Let ABC be an isosceles triangle. Suppose that the sides AB and AC are equal and let the length of AB be x cm. Let b denote the angle ∠ABC and sin b = 3/5. If the area of the triangle ABC is M square cm, then which of the following is true about M?

Consider the function f(x) = (x + 4)(x + 6)(x + 8) ⋯ (x + 98). The number of integers x for which f(x) < 0 is:

If x² + x + 1 = 0, then x^2018 + x^2019 equals which of the following:

The figure below shows two right angled triangles ΔOAB and ΔOQP with right angles at vertex A and P, respectively, having the common vertex O. The lengths of some of the sides are indicated in the figure: OA = 3, AB = 1, OP = 2, PQ = 1. (Note that the figure is not drawn to scale…

We have two unknown positive integers m and n, whose product is less than 100. There are two additional statement of facts available: 1. mn is divisible by six consecutive integers {j, j + 1, ..., j + 5} 2. m + n is a perfect square. Which of the two statements above, alone or in…

What is the maximum number of points that can be placed on a circular disk of radius 1 metre (some of the points could be placed on the bounding circle of the disk) such that no two points are at a distance of less than 1 metre from each other?

A bag contains marbles of three colours – red, blue and green. There are 8 blue marbles in the bag. There are two additional statement of facts available: 1. If we pull out marbles from the bag at random, to guarantee that we have at least 3 green marbles, we need to extract 17 m…

In the picture below, EFGH, ABCD are squares, and ABE, BCF, CDG, DAH are equilateral triangles (each built outward on a side of ABCD, with apex at a corner of EFGH). What is the ratio of the area of the square EFGH to that of ABCD? [Figure: see page 16 of source PDF]

From the passage: The break-up of the students in a university by subject major is given...

How many students major in chemistry?