Quantitative Ap...

The equation x² −10x + 2[x] + 16 = x[x] where [x] denotes the greatest integer function. Choose the statement which best reflects the number of solutions x can have.

Two mutually perpendicular chords AB and CD meet at point P inside the circle such that AP = 12cm, PB = 8 units, and DP = 6 units. Calculate the perimeter of the circle.

A work is done by hiring some men and some boys. The work requires constructing a wall or breaking a wall. Each of these men or boys can either construct the wall or break the wall. During working, the speed of each man or boy to construct the wall is 10 times the speed of each man or boy respectively to break the wall. It is known that the speed of each man is the same and the speed of each boy is also the same and not equal to that of each man. One man & 7 boys can break the wall in 6 days while 1 man & 3 boys can build the wall in 1 day. In how many days will 1 man and 1 boy together break a wall?

Abhi wrote down several distinct positive integers, not exceeding 60. Their product was not divisible by 36. At most how many numbers could he have written?

The average of 8 numbers is 75. If the smallest number is deleted, then the average of the remaining numbers is A and if the largest number is deleted, then the average of the remaining numbers is B. If A + B = 90, then what is the average of the smallest and largest numbers?

In a race, cyclist X completes the race 20 meters ahead of cyclist Y, cyclist Y completes 15 meters ahead of cyclist Z, and cyclist X completes 33 meters ahead of cyclist Z. What is the total length of the race in meters?

A was born two years after B, who is four years old. At present, the average age (in years) of A, B, C and D is a perfect square. Also the difference between the ages of any two persons is not more than five years. Which of the following could be the ages of C and D (in years)?

The series A0, A1, A2, A3,......A0, A1, A2, A3,...... is a strictly increasing arithmetic progression of positive integers such that 

A cement trader bought cement for Rs.15 lakhs from a cement factory. Each day, he transports 12 lorry loads of cement from the factory to his godown at Rs.2,500 per lorry load. From the 11th day onwards, the factory charged him Rs.2,000 per day for using their godown. It took the trader 20 days to transport all the cement to his site. If the trader sold the cement to a retailer for Rs.26.5 lakhs, then what was his profit percentage?