q: 189. The inside dimensions of a rectangular wooden box
are 2 inches by 4 inches by 6 inches. A cylindrical
canister is to be placed inside the box so that it stands
upright when the closed box rests on one of its six
faces. Of all such canisters that could be used, what is
the radius, in inches, of the one that has maximum
volume?
Options:
(A) 2
(B) 4
(C) 5
(D) 6
(E) 8
a: Stream of consciousness: Since the radius is squared, the biggest volume cylinder will have the biggest possible radius. To achieve that, let the smaller dimension of the rectangular box be the height. So, it will have 6x4 width x length. The biggest cylinder must fit both dimensions, so it must have at most a diameter of 4, so the radius will be 2. The answer is (A).

question: The floor of a rectangular room is 18 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is :
Options:
(A) 124 m2
(B) 126 m2
(C) 136 m2
(D) 158 m2
(E) None of these
answer: Stream of consciousness: Area of the outer rectangle = 22 16 = 352 m2
Area of the inner rectangle = 18 12 = 216 m2
Required area = (352 216) = 136 m2 The answer is (C).

q: A daughter lent $750 to her mother to help pay her rent. At the end of the month, the daughter received y dollars more than than the amount that was lent due to interest. The mother also gave her daughter an additional $5 for goodwill. In terms of y, what fraction of the total amount that the daughter received was the goodwill amount?
Options:
(A) (5y-1) /(755-y)
(B) 5/(755+y)
(C) 5y/(755+y) -1
(D) 5y/(755+y)
(E) 5y
a: Stream of consciousness: The amount of money the daughter received was (750 + 5+ y) dollars. The $5 goodwill gift as a fraction of the amount received was, therefore, 5/(755+y). The answer is (B).

question: 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) 22 kmph
(B) 40 kmph
(C) 78 kmph
(D) 50 kmph
(E) 23 kmph
answer: Stream of consciousness: Speed downstream = 70 + 20 = 90 kmph
Speed upstream = 70 - 20 = 50 kmph The answer is (D).

q: Look at this series: 72, 76, 73, 77, 74, __, 75, ... What number should fill the blank?
Options:
(A) 70
(B) 71
(C) 75
(D) 78
(E) 74
a: Stream of consciousness: There will be 2 series
1st: 72 73 74 75 76 (Increasing by 1)
2nd: 76 77 78 79 (Increasing by 1)
Final: 72 76 73 77 74 78 75 The answer is (D).

q: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
(A) 22
(B) 88
(C) 27
(D) 89
(E) 287
a:
Stream of consciousness: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27 The answer is (C).