question: An archer is shooting arrows from various distances. She shoots at a target from 30 yards, 40 yards, and 50 yards. The probability that she hits within the bullseye from 30 yards is 5/6, the probability that she hits within the bullseye from 40 yards is 4/5, and the probability that she hits within the bullseye from 50 yards is 3/4. What is the probability that she hits the bullseye at least once in three shots, one from each distance listed.
Options:
(A) 104/105
(B) 119/120
(C) 139/140
(D) 9/10
(E) 14/15
answer: Stream of consciousness: The probability that she hits the bullseye at least once = 1 - (the probability that she misses the bullseye every shot)
The probability that she misses all shots = (prob that she misses from 30 yards)*(prob that she misses from 40 yards)*(prob that she misses from 50 yards)
Prob that she misses from 30 yards = 1 - 5/6 = 1/6; Prob that she misses from 40 yards = 1 - 4/5 = 1/5; Prob that she misses from 50 yards = 1 - 3/4 = 1/4
Thus the probability that she misses all shots = (1/6)*(1/5)*(1/4) = 1/120
Thus the probability that she makes at least one shot = 1 - (1/120) = 119/120 The answer is (B).

q: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Options:
(A) 17 1/9
(B) 17 1/0
(C) 17 1/7
(D) 17 1/2
(E) 17 1/3
a: Stream of consciousness: 1/20 + 1/30 - 1/40 = 7/120
120/7 = 17 1/7 The answer is (C).

question: If P(A) = 6/17, P(B) = 5/17, and P(A B) = 4/17 Find P(B|A)?
Options:
(A) 2/3
(B) 3/5
(C) 2/7
(D) 3/7
(E) 4/9
answer: Stream of consciousness: P(B|A) = P(A B)/P(A)
P(B|A) = (4/17)/(6/17) = 4/6 = 2/3. The answer is (A).

q: A lady starts from P towards Q and realizes that at a point R, if he walks 50 km further he will be at a point S, which is as far away from R as it is from Q. What is the distance between P and Q if the distance between P and R is half the distance from R to Q?( Assume that P, Q, R and S are all on the same straight line)
Options:
(A) 150 km
(B) 200 km
(C) 250 km
(D) 125 km
(E) 155 km
a: Stream of consciousness: P___50_____ R ___50_____S____50 ___Q
The above figure gives the locations of P, R, S &Q in relation to each other. The answer is (A).

question: A 250 meter long train crosses a man standing on the platform in 12 sec. What is the speed of the train?
Options:
(A) 228
(B) 108
(C) 1266
(D) 75
(E) 211
answer: Stream of consciousness: S = 250/12 * 18/5 = 75kmph The answer is (D).

question: A train 260 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
(A) 40
(B) 32
(C) 26
(D) 21
(E) 14
answer:
Stream of consciousness: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 260 + 140 = 400 m
Required time = 400 * 2/25 = 32 sec The answer is (B).