For a real number x, int(x) denotes integral part of x, that is int(x) is the…
2026
For a real number x, int(x) denotes integral part of x, that is int(x) is the largest integer less than or equal to x. The value of int(1/2)+int(1/ 2+1/100)+int(1/2+2/100)...... int(1/2+99/100) is
- A.
50
- B.
49
- C.
51
- D.
48
Attempted by 3 students.
Show answer & explanation
Correct answer: A
Key insight: int(x) is the floor (largest integer ≤ x).
Rewrite the sum as Σ int(1/2 + k/100) for k = 0 to 99.
Find when the inside reaches 1: 1/2 + k/100 ≥ 1 ⇒ k/100 ≥ 1/2 ⇒ k ≥ 50.
Therefore for k = 0,…,49 the floor is 0 (50 terms), and for k = 50,…,99 the floor is 1 (50 terms).
Sum = 0·50 + 1·50 = 50.