q: The smallest number which when subtracted from the sum of squares of 11 and 13 gives a perfect square is
Options:
(A) 1
(B) 4
(C) 5
(D) 9
(E) 8
a: Stream of consciousness: 11^2 + 13^2 = 121 + 169 = 290
290 - 1 = 289 = 17^2
1 must be subtracted to give a perfect square. The answer is (A).

question: The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the numbers is 480, then the other is:
Options:
(A) 11
(B) 10
(C) 8
(D) 15
(E) 12
answer: Stream of consciousness: Other number = (12 x 600)/480 = 15. The answer is (D).

q: A dragon has 100 heads. A soldier can cut off 15, 17, 20 or 5 heads, respectively with one blow of his sword. In each of these cases, 24, 2, 14, 17 new heads grow on its shoulders. If all heads are cut off, the dragon dies. Can the dragon ever die?
Options:
(A) 61
(B) 3
(C) 5
(D) 6
(E) 1
a: Stream of consciousness: Here the difference in the cutoff heads and newly grown heads is 3. 100 is not divisible by 3. The dragon never die. The answer is (B).

question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
Options:
(A) 150 m
(B) 155 m
(C) 180 m
(D) 190 m
(E) 205 m
answer: Stream of consciousness: Answer: Option A
Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (distance) = speed * Time
(50/3) * 9 = 150 meter The answer is (A).

q: P can do a work in 24 days. Q can do the samework in 9 days & R can do the same work in 12 days. Q & R start the work and leave after 3 days. P finishes the remaining work in how many days.
Options:
(A) 8
(B) 10
(C) 14
(D) 16
(E) 19
a: Stream of consciousness: Work done by P in 1 day = 1/24
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 37/36 = 7/12
Remaining work = 1 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/24) = 10 The answer is (B).

q: A train running at the speed of 60 km/hr crosses a pole in 12 sec. What is the length of the train?
Options:
(A) 118
(B) 150
(C) 277
(D) 200
(E) 191
a:
Stream of consciousness: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 12 = 200 m The answer is (D).