XAT PYQs 2025

There are 25 rooms in a hotel. Each room can accommodate at most three people. For each room, the single occupancy charge is Rs. 2000 per day, the double occupancy charge is Rs. 3000 per day, and the triple occupancy charge is Rs. 3500 per day.

Q.If there are 55 people staying in the hotel today, what is the maximum possible revenue from room occupancy charges today?

Ramesh bought a mobile from a local store. He paid 1/6 of the price via UPI and 1/3 of the price via cash. He agreed to pay the balance amount a year later. While paying back the balance amount, Ramesh paid 10% interest on the balance amount.

Q.If the interest paid was Rs. 6000, what was the original price of the mobile?

Adu and Amu have bought two pieces of land on the Moon from an e-store. Both the pieces of land have the same perimeters, but Adu’s piece of land is in the shape of a square, while Amu’s piece of land is in the shape of a circle.

Q.The ratio of the areas of Adu’s piece of land to Amu’s piece of land is:

The market value of beams, made of a rare metal, has a unique property: the market value of any such beam is proportional to the square of its length. Due to an accident, one such beam got broken into two pieces having lengths in the ratio 4:9.

Q.Considering each broken piece as a separate beam, how much gain or loss, with respect to the market value of the original beam before the accident, is incurred?

ABCD is a rectangle, where the coordinates of C and D are (−2,0) and (2,0), respectively.

Q.If the area of the rectangle is 24, which of the following is a possible equation representing the line AB?

Consider the quadratic function f(x) = ax² + bx + a  having two irrational roots, with a and b being two positive integers, such that  a,b < 9. If all such permissible pairs (a,b)are equally likely, what is the probability that a + b is greater than 9?

A farmer has a quadrilateral parcel of land with a perimeter of 700 feet. Two opposite angles of that parcel of land are right angles, while the remaining two are not. The farmer wants to do organic farming on that parcel of land. The cost of organic farming is Rs. 400 per square foot.

Consider the following two additional pieces of information:

The length of one of the sides of that parcel of land is 110 feet.

The distance between the two corner points where the non-perpendicular sides of that parcel of land intersect is 265 feet.

Q.To determine the amount of money the farmer needs to spend to do organic farming on the entire parcel of land, which of the above additional pieces of information are MINIMALLY SUFFICIENT?

A straight line L₁ has the equation y = k(x - 1), where k is some real number. The straight line L₁ intersects another straight line L₂ at the point (5, 8).

Q.If L₂ has a slope of 1, which of the following is definitely FALSE?

For how many distinct real values of x does the equation below hold true? (Consider a > 0)

In a computer game, each move requires pressing a button. When the button is pressed for the first time, as a move, the computer randomly chooses a cell from a 4x4 grid of sixteen cells and puts an "X" mark on that cell. When the button is pressed subsequently, the computer randomly chooses a cell from the remaining unmarked cells and puts an "X" mark on that cell. This goes on till the end of the game. The game ends when either all the cells in any one row, or all the cells in any one column, are marked with "X".

Q.What is the maximum possible number of times a player has to press the button to finish the game?