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 marbles. 2. If we pull out marbles from the bag at random, to guarantee that we have at least 2 red marbles, we need to extract 19 marbles. Which of the two statements above, alone or in combination shall be sufficient to answer the question "how many green marbles are there in the bag"?

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…

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

How many students major in chemistry?

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

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:

From the passage: Given below is the time table for a trans-continental train that cuts...

Which of the following pairs of cities are in the same time zone?

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…

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?