Reasoning: On the first three flips, you must get heads. Whats the probability of getting heads ? Its 1/2
So for the first three flips, your probability is (1/2)^3 = 1/8
Now for the last two, you want to get tails only. Whats the prob of getting tails ? Well, its the same as prob of getting a heads, namely, 1/2
For the last two flips, your probability is (1/2)^2 = 1/4
So your overall probability for the event in question is 1/8*1/4 = 1/32
Ans: (E)
Question: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?
Options:
(A) 3/5
(B) 1/2
(C) 1/5
(D) 1/8
(E) 1/32
Rationale: (x - 1)! = (x - 2)! * (x-1)
(x - 1)!/(x-2)! = x - 1
The answer: (E)
Question: Which of the following is equal to (x-1)!/(x-2)!?
Options:
(A) x-1
(B) 1+(1/x) 
(C) 1
(D) x+1
(E) x-1
Reasoning: 3/6 * 32000 = 16000
5/6 * 32000 = 16000
Ans: (C)
Question: Divide Rs.32000 in the ratio 3:3?
Options:
(A) 12000, 20000
(B) 12000, 200098
(C) 16000, 16000
(D) 12000, 20006
(E) 12000, 20001
Rationale: 200 * 100 * 3 = 60000
The answer: (D)
Question: In digging a grave 200 m * 100 m * 3 m the volumes of the dirt to be extracted will be?
Options:
(A) 600 cu.m
(B) 12000 cu.m
(C) 6000 cu.m
(D) 60000 cu.m
(E) 4000 cu.m
Reasoning: 1 to 11 = 11 * 52 = 572
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 572 = 34
Ans: (B)
Question: The average of 11 results is 52, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
(A) A) 46
(B) B) 34
(C) C) 66
(D) D) 76
(E) E) 74
Reasoning: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 410 + 140 = 550 m
Required time = 550 * 2/25 = 44 sec
Ans: (E)

Question: A train 410 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) 87
(C) 26
(D) 21
(E) 44
Reasoning: On the first three flips, you must get heads. Whats the probability of getting heads ? Its 1/2
So for the first three flips, your probability is (1/2)^3 = 1/8
Now for the last two, you want to get tails only. Whats the prob of getting tails ? Well, its the same as prob of getting a heads, namely, 1/2
For the last two flips, your probability is (1/2)^2 = 1/4
So your overall probability for the event in question is 1/8*1/4 = 1/32
Ans: (E)
Question: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?
Options:
(A) 3/5
(B) 1/2
(C) 1/5
(D) 1/8
(E) 1/32
Rationale: (x - 1)! = (x - 2)! * (x-1)
(x - 1)!/(x-2)! = x - 1
The answer: (E)
Question: Which of the following is equal to (x-1)!/(x-2)!?
Options:
(A) x-1
(B) 1+(1/x) 
(C) 1
(D) x+1
(E) x-1
Reasoning: 3/6 * 32000 = 16000
5/6 * 32000 = 16000
Ans: (C)
Question: Divide Rs.32000 in the ratio 3:3?
Options:
(A) 12000, 20000
(B) 12000, 200098
(C) 16000, 16000
(D) 12000, 20006
(E) 12000, 20001
Rationale: 200 * 100 * 3 = 60000
The answer: (D)
Question: In digging a grave 200 m * 100 m * 3 m the volumes of the dirt to be extracted will be?
Options:
(A) 600 cu.m
(B) 12000 cu.m
(C) 6000 cu.m
(D) 60000 cu.m
(E) 4000 cu.m
Reasoning: 1 to 11 = 11 * 52 = 572
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 572 = 34
Ans: (B)
Question: The average of 11 results is 52, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
(A) A) 46
(B) B) 34
(C) C) 66
(D) D) 76
(E) E) 74
Reasoning: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 410 + 140 = 550 m
Required time = 550 * 2/25 = 44 sec
Ans: (E)

user
Question: A train 410 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) 87
(C) 26
(D) 21
(E) 44
assistant
Reasoning: On the first three flips, you must get heads. Whats the probability of getting heads ? Its 1/2
So for the first three flips, your probability is (1/2)^3 = 1/8
Now for the last two, you want to get tails only. Whats the prob of getting tails ? Well, its the same as prob of getting a heads, namely, 1/2
For the last two flips, your probability is (1/2)^2 = 1/4
So your overall probability for the event in question is 1/8*1/4 = 1/32
Ans: (E)
Question: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?
Options:
(A) 3/5
(B) 1/2
(C) 1/5
(D) 1/8
(E) 1/32
Rationale: (x - 1)! = (x - 2)! * (x-1)
(x - 1)!/(x-2)! = x - 1
The answer: (E)
Question: Which of the following is equal to (x-1)!/(x-2)!?
Options:
(A) x-1
(B) 1+(1/x) 
(C) 1
(D) x+1
(E) x-1
Reasoning: 3/6 * 32000 = 16000
5/6 * 32000 = 16000
Ans: (C)
Question: Divide Rs.32000 in the ratio 3:3?
Options:
(A) 12000, 20000
(B) 12000, 200098
(C) 16000, 16000
(D) 12000, 20006
(E) 12000, 20001
Rationale: 200 * 100 * 3 = 60000
The answer: (D)
Question: In digging a grave 200 m * 100 m * 3 m the volumes of the dirt to be extracted will be?
Options:
(A) 600 cu.m
(B) 12000 cu.m
(C) 6000 cu.m
(D) 60000 cu.m
(E) 4000 cu.m
Reasoning: 1 to 11 = 11 * 52 = 572
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 572 = 34
Ans: (B)
Question: The average of 11 results is 52, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
(A) A) 46
(B) B) 34
(C) C) 66
(D) D) 76
(E) E) 74
Reasoning: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 410 + 140 = 550 m
Required time = 550 * 2/25 = 44 sec
Ans: (E)

Question: A train 410 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) 87
(C) 26
(D) 21
(E) 44