2017 · Q4
If x=111…1 (20 digits) , y=333…3 (10 digits) and z=222…2 (10 digits) ,then what is (x-y²)/z equal to ?
Elementary MathematicsNumber System
- A1/2
- B1
- C2
- D3
Explanation
Write the repunits as powers of 10: x = (10²⁰−1)/9, y = 3(10¹⁰−1)/9 = (10¹⁰−1)/3, z = 2(10¹⁰−1)/9. Then x−y² = [(10²⁰−1)−(10¹⁰−1)²]/9 = [10²⁰−1−10²⁰+2·10¹⁰−1]/9 = 2(10¹⁰−1)/9. Dividing by z gives [2(10¹⁰−1)/9]/[2(10¹⁰−1)/9] = 1. Hence option (B) 1.