Ramesh and Reena are playing with triangle ABC. Ramesh draws a line that bisects ∠BAC; this line cuts BC at D. Reena then extends AD to a point P. In response, Ramesh joins B and P. Reena then announces that BD bisects ∠PBA, what a surprise! Together, Ramesh and Reena find that BD = 6 cm, AC = 9 cm, DC = 5 cm, BP = 8 cm, and DP = 5 cm. How long is AP?

Some members of a social service organization in Kolkata decide to prepare 2400 laddoos to gift to children in various orphanages and slums in the city, during Durga puja. The plan is that each of them makes the same number of laddoos. However, on the laddoo-making day, ten membe…

Sheela purchases two varieties of apples - A and B - for a total of Rupees 2800. The weights in kg of A and B purchased by Sheela are in the ratio 5 : 8 but the cost per kg of A is 20% more than that of B. Sheela sells A and B with profits of 15% and 10% respectively. What is the…

A supplier receives orders from 5 different buyers. Each buyer places their order only on a Monday. The first buyer places the order after every 2 weeks, the second buyer, after every 6 weeks, the third buyer, after every 8 weeks, the fourth buyer, every 4 weeks, and the fifth bu…

A marble is dropped from a height of 3 metres onto the ground. After hitting the ground, it bounces and reaches 80% of the height from which it was dropped. This repeats multiple times. Each time it bounces, the marble reaches 80% of the height previously reached. Eventually, the…

The sum of the cubes of two numbers is 128, while the sum of the reciprocals of their cubes is 2. What is the product of the squares of the numbers?

Nadeem’s age is a two-digit number X, squaring which yields a three-digit number, whose last digit is Y. Consider the statements below: Statement I: Y is a prime number. Statement II: Y is one-third of X. To determine Nadeem’s age uniquely:

A tall tower has its base at point K. Three points A, B and C are located at distances of 4 metres, 8 metres and 16 metres respectively from K. The angles of elevation of the top of the tower from A and C are complementary. What is the angle of elevation (in degrees) of the tower…

From the passage: The enrolment of students (in 1000s) at each of the five universities...

Which of the five universities can Univ 4 possibly be?