25
b) 6.5
c) 6.75
d) 7

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Answer a) 6.25
Required run rate = 282 – (3.2 x 10) / 40 =250 /40 = 6.25

6) A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
a) 28 4/7 years
b) 31 5/7 years
c) 32 1/7 years
d) None of these

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Answer b) 31 5/7 years
Required average
= [67 x 2 + 35 x 2 + 6 x 3 / 2 + 2 + 3] = 134 + 70 + 18 / 7
= 222/7
= 31 5/7 years.

7) The average weight of 8 person’s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
a) 76 kg
b) 76.5 kg
c) 85 kg
d) Data inadequate
e) None of these

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Answer c) 85 kg
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.

8) The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
a) 0
b) 1
c) 10
d) 19

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Answer d) 19
Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).

9) A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
a) Rs. 4991
b) Rs. 5991
c) Rs. 6001
d) Rs. 6991

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Answer a) Rs. 4991
Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) – 34009 ] = Rs. (39000 – 34009)
= Rs. 4991.

10) The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
a) 23 years
b) 24 years
c) 25 years
d) None of these

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Answer a) 23 years
Let the average age of the whole team by x years.
11x – (26 + 29) = 9(x -1)
11x – 9x = 46
2x = 46
x = 23.
So, average age of the team is 23 years.