question: What number comes next in the following number series? 12, 50, 202, 810, 3242, _____
Options:
(A) 12400
(B) 12800
(C) 12970
(D) 13015
(E) 16000
answer: Stream of consciousness: 12
12 × 4 + 2 = 50
50 × 4 + 2 = 202
202 × 4 + 2 = 810
810 × 4 + 2 = 3242
3242 × 4 + 2 = 12970 The answer is (C).


q: Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter?
Options:
(A) Rs.1185
(B) Rs.1285
(C) Rs.1385
(D) Rs.1485
(E) Rs.1495
a: Stream of consciousness: 22/7 * 14 * 3/2 * 3/2 = 99 m2
99 * 15 = 1485 The answer is (D).


question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
(A) 3:5
(B) 4:5
(C) 2:5
(D) 2:4
(E) 2:7
answer: Stream of consciousness: T = 160/32 = 5 h
T = 5 - 3 = 2
Time Ratio = 5:2
Speed Ratio = 2:5 The answer is (C).


q: There are 10 female and 15 male in a work place. In how many ways can a person can be selected?
Options:
(A) 20
(B) 15
(C) 18
(D) 40
(E) 25
a: Stream of consciousness: No of ways = 10+ 15 = 25 The answer is (E).


question: Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 10 km/hr downstream and 4 km/hr upstream.
Options:
(A) 7 kmph
(B) 8 kmph
(C) 9 kmph
(D) 7 kmph
(E) 6 kmph
answer: Stream of consciousness: Speed in still water = (10 + 4)1/2 kmph = 7 kmph. The answer is (A).


question: If f(x) = x^3/(x^4 - 1), what is f(1/x) in terms of f(x)?
Options:
(A) -f(x) 
(B) f(x) 
(C) 2*f(x) 
(D) 1/f(x) 
(E) 2/f(x) 
answer:
question: What number comes next in the following number series? 12, 50, 202, 810, 3242, _____
Options:
(A) 12400
(B) 12800
(C) 12970
(D) 13015
(E) 16000
answer: Stream of consciousness: 12
12 × 4 + 2 = 50
50 × 4 + 2 = 202
202 × 4 + 2 = 810
810 × 4 + 2 = 3242
3242 × 4 + 2 = 12970 The answer is (C).


q: Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter?
Options:
(A) Rs.1185
(B) Rs.1285
(C) Rs.1385
(D) Rs.1485
(E) Rs.1495
a: Stream of consciousness: 22/7 * 14 * 3/2 * 3/2 = 99 m2
99 * 15 = 1485 The answer is (D).


question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
(A) 3:5
(B) 4:5
(C) 2:5
(D) 2:4
(E) 2:7
answer: Stream of consciousness: T = 160/32 = 5 h
T = 5 - 3 = 2
Time Ratio = 5:2
Speed Ratio = 2:5 The answer is (C).


q: There are 10 female and 15 male in a work place. In how many ways can a person can be selected?
Options:
(A) 20
(B) 15
(C) 18
(D) 40
(E) 25
a: Stream of consciousness: No of ways = 10+ 15 = 25 The answer is (E).


question: Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 10 km/hr downstream and 4 km/hr upstream.
Options:
(A) 7 kmph
(B) 8 kmph
(C) 9 kmph
(D) 7 kmph
(E) 6 kmph
answer: Stream of consciousness: Speed in still water = (10 + 4)1/2 kmph = 7 kmph. The answer is (A).


question: If f(x) = x^3/(x^4 - 1), what is f(1/x) in terms of f(x)?
Options:
(A) -f(x) 
(B) f(x) 
(C) 2*f(x) 
(D) 1/f(x) 
(E) 2/f(x) 
answer:
user
[Question] What number comes next in the following number series? 12, 50, 202, 810, 3242, _____.
[Answer] The answer is (C).

[Question] Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter?
[Answer] The answer is (D).

[Question] A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
[Answer] The answer is (C).

[Question] There are 10 female and 15 male in a work place. In how many ways can a person can be selected?
[Answer] The answer is (E).

[Question] Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 10 km/hr downstream and 4 km/hr upstream.
[Answer] The answer is (A).

