The number of positive integers not exceeding 100 that are either odd or the…
2020
The number of positive integers not exceeding 100 that are either odd or the square of an integer is _______
- A.
63
- B.
59
- C.
55
- D.
50
Attempted by 91 students.
Show answer & explanation
Correct answer: C
Solution: Use inclusion–exclusion to count integers ≤ 100 that are odd or perfect squares.
Count odd numbers ≤ 100: 50 (all odd integers from 1 to 99).
Count perfect squares ≤ 100: 10 (1, 4, 9, 16, 25, 36, 49, 64, 81, 100).
Count numbers that are both odd and perfect squares: 5 (1, 9, 25, 49, 81).
Apply inclusion–exclusion: 50 + 10 − 5 = 55.
Answer: 55.
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