△ABC and △XYZ are equilateral triangles of 54 cm sides. All smaller triangles like △ANM, △OCP, △QPX etc. are also equilateral triangles. Find the area of the shape MNOPQRM. (Figure: two overlapping equilateral triangles forming a six-pointed star; MNOPQR is the central hexagon.) [Figure: see page 16 of source PDF]

In an amusement park, a visitor gets to ride on three different rides (A, B and C) for free. On a particular day 77 opted for ride A, 55 opted for B and 50 opted for C; 25 visitors opted for both A and C, 22 opted for both A and B, while no visitor opted for both B and C. 40 visi…

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…

In the figure below, AB = AC = CD. If ∠ADB = 20°, what is the value of ∠BAD? (Figure: triangle ABD with C on BD between B and D.) [Figure: see page 16 of source PDF]

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…

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.

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:

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)

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.