Competitive Exam PYQ : 1
Q. What is the average of all natural numbers from 1 to 95 ?
Solution:
Numbers: 1,2,3,4,…,95
Trick
For consecutive numbers:
Average = First number + Last number / 2 = 1+95/2 = 96/2 = 48
Ans: (D) 48
Note:
For numbers from 1 to n:
Average = n+1/2
For n = 95:
Q. What is the average of all natural numbers from 1 to 95 ?
Solution:
1, 2, 3, 4, ........, 95
Formula:
Ans: (D) 48
Trick
For consecutive natural numbers from 1 to n:
Here, n = 95:
Ans: 48
Q. What is the average of the first 9 prime numbers ?
Solution:
The first 9 prime numbers are:
1st: Find the sum :
2nd: Find the average
Ans: 11.11
Trick
Average = Sum ÷ Number of terms
Q. The average of odd numbers up to 100 is:
Solution:
Odd numbers up to 100 are: 1,3,5,7,…,99
Since these are consecutive odd numbers, use: Average = First term + Last term/2 = 1 + 99/2 = 100/2 = 50
Ans: (B) 50
Trick
For consecutive odd numbers: Average = First Odd + Last Odd / 2
So,
= 1+99 /2 = 100/2 = 50
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Q. What is the average of the first 30 natural numbers ?
The first 30 natural numbers are:
Trick
For consecutive numbers:
Ans: (A) 15.5
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Q.Find the average of the first 10 composite numbers.
(A) 11.2 (B) 12.9 (C) 10.2 (D) 11.5
Solution:
The first 10 composite numbers are: 4,6,8,9,10,12,14,15,16,18
Sum: 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18= 112
Average:
Average = 112/10 = 11.2
Ans: (A) 11.2
Shortcut:
Percentage – Quick Trick
Q. If the side of a square is increased by 20%, by what percentage will its perimeter increase ?
Soln
Let the original side = 100
Original perimeter: 4 × 100 = 400
New side: 100 + 20% = 120
New perimeter: 4 × 120 = 480
Increase: 480 − 400 = 80
Percentage increase: 80/400 × 100 = 20%
Trick
For a square, perimeter is directly proportional to its side. Side increases by 20% ⇒ Perimeter also increases by 20%
Ans: 20%
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