Question:medium

For any natural Number 'n', let a_n be the largest number not exceeding \(\sqrt{n}\) , then a1 + a2 + a3... +a50 =

Updated On: Nov 24, 2025

Top Questions on Number Systems

Arun selected an integer \( x \) between 2 and 40, both inclusive. He noticed that the greatest common divisor of the selected integer \( x \) and any other integer between 2 and 40, both inclusive, is 1. How many different choices for such an \( x \) are possible?
- XAT - 2025
- Quantitative Ability and Data Interpretation
- Number Systems
View Solution
A king has distributed all his rare jewels in three boxes. The first box contains 1/3 of the rare jewels, while the second box contains k/5 of the rare jewels, for some positive integer value of k. The third box contains 66 rare jewels.
How many rare jewels does the king have?
- XAT - 2024
- Quantitative Ability and Data Interpretation
- Number Systems
View Solution
Consider a 4-digit number of the form abbb, i.e., the first digit is a (a > 0) and the last three digits are all b.
Which of the following conditions is both NECESSARY and SUFFICIENT to ensure that the 4- digit number is divisible by a?
- XAT - 2024
- Quantitative Ability and Data Interpretation
- Number Systems
View Solution
The roots of the polynomial are the radii of three concentric circles. \(P(x) = 2x^3-11x^2 +17x-6.\) The ratio of their area, when arranged from the largest to the smallest, is:
- XAT - 2024
- Quantitative Ability and Data Interpretation
- Number Systems
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in CAT exam

Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayana in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayana on the second day, Mohit and Ayana on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is

CAT - 2024
Time and Work

The midpoints of sides AB, BC, and AC in ∆ABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of ∆ABC is 1440 sq cm, then the area, in sq cm, of ∆XYZ is

CAT - 2024
Mensuration

Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is

CAT - 2024
Profit and Loss

For some constant real numbers p, k and a, consider the following system of linear equations in x and y:
px - 4y = 2
3x + ky = a
A necessary condition for the system to have no solution for (x, y), is

CAT - 2024
System of Linear Equations