If the length of an edge of cube P is twice the length of an edge of cube Q, what is the ratio of the volume of cube Q to the volume of cube P?
Options:
(A) 1/8
(B) 1/4
(C) 1/3
(D) 1/7
(E) 1/9
Answer and stream of consciousness: (A)
Stream of consciousness: The length of cube Q = 1;
The length of cube P = 2;
The ratio of the volume of cube Q to the volume of cube P = 1^3/2^3 = 1/8.


Count the two-digit whole numbers which yield a remainder of 5 when divided by 10 and also yield a remainder of 0 when divided by 3?
Options:
(A) Two
(B) Five
(C) Three
(D) One
(E) Six
Answer and stream of consciousness: (C)
Stream of consciousness: Answer = C) Three
Two digit Numbers giving remainder 5 when divided by 10 = 15, 25, 35, 45, 55, 65, 75, 85, 95
The numbers giving remainder 0 when divided by 3 = 15, 45, 75 = 3


How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
Options:
(A) Rs.482
(B) Rs.424
(C) Rs.842
(D) Rs.512
(E) Rs.524
Answer and stream of consciousness: (A)
Stream of consciousness: 20000(11/10)4 - 20000(6/5)2 = 482


If X is the sum of first 40 positive even integers and Y is the sum of first 40 positive odd integers, what is the value of x-y?
Please try to explain your answers
Options:
(A) 0
(B) 25
(C) 40
(D) 75
(E) 100
Answer and stream of consciousness:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
(C)
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 40 positive even integers minus the sum of first 40 positive odd integers will be 40.