Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is

A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stoc…

How many distinct positive integer-valued solutions exist to the equation (x² − 7x + 11)^(x² − 13x + 42) = 1?

The mean of all 4-digit even natural numbers of the form ‘aabb’, where a > 0, is

The number of real-valued solutions of the equation 2^x + 2^(−x) = 2 − (x − 2)² is

In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old people among the illiterates is nearest to

How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

A person spent Rs. 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profit and the laptop at 10% loss. If overall he made a 2% profit then the purchase price, in rupees, of the desktop is

A solution, of volume 40 litres, has dye and water in the proportion 2 : 3. Water is added to the solution to change this proportion to 2 : 5. If one-fourths of this diluted solution is taken out, how many litres of dye must be added to the remaining solution to bring the proport…