[Question] If f(x) = x^3/(x^4 - 1), what is f(1/x) in terms of f(x)?
[Answer] The answer is (B).
assistant
question: What number comes next in the following number series? 12, 50, 202, 810, 3242, _____
Options:
(A) 12400
(B) 12800
(C) 12970
(D) 13015
(E) 16000
answer: Stream of consciousness: 12
12 × 4 + 2 = 50
50 × 4 + 2 = 202
202 × 4 + 2 = 810
810 × 4 + 2 = 3242
3242 × 4 + 2 = 12970 The answer is (C).


q: Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter?
Options:
(A) Rs.1185
(B) Rs.1285
(C) Rs.1385
(D) Rs.1485
(E) Rs.1495
a: Stream of consciousness: 22/7 * 14 * 3/2 * 3/2 = 99 m2
99 * 15 = 1485 The answer is (D).


question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
(A) 3:5
(B) 4:5
(C) 2:5
(D) 2:4
(E) 2:7
answer: Stream of consciousness: T = 160/32 = 5 h
T = 5 - 3 = 2
Time Ratio = 5:2
Speed Ratio = 2:5 The answer is (C).


q: There are 10 female and 15 male in a work place. In how many ways can a person can be selected?
Options:
(A) 20
(B) 15
(C) 18
(D) 40
(E) 25
a: Stream of consciousness: No of ways = 10+ 15 = 25 The answer is (E).


question: Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 10 km/hr downstream and 4 km/hr upstream.
Options:
(A) 7 kmph
(B) 8 kmph
(C) 9 kmph
(D) 7 kmph
(E) 6 kmph
answer: Stream of consciousness: Speed in still water = (10 + 4)1/2 kmph = 7 kmph. The answer is (A).


question: If f(x) = x^3/(x^4 - 1), what is f(1/x) in terms of f(x)?
Options:
(A) -f(x) 
(B) f(x) 
(C) 2*f(x) 
(D) 1/f(x) 
(E) 2/f(x) 
answer:
user
Stream of consciousness: f(1/x) = (1/x)^3 / ((1/x)^4 - 1) = (x^3) / (x^4 - x^0) = (x^3) / (x^4 - 1)
This is the same as f(x). So, the answer is (B).
Confidence: 95%
assistant
question: What number comes next in the following number series? 12, 50, 202, 810, 3242, _____
Options:
(A) 12400
(B) 12800
(C) 12970
(D) 13015
(E) 16000
answer: Stream of consciousness: 12
12 × 4 + 2 = 50
50 × 4 + 2 = 202
202 × 4 + 2 = 810
810 × 4 + 2 = 3242
3242 × 4 + 2 = 12970 The answer is (C).


q: Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter?
Options:
(A) Rs.1185
(B) Rs.1285
(C) Rs.1385
(D) Rs.1485
(E) Rs.1495
a: Stream of consciousness: 22/7 * 14 * 3/2 * 3/2 = 99 m2
99 * 15 = 1485 The answer is (D).


question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
(A) 3:5
(B) 4:5
(C) 2:5
(D) 2:4
(E) 2:7
answer: Stream of consciousness: T = 160/32 = 5 h
T = 5 - 3 = 2
Time Ratio = 5:2
Speed Ratio = 2:5 The answer is (C).


q: There are 10 female and 15 male in a work place. In how many ways can a person can be selected?
Options:
(A) 20
(B) 15
(C) 18
(D) 40
(E) 25
a: Stream of consciousness: No of ways = 10+ 15 = 25 The answer is (E).


question: Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 10 km/hr downstream and 4 km/hr upstream.
Options:
(A) 7 kmph
(B) 8 kmph
(C) 9 kmph
(D) 7 kmph
(E) 6 kmph
answer: Stream of consciousness: Speed in still water = (10 + 4)1/2 kmph = 7 kmph. The answer is (A).


question: If f(x) = x^3/(x^4 - 1), what is f(1/x) in terms of f(x)?
Options:
(A) -f(x) 
(B) f(x) 
(C) 2*f(x) 
(D) 1/f(x) 
(E) 2/f(x) 
answer:
user
[Question] What number comes next in the following number series? 12, 50, 202, 810, 3242, _____.
[Answer] The answer is (C).

[Question] Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter?
[Answer] The answer is (D).

[Question] A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
[Answer] The answer is (C).

