In 2 bags, there are to be put together 5 red and 12 white balls, neither bag being empty. How must the balls be divided so as to give a person who draws 1 ball from either bag-
Options:
(A) 9/18
(B) 9/16
(C) 9/11
(D) 9/12
(E) 9/13

(1) Put 1 white in first bag, and all the remaining ball in second bag. Probability = 12×0+12×51612×0+12×516 = 532532
(2) To maximize, we put 1 red in the first bag, and all the remaining in the second. Probability = 12×1+12×43212×1+12×432 = 9/16 So the answer is: (B).

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

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. So the answer is: (A).

A no.when divided by 242 gives a remainder 100, what remainder will be obtainedby dividingthe same no.18?
Options:
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19

242 + 100 = 342/18 = 19 (Remainder) So the answer is: (E).

If X is the sum of first 100 positive even integers and Y is the sum of first 100 positive odd integers, what is the value of x-y?
Please try to explain your answers
Options:
(A) 0
(B) 25
(C) 50
(D) 75
(E) 100


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 100 positive even integers minus the sum of first 100 positive odd integers will be 100. So the answer is: (E).