q: What is the greatest positive integer x such that 2^x is a factor of 8^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
a: Stream of consciousness: 8^10 = (2^3)^10 = 2^30 The answer is (E).

question: a school has 4 maths 3 physics and 3 chemistry teachers each teacher can teach 2 subjects max what is he minimum number of teachers required
Options:
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
answer: Stream of consciousness: Total subjects = 4 +3 +3 = 10
Max subjects by 1 teacher = 2
So, min of teachers required = 10/2 = 5 The answer is (B).

q: The length T of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
Options:
(A) Decreases by 19%
(B) Decreases by 25%
(C) Increases by 6%
(D) Increases by 19%
(E) Increases by 25%
a: Stream of consciousness: Let the length T of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence The answer is (D).

question: If n is the greatest positive integer for which 4^n is a factor of 8!, then n =?
Options:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
answer: Stream of consciousness: 8! = 40320
E. 4^10 = 1048576 (40320/1048576) - this is not a factor of 8!
D. 4^8 = 65536 (40320/65536) - this is not a factor of 8!
C. 4^6 = 4096 (40320/4096) - this is not a factor of 8!
B. 4^4 = 256 (40320/256) - this is not a factor of 8!
A. 4^2 = 16 (40320/16) - this is a factor of 8! The answer is (A).

q: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Options:
(A) 7 1/8
(B) 7 1/6
(C) 7 1/5
(D) 7 1/2
(E) 7 1/1
a: Stream of consciousness: 70 + 50 = 120 * 5/18 = 100/3 mps
D = 150 + 100 = 250 m
T = 250 * 3/100 = 15/2 = 7 1/2 sec The answer is (D).

q: If M is the least positive integer that is divisible by every integer from 4 to 12 inclusive, then M/11 is =
Options:
(A) 40320
(B) 27720
(C) 20160
(D) 6720
(E) 2520
a:
Stream of consciousness: The integer should be divisible by: 4, 5, 6, 7, 8, 9, 10, 11 and 12, that is 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 3*2^2. The least common multiple of these integers is the product of 11, 7, 5, 3^2 and 2^3. Then, M/11 is (11 * 7 * 5 * 3^2 * 2^3)/11 = 7*5*9*8 = 2520. The answer is (E).