[Question] There are 10 female and 15 male in a work place. In how many ways can a person can be selected?
[Answer] The answer is (E).

[Question] Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 10 km/hr downstream and 4 km/hr upstream.
[Answer] The answer is (A).

[Question] If f(x) = x^3/(x^4 - 1), what is f(1/x) in terms of f(x)?
[Answer] The answer is (B).
assistant
<|system|>
 
<|user|>
question: What number comes next in the following number series? 12, 50, 202, 810, 3242, _____
Options:
(A) 12400
(B) 12800
(C) 12970
(D) 13015
(E) 16000
answer: Stream of consciousness: 12
12 × 4 + 2 = 50
50 × 4 + 2 = 202
202 × 4 + 2 = 810
810 × 4 + 2 = 3242
3242 × 4 + 2 = 12970 The answer is (C).


q: Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter?
Options:
(A) Rs.1185
(B) Rs.1285
(C) Rs.1385
(D) Rs.1485
(E) Rs.1495
a: Stream of consciousness: 22/7 * 14 * 3/2 * 3/2 = 99 m2
99 * 15 = 1485 The answer is (D).


question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
(A) 3:5
(B) 4:5
(C) 2:5
(D) 2:4
(E) 2:7
answer: Stream of consciousness: T = 160/32 = 5 h
T = 5 - 3 = 2
Time Ratio = 5:2
Speed Ratio = 2:5 The answer is (C).


q: There are 10 female and 15 male in a work place. In how many ways can a person can be selected?
Options:
(A) 20
(B) 15
(C) 18
(D) 40
(E) 25
a: Stream of consciousness: No of ways = 10+ 15 = 25 The answer is (E).


question: Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 10 km/hr downstream and 4 km/hr upstream.
Options:
(A) 7 kmph
(B) 8 kmph
(C) 9 kmph
(D) 7 kmph
(E) 6 kmph
answer: Stream of consciousness: Speed in still water = (10 + 4)1/2 kmph = 7 kmph. The answer is (A).


question: If f(x) = x^3/(x^4 - 1), what is f(1/x) in terms of f(x)?
Options:
(A) -f(x) 
(B) f(x) 
(C) 2*f(x) 
(D) 1/f(x) 
(E) 2/f(x) 
answer: 
<|assistant|>
Stream of consciousness: Let y = x^3/(x^4 - 1)
x/x = y/f(x)
x - y = x^2(x + 1)/f(x)
f(1/x) = (1 - 1/x^3)/(1 - 1/x)
f(1/x) = f(x)/(f(x)/x - 1/x^2)
f(1/x) = (f(x)/x)/(1 - f(x)/x^2)
f(1/x) = 1/(1 - 2/x^3) 
The answer is (D).


q: A train 400m long is running at a speed of 72km/hr. How much time does it take to cross a telegraph post?
Options:
(A) 2 sec
(B) 4 sec
(C) 6 sec
(D) 8 sec
(E) 10 sec
a: Stream of consciousness: Length of moving train = 400 + 720 = 1120/36 = 310m
Time taken = Length of train/Speed = 310/72 = 4.38 sec
The answer is (B).


q: A man bought a painting for Rs.5100, he painted it by himself and sold for Rs. 7000. How much profit did he make ?
Options:
(A) Rs. 1900
(B) Rs. 2000
(C) Rs. 2100
(D) Rs. 2200
(E) Rs. 2300
a: Stream of consciousness: Cost of painting = 5100
Purchase Price + Paint Price = Selling Price
(5100 + Paint Price) x 2 = 7000
Paint Price = (7000 - 5100)/2 = Rs.2950
Profit = selling price - cost of painting - paint price
profit = 7000 - 8050 - 2950 = Rs. 1000
The answer is (E).
Stream of consciousness:

f(x) = x^3/(x^4 - 1)

f(1/x) = (1/x)^3/(1/x)^4 - 1)

f(1/x) = x^3/(x^4 - 1)

Therefore, f(1/x) = f(x)

The answer is (B).
Stream of consciousness:

f(x) = x^3/(x^4 - 1)

f(1/x) = (1/x)^3/(1/x)^4 - 1)

= x^3/(x^4 - 1)

= f(x)

The answer is (B).