Average- Aptitude Questions and Answers

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Average of two numbers is 14.5 and square root of their product is 10. What are the numbers?

A)
16 and 9

B)
25 and 4

C)
4 and 16

D)
25 and 9


Correct Answer :

25 and 4


Explanation :

Let the number be a and b. Then Average is, (a +b) / 2 = 14.5
a + b = 29

as given square root of their product is √ab = 10
ab = 100

(a - b)2 = (a + b)2 - 4ab
(29)2 -(4 *100)= 441
(a - b) = 21
On solving a + b = 29 and a - b = 21, we get a =25 and b = 4.

The average age of a group of four men whose ages are in the ratio 2 : 3 : 4 : 5 is 42 yr, what is the age of the eldest person in this group?

A)
60 yr

B)
48 yr

C)
36 yr

D)
24 yr


Correct Answer :

60 yr


Explanation :

Let the ages of the four men be 2x, 3x, 4x and 5x year respectively.
Then, 42 =(2x + 3x + 4x + 5x)/4
14x = 42 *4
x =(42 *4)/14 = 12
Hence, the age of the eldest person = 5x = (5 *12) year = 60 year

If the mean of first n natural numbers is 13 then n=?

A)
26

B)
25

C)
24

D)
20


Correct Answer :

25


Explanation :

Sum of (1 + 2 + 3 +…. + n) =n(n+1)/2

Mean = [n(n+1)/2] / n => (n+1)/2

As given, (n+1)/2 = 13
n+1 =26
n=25

Find the median of the series: 38,28,34,42,50,40,48?

A)
40

B)
48

C)
42

D)
28


Correct Answer :

40


Explanation :

The median of a series of numbers is the number that appears in the middle .
arranged series from smallest to largest => 28,34,38,40,42,48,50

Median =40

Note:If the number of members of the series was even, the average of the two middle numbers would be the median

What is the range of the data given below- 20, 35, 70, 65, 45, 95, 15, 80

A)
15

B)
80

C)
45

D)
95


Correct Answer :

80


Explanation :

Ordering the data from least to greatest, we get:
15, 20, 35, 45, 65, 70, 80, 95

highest - lowest = 95 - 15 = 80
The range is 80

What is the Arithmetic Mean of first 100 natural numbers?

A)
50

B)
50.5

C)
51

D)
55


Correct Answer :

50.5


Explanation :

Mean=(Total Sum of all the Values)/(No of Values)

The Sum of first ’n' natural numbers is given by,Sum=n*(n+1)/2
then, Mean=[n*(n+1)/2] / n
=n*(n+1) / 2*n

So,the mean of first 100 natural numbers, Mean=100*101 / 2*100
=101/2
=50.5

Find the mean, median, mode, and range for the following list of values ?
13, 18, 13, 14, 13, 16, 14, 21, 13

A)
15, 14, 13 and 8

B)
15, 14, 14 and 13

C)
13, 13, 13 and 13

D)
15, 14, 13 and 15


Correct Answer :

15, 14, 13 and 8


Explanation :

Mean :To find the mean, add all the numbers together then divide by the number of numbers.
Mean = (13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) / 9 = 15

Median:To find the median, order the numbers and see which one is in the middle of the list.
Reordered = 13, 13, 13, 13, 14, 14, 16, 18, 21 - the middle term is 14 ie Median=14

Mode:To find the mode, order the numbers lowest to highest and see which number appears the most often.
13 is the number which appears the most often

Range:To find the range, subtract the lowest number from the biggest number.
Reordered = 13, 13, 13, 13, 14, 14, 16, 18, 21
Range = ( 21- 13 ) = 8

The average of the first 10 prime numbers?

A)
10.1

B)
10

C)
12.9

D)
13


Correct Answer :

10.1


Explanation :

average =(1+2+3+5+7+11+13+17+19+23)/10
=101/10
=10.1

Two years ago, the average age of a family of 8 members was 18 years. The average age of the family after the birth of a child is the same today. How old is the child?

A)
2 years

B)
1*(1/2) years

C)
1 year

D)
2*(1/2) years


Correct Answer :

2 years


Explanation :

As given, after birth of child average age is same ie 18 years.
hence age of child is 2 years

The average of 9 full numbers is 11 but after calculation, it was seen that while computing by the mistake the 23 was written to 32. What will be the new average after making appropriate amendment?

A)
10

B)
9

C)
10.1

D)
9.5


Correct Answer :

10


Explanation :

The average of 9 numbers = 11
Therefore, the total is = 9*11 =99
But by mistake the 23 was written 32
So, new avarage =(99+23-32)/9
=90/9
=10

The average of first three numbers out of four numbers are 18 and the average of the last three numbers is 16. If the last number is 19, then the first number is?

A)
19

B)
18

C)
20

D)
25


Correct Answer :

25


Explanation :

Let the numbers are A, B ,C and D, then as given
A+B+C=18*3=54
B+C+D=16*3=48
After resolving the above equations -
A-D=6
the last number is 19 ie D=19
So, A=6+19 =25

The average of seven consecutive numbers is 20, then the largest number in those numbers is?

A)
24

B)
23

C)
22

D)
20


Correct Answer :

23


Explanation :

Let the numbers are X to ..(X+6).
As given,
X+(X+1)+(X+2)+(X+3)+(X+4)+(X+5)+(X+6)=20*7
7*X+21=140
7*X=119
X=17
Hence, the largest number is=(X+6) =17+6 =23

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