Practice Find nth term - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) Out of seven given numbers, the average of the first four numbers is 4 and that of the last four numbers is also 4. If the average of all the seven numbers is 3, fourth number is
(a)
(b)
(c)
(d)
Using Rule 1,
Average of two or more numbers/quantities is called the mean of these numbers, which is given by
$\text"Average(A)" = \text"Sumof observation / quantities"/\text"No of observation / quantities"$
∴ S = A × n
Fourth number
= (4×4+4×4 – 3×7)
= (16 +16-21) = 11
Q-2) The average of two numbers is 8 and the average of other three numbers is 3. The average of the five numbers is :
(a)
(b)
(c)
(d)
Average of five numbers
= ${2×8+3×3}/{2+3}$
= ${16+ 9}/5$ = $25/5$ = 5
Q-3) 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)
(b)
(c)
(d)
Using Rule 1,
The sixth number
= 9 × 50 – 5 × 54 – 3 × 52
= 450 – 270 – 156 = 24
Q-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)
(b)
(c)
(d)
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
Q-5) The average of three numbers is 135. The largest number is 195 and the difference between the other two is 20. The smallest number is
(a)
(b)
(c)
(d)
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
Q-6) 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)
(b)
(c)
(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
Q-7) 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)
(b)
(c)
(d)
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
Q-8) Out of four numbers, the average of the first three is 15 and that of the last three is 16. If the last number is 19, the first is
(a)
(b)
(c)
(d)
Using Rule 1,
a + b + c = 45 and
b + c + d = 48
⇒ b + c = 48 – 19 = 29
∴ a + b + c = 45
⇒ a = 45 – 29 = 16
Q-9) Out of four numbers, the average of the first three is 18 and that of the last three is 16. If the last number is 19, the first is
(a)
(b)
(c)
(d)
Using Rule 1,
Average of two or more numbers/quantities is called the mean of these numbers, which is given by
$\text"Average(A)" = \text"Sumof observation / quantities"/\text"No of observation / quantities"$
∴ S = A × n
a + b + c = 18 × 3 = 54
and, b + c + d = 16 × 3 = 48
∴ a + b + c – b – c – d
⇒ 54 – 48 = 6
⇒ a – d = 6
⇒ a – 19 = 6
⇒ a = 19 + 6 = 25
Q-10) The average of 30 numbers is 12. The average of the first 20 of them is 11 and that of the next 9 is 10. The last number is
(a)
(b)
(c)
(d)
Using Rule 1,
Average of two or more numbers/quantities is called the mean of these numbers, which is given by
$\text"Average(A)" = \text"Sumof observation / quantities"/\text"No of observation / quantities"$
∴ S = A × n
Last number
= 30 × 12 – 20 × 11 – 9 × 10
= 360 – 220 – 90
= 360 – 310 = 50