There are 56 lights which are functional and each is controlled by a separate On/Off switch. Two children X and Y start playing with the switches. X starts by pressing every third switch till he reaches the end. Y, thereafter, presses every fifth switch till he too reaches the end. If all switches were in Off position at the beggining, How many lights are switched On by the end of this operation?  Choose the correct answer
A) 18	B) 19	C) 17	D) 15	E) 16

Rationale: editing my solution : number of switches = 56 number of switches turned on by x : 3 , 6 , . . . 54 = 18 number of switches turned on by y : 5 , 10 , . . . . 55 = 11 few switches are turned on by x and later turned off by y : lcm ( 35 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both x and y as they are turned off . number of switches that are turned on = ( 18 - 6 ) + ( 11 - 6 ) = 17 answer : c
Answer: C