XAT 2023 QADI Previous Year Questions with Detailed Solutions

Amit has forgotten his 4-digit locker key. He remembers that all the digits are positive integers and are different from each other. Moreover, the fourth digit is the smallest and the maximum value of the first digit is 3. Also, he recalls that if he divides the second digit by the third digit, he gets the first digit. How many different combinations does Amit have to try for unlocking the locker?

The problem below consists of a question and two statements numbered 1 & 2.

You have to decide whether the data provided in the statements are sufficient to answer the question.

Rahim is riding upstream on a boat, from point A to B, at a constant speed. The distance from A to B is 30 km. One minute after Rahim leaves from point A, a speedboat starts from point A to go to point B. It crosses Rahim’s boat after 4 minutes. If the speed of the speedboat is constant from A to B, what is Rahim’s speed in still water?

1. The speed of the speedboat in still water is 30 km/hour.

2. Rahim takes three hours to reach point B from point A.

Rajnish bought an item at 25% discount on the printed price. He sold it at 10% discount on the printed price. 

What is his profit in percentage?

The problem below consists of a question and two statements numbered 1 & 2.

You have to decide whether the data provided in the statements are sufficient to answer the question.

In a cricket match, three slip fielders are positioned on a straight line. The distance between 1st slip and 2nd slip is the same as the distance between 2nd slip and the 3rd slip. The player X, who is not on the same line of slip fielders, throws a ball to the 3rd slip and the ball takes 5 seconds to reach the player at the 3rd slip. If he had thrown the ball at the same speed to the 1st slip or to the 2nd slip, it would have taken 3 seconds or 4 seconds, respectively. What is the distance between the 2nd slip and the player X?

1. The ball travels at a speed of 3.6 km/hour.

2. The distance between the 1st slip and the 3rd slip is 2 meters.

Given \(A = |x+3| + |x-2| - |2x-8|\).

The maximum value of |A| is:

ABC is a triangle with BC = 5 .D is the foot of the perpendicular from A on BC. E is a point on CD such that BE=3. The value of \(AB^2 - AE^2\)−AE2+6CD is:

The addition of 7 distinct positive integers is 1740. 

What is the largest possible “greatest common divisor” of these 7 distinct positive integers?

Jose borrowed some money from his friend at simple interest rate of 10% and invested the entire amount in stocks. At the end of the first year, he repaid 1/5th of the principal amount. At the end of the second year, he repaid half of the remaining principal amount. At the end of third year, he repaid the entire remaining principal amount. At the end of the fourth year, he paid the last three years’ interest amount. As there was no principal amount left, his friend did not charge any interest in the fourth year. At the end of fourth year, he sold out all his stocks. Later, he calculated that he gained Rs. 97500 after paying principal and interest amounts to his friend. If his invested amount in the stocks became double at the end of the fourth year, how much money did he borrow from his friend?

The Guava club has won 40% of their football matches in the Apple Cup that they have played so far. If they play another n matches and win all of them, their winning percentage will improve to 50. Further, if they play 15 more matches and win all of them, their winning percentage will improve from 50 to 60. How many matches has the Guava club played in the Apple Cup so far? In the Apple Cup matches, there are only two possible outcomes, win or loss; draw is not possible.

Find the value of: \[ \frac{\sin^6 15^\circ+\sin^6 75^\circ+6\sin^2 15^\circ\sin^2 75^\circ} {\sin^4 15^\circ+\sin^4 75^\circ+5\sin^2 15^\circ\sin^2 75^\circ} \]