f is a function for which f(1) = 1 and f(x) = 2x + f(x - 1) for each natural number x ≥ 2. Find f(31)

Consider the set of numbers {1, 3, 3², 3³, ..., 3¹⁰⁰}. The ratio of the last number and the sum of the remaining numbers is closest to:

Two numbers in the base system B are 2061_B and 601_B. The sum of these two numbers in decimal system is 432. Find the value of 1010_B in decimal system.

Rani bought more apples than oranges. She sells apples at Rs. 23 apiece and makes 15% profit. She sells oranges at Rs. 10 apiece and makes 25% profit. If she gets Rs. 653 after selling all the apples and oranges, find her profit percentage.

A water tank has M inlet pipes and N outlet pipes. An inlet pipe can fill the tank in 8 hours while an outlet pipe can empty the full tank in 12 hours. If all pipes are left open simultaneously, it takes 6 hours to fill the empty tank. What is the relationship between M and N?

Anita, Biplove, Cheryl, Danish, Emily and Feroze compared their marks among themselves. Anita scored the highest marks, Biplove scored more than Danish. Cheryl scored more than at least two others and Emily had not scored the lowest. Statement I: Exactly two members scored less t…

Company ABC starts an educational program in collaboration with Institute XYZ. As per the agreement, ABC and XYZ will share profit in 60 : 40 ratio. The initial investment of Rs. 100,000 on infrastructure is borne entirely by ABC whereas the running cost of Rs. 400 per student is…

Akhtar plans to cover a rectangular floor of dimensions 9.5 meters and 11.5 meters using tiles. Two types of square shaped tiles are available in the market. A tile with side 1 meter costs Rs. 100 and a tile with side 0.5 meters costs Rs. 30. The tiles can be cut if required. Wha…

Study the figure below and answer the question: (Figure: triangle ABD with C on AD between A and D, and segment BC.) [Figure: see page 17 of source PDF] Four persons walk from Point A to Point D following different routes. The one following ABCD takes 70 minutes. Another person t…