model 4 find nth average from 1st & last number Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on average topic of quantitative aptitude
(a) 95
(b) 115
(c) 105
(d) 65
The correct answers to the above question in:
Answer: (a)
Using Rule 1,
According to the question,
195 + x + x + 20 = 135 × 3
⇒ 2x + 215 = 405
⇒ 2x = 405 – 215 = 190
∴ x =$190/2$ = 95
x = Smallest number
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Read more find nth term Based Quantitative Aptitude Questions and Answers
Question : 1
Out of four numbers the average of the first three is 16 and that of the last three is 15. If the last number is 20 then the first number is
a) 25
b) 21
c) 28
d) 23
Answer »Answer: (d)
Let three numbers be a,b and c respectively.
∴ a + b + c = 16 × 3 = 48 ---(i)
b + c + 20 = 15 × 3 = 45
⇒ b + c = 45 – 20 = 25 ---(ii)
By equation (i) - (ii),
a = 48 – 25 = 23
Aliter : Using Rule 16,
Here, n = 3, F = 16, L = 15
l = 20, f= ?
f – l= n (F – L)
f – 20= 3 (16 – 15)
f = 3 + 20
f = 23
Question : 2
The average of 13 results is 70. The average of first seven is 65 and that of the last seven is 75, the seventh result is :
a) 70
b) 70.5
c) 68
d) 67
Answer »Answer: (a)
Seventh observation
= 65 × 7 + 7 × 75 – 13 × 70
= 455 + 525 – 910
= 980 – 910 = 70
Aliter :
Here, n = 13, x = 70
m =7, y = 65
m = 7, z = 75
Seventh result = m (y + z) – nx
= 7 (65 + 75) – 13 × 70
= 7 × (140) – 910
= 980 – 910 = 70
Question : 3
The average of 20 numbers is 12. The average of the first 12 numbers is 11 and that of the next 7 numbers is 10. The last number is :
a) 38
b) 50
c) 48
d) 40
Answer »Answer: (a)
Using Rule 1,
Average of two or more numbers/quantities is called the mean of these numbers, which is given by
$\text"Average(A)" = \text"Sum of observation / quantities"/\text"No of observation / quantities"$
∴ S = A × n
Last number = Sum of 20 numbers
– sum of first 12 numbers – sum of next 7 numbers
= 20 × 12 – 11 × 12 – 7 × 10
= 240 – 132 – 70 = 38
Question : 4
The average of 8 numbers is 20. The average of first two numbers is 15$1/2$ and that of the next three is 21$1/3$. If the sixth number be less than the seventh and eighth numbers by 4 and 7 respectively, then the eighth number is :
a) 22
b) 27
c) 25
d) 18
Answer »Answer: (c)
Using Rule 1,
Sum of 8 numbers = 20 × 8 = 160
Sum of the first two numbers =$31/2$ ×2 = 31
Sum of next three numbers = $64/3$×3=64
Sum of the remaining three numbers = 160 – (31 + 64) = 160 – 95 = 65
Let 6th number = x
∴ 7th number = x + 4,
8th number = x + 7
⇒ x + x + 4 + x + 7 = 65
⇒ 3x = 65 – 11
⇒ x = $54/3$ =18
∴ Eighth number = 18 + 7 = 25
Question : 5
The average of nine numbers is 50. The average of the first five numbers is 54 and that of the last three numbers is 52. Then the sixth number is
a) 34
b) 44
c) 24
d) 30
Answer »Answer: (c)
Using Rule 1,
The sixth number
= 9 × 50 – 5 × 54 – 3 × 52
= 450 – 270 – 156 = 24
Question : 6
Average of n numbers is a. The first number is increased by 2, second one is increased by 4, the third one is increased by 8 and so on. The average of the new numbers is
a) a+2 ${2^{n} – 1}/n$
b) a+${2^{n }- 1}/n$
c) a+$2^{n-1} /n$
d) a+${2^{n-1} – 1}/n$
Answer »Answer: (a)
Sum of new numbers
= na + (2 + 4 + 8 + 16 ..... to n terms)
Now, S = 2 + 4 + 8 + 16 + ..... to n terms
Here, a = first term = 2
r = common ratio = $4/2$ = 2
It is a geometric series.
∴ S =${a({r^n} - 1)}/{r-1}$= ${2({2^n} - 1)}/{2-1}$
= 2 ($2^n$ –1)
∴ Required average
= ${na +2({2^n}-1)}/n$
a +${2({2^n}-1)}/n$
GET average PRACTICE TEST EXERCISES
model 1 basic average questions
model 2 average of consecutive numbers
model 3 twice, thrice, one third etc. of numbers
model 4 find nth average from 1st & last number
model 5 find new average from error
model 6 find average of excluded number
model 7 average on ages/weight
model 8 find monthly income
model 9 average on cricket/exam
average Shortcuts and Techniques with Examples
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model 1 basic average questions
Defination & Shortcuts … -
model 2 average of consecutive numbers
Defination & Shortcuts … -
model 3 twice, thrice, one third etc. of numbers
Defination & Shortcuts … -
model 4 find nth average from 1st & last number
Defination & Shortcuts … -
model 5 find new average from error
Defination & Shortcuts … -
model 6 find average of excluded number
Defination & Shortcuts … -
model 7 average on ages/weight
Defination & Shortcuts … -
model 8 find monthly income
Defination & Shortcuts … -
model 9 average on cricket/exam
Defination & Shortcuts …
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