InfyTQ Averages Quiz 4

Solution:
Average of squares of first 'n' natural numbers = \frac{(n+1)(2n+1)}{6}
Here, n= 6
Therefore,
Average of the squares of natural numbers from 1 to 6 = \frac{(6+1)(2\times 6+1)}{6}

=\frac{7 \times 13}{6} = 15.16

Solution:
Average of cubes of first 'n' natural numbers = \frac{n(n+1)^{2}}{4}
Here, n= 4
Therefore,
Average of the cubes of natural numbers from 1 to 4 =\frac{4(4+1)^{2}}{4} = 25

Solution:
Let number of innings be N.
Since increase in average is by 2 runs (from 68 to 70), runs in each innings would
increase by 2 runs
Total increase in runs = 2 x N = 2N
Also, Sachin needs to score 22 runs more to increase average.
∴ 2N = 22
∴ N = 11 = Number of innings

Solution:

Sum of Averages all 6 Numbers = 6 x 18 = 108

Sum of Averages First 3 Numbers = 3 x 6 = 18

Sum of Averages of Last 3 Numbers = 108-18 = 90

∴ Average of the Last 3 numbers = \frac{90}{3} = 30

Solution:
Total of 8 tests = 8x83 = 664
Total of first 5 tests = 5x89 = 445
Total of last 3 tests = 664-445 =219
Average of last 3 tests = \frac{219}{3} = 73

Solution:

33+46+27+M = 35+35+35+35

M = 34

Solution:

Average after 13 innings should be 23

So, required score = (13x23) – (12x18)

= 83

Solution:

Sum of all the ages of father and his sons = 12x7 = 84

Sum of all the ages of sons = (12-5) x 6 = 42

Age of father = 84 – 42 = 42 years

 

Solution:
Prime numbers between 10 and 30 are 11, 13,17,19,23, and 29
Average of prime numbers between 10 and 30 will be =\frac {(11+13+17+19+23+29)}{6}

=18.67

Solution:
Average = \frac{(55+5)}{2} =\frac{60}{2}= 30