Aman decides to buy only onion and potato, both in positive integer kilogram, in such a way that the money left with him after the purchase will be insufficient to buy a full kilogram of either of the two vegetables. If all such permissible combinations of purchases are equally likely, what is the probability that Aman buys more onion than potato?

From the passage: 41 applicants have been shortlisted for interviews for some data analy...

What BEST can be concluded about the value of x?

A king has distributed all his rare jewels in three boxes. The first box contains 1/3 of the rare jewels, while the second box contains k/5 of the rare jewels, for some positive integer value of k. The third box contains 66 rare jewels. How many rare jewels does the king have?

Consider a right-angled triangle ABC, right angled at B. Two circles, each of radius r, are drawn inside the triangle in such a way that one of them touches AB and BC, while the other one touches AC and BC. The two circles also touch each other (see the image below). If AB = 18 c…

From the passage: The upper hinge of a dataset is the median of all the values to the ri...

Which of the following is a possible value of B?

Consider a 4-digit number of the form abbb, i.e., the first digit is a (a > 0) and the last three digits are all b. Which of the following conditions is both NECESSARY and SUFFICIENT to ensure that the 4-digit number is divisible by a?

Consider the system of two linear equations as follows: 3x + 21y + p = 0; and qx + ry – 7 = 0, where p, q, and r are real numbers. Which of the following statements DEFINITELY CONTRADICTS the fact that the lines represented by the two equations are coinciding?

A local restaurant has 16 vegetarian items and 9 non-vegetarian items in their menu. Some items contain gluten, while the rest are gluten-free. One evening, Rohit and his friends went to the restaurant. They planned to choose two different vegetarian items and three different non…

The roots of the polynomial P(x) = 2x³ − 11x² + 17x + 6 are the radii of three concentric circles. The ratio of their area, when arranged from the largest to the smallest, is: