For real number x, int(x) denotes integer part of x.int(x) is the largest…
2026
For real number x, int(x) denotes integer part of x.int(x) is the largest integer less than or equal to x.int(1,2)=1,int(-2,4)=-3.
Find the value of int(1/2)+int(1/2+ 100)+int(1/2+2/100)+....+int(1/2+99/100)
- A.
350
- B.
150
- C.
200
- D.
280
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Interpretation of the terms:
We evaluate the floors of the numbers: floor(1/2), floor(1/2 + 100), floor(1/2 + 2/100), …, floor(1/2 + 99/100).
floor(1/2) = 0.
floor(1/2 + 100) = floor(100.5) = 100.
For k = 2,3,…,49, each term floor(1/2 + k/100) < 1, so these terms equal 0.
For k = 50,51,…,99, each term satisfies 1.0 ≤ 1/2 + k/100 < 2, so floor(1/2 + k/100) = 1. There are 50 such values of k.
Summing contributions:
Large term: 100
Ones from fractional terms: 50 × 1 = 50
Zeros from other terms: contribute 0
Total = 100 + 50 = 150.
Note: the original solution had a typographical ambiguity but the corrected step-by-step evaluation above shows why the sum equals 150.