Quantitative Aptitude - Arithmetic Ability Questions

The smallest value will be obtained by giving x the smallest possible value while y gets the largest possible value. The smallest value for x = 7. This means that y will have to be less than or equal to 3 (so that x + y <11), but we want the largest value of y which is 3.

The difference, x - y will be 4.

Let the required numbers be 33a and 33b. 

Then 33a +33b= 528   =>   a+b = 16.

Now, co-primes with sum 16 are (1,15) , (3,13) , (5,11) and (7,9).

Therefore, Required numbers are  ( 33 x 1, 33 x 15), (33 x 3, 33 x 13), (33 x 5, 33 x 11), (33 x 7, 33 x 9)

The number of such pairs is 4

To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces.
55 min. spaces gained in 60 min.

45 min. spaces are gained in 6055×45 min  or 49111min

A team of 6 members has to be selected from the 10 players. This can be done in 10C6 or 210 ways. 

Now, the captain can be selected from these 6 players in 6 ways.
Therefore, total ways the selection can be made is 210×6= 1260