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3 votes
3 votes

The number of positive integers not exceeding $100$ that are either odd or the square of an integer is _______

  1. $63$
  2. $59$
  3. $55$
  4. $50$
in Set Theory & Algebra recategorized by
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3 Answers

3 votes
3 votes

Required numbers = n(Odd numbers) + n(Square of integers) – n(odd number & square of integer)

From $1$ to $100$ there are $50$ odd and $50$ even numbers

Square of integers = $1,4,9,16,25,64,49,64,81,100$ = $10$ numbers

Both odd & square of integer= $1,9,25,49,81 = 5$ numbers

Hence required numbers= $50+10-5 = 55$

1 vote
1 vote
total number=100

odd=even=total/2=100/2=50

square number=1,4,9,16,25,36,49,64,81,100

total square number=10

odd and square =1,9,25,49,81

required number=50+10-5

ans=55
0 votes
0 votes
Number of odd numbers between 1 and 100 is 50 and even squares are 4,16,36,64,100 so the answer is 55 for this.
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