q: The entire range of values of x is marked by the dark region on the number line, as shown above. Which of the following expressions describes the range of values of x?
Options:
(A) (3+x) (2x) 0
(B) (3x) (2+x) 0
(C) (x3) (x+2) 0
(D) (x+3) (2x) 0
(E) (3x) (2x) 0
a: Stream of consciousness: Given: x3x3 and x2 x2
(x+3)0(x+3)0 and (x2)0(x2)0
(x+3)0(x+3)0 and (2x)0(2x)0 The answer is (D).

question: A certain number when divided by 39 leaves a remainder 20, what is the remainder when the same number is divided by 13?
Options:
(A) 7
(B) 8
(C) 9
(D) 0
(E) 1
answer: Stream of consciousness: 39 + 20 = 59/13 = 7 (Remainder) The answer is (A).

q: Find the largest 4 digit number which isexactly divisible by 88?
Options:
(A) 5678
(B) 7654
(C) 9944
(D) 9950
(E) 10000
a: Stream of consciousness: Largest 4 digit number is 9999
After doing 9999 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 The answer is (C).

question: Find the value of y from (12)^3 x 6^4 432 = y?
Options:
(A) 4567
(B) 4689
(C) 5004
(D) 5678
(E) 5184
answer: Stream of consciousness: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62 The answer is (E).

q: A train 400 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
Options:
(A) 22 kmph
(B) 77 kmph
(C) 54 kmph
(D) 71 kmph
(E) 90 kmph
a: Stream of consciousness: S = 400/16 * 18/5 = 90 kmph The answer is (E).

q: The speed of a boat in still water is 70kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
(A) kmph
(B) kmph
(C) kmph
(D) kmph
(E) kmph
a:
Stream of consciousness: Speed downstream = 70 + 20 = 90 kmph
Speed upstream = 70 - 20 = 50 kmph The answer is (D).