question:If X is the sum of first 20 positive even integers and Y is the sum of first 20 positive odd integers, what is the value of x-y?
Please try to explain your answers
Options:
(A) 0
(B) 20
(C) 50
(D) 75
(E) 100
answer:(B)
Stream of consciousness:First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
We can see the patterns here, so the sum of first 20 positive even integers minus the sum of first 20 positive odd integers will be 20.

question:Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 4 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
Options:
(A) 60 gallons
(B) 100 gallons
(C) 120 gallons
(D) 160 gallons
(E) 130 gallons
answer:(D)
Stream of consciousness:Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 4 gallonsVolume of whole = 4 * 40 = 160 gallons.

question:If x, y, and z are positive integers such that x is a factor of y and y is a factor of z, which of the following is NOT necessarily an integer?
Options:
(A) (x + y) /z
(B) (y + z) /x
(C) yz/x
(D) (2y + 3z) /x
(E) (xy + z) /y
answer:
(A)
Stream of consciousness:As per the question, let x = 2, y = 6, and z = 12. Plugging these into the answer choices, only A does not yield an integer.