[User]
[Ques]: What will come in place of the x in the following Number series? 612, 207, 72, 27, 12, x
Options:
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
*Ans*: (B)
--CoT--: 612
612 / 3 + 3 = 207
207 / 3 + 3 = 72
72 / 3 + 3 = 27
27 / 3 + 3 = 12
12 / 3 + 3 = 7

[Ques]: Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 54% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
Options:
(A) 60%
(B) 50%
(C) 25%
(D) 19%
(E) 10%
*Ans*: (D)
--CoT--: {Total} = {finance} + {marketing} - {both} + {neither}
100 = 25 + 54 - {both} + 40
{both} = 19%.

[Ques]: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
(A) 9 sec
(B) 6 sec
(C) 8 sec
(D) 10 sec
(E) 11 sec
*Ans*: (B)
--CoT--: T = 60/36 * 18/5 = 6 sec

[Ques]: 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
*Ans*: (B)

[Assistant] --CoT--: Here the difference in the cutoff heads and newly grown heads is 3. 100 is not divisible by 3. The dragon never die.


[User]
Reasoning: We have 3 scenarios here:
1) 1 tech2 businessmen: 4C1 x 8C2 = 112
2) 2 tech1 businessman: 4C2 x 8C1 = 48
3) 3 tech0 businessmen: 4C3 = 4
Total: 112+48+4 = 164
Ans: (C)
Question: An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 8 businessmen, how many possible team submissions are possible?
Options:
(A) 76
(B) 100
(C) 164
(D) 198
(E) 202

Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 340 = 700 m
Required time = 700 * 2/25 = 56 sec
The answer: (A)
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 340 m long?
Options:
(A) 56 sec
(B) 42 sec
(C) 45 sec
(D) 48 sec
(E) 50 sec

Reasoning: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Ans: (A)
Question: A train 360 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 sec
(B) 42 sec
(C) 45 sec
(D) 48 sec
(E) 58 sec

Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 21 = 350 m
The answer: (A)
Question: A train running at the speed of 60 km/hr crosses a pole in 21 sec. What is the length of the train?
Options:
(A) 350 m
(B) 490 m
(C) 115 m
(D) 210 m
(E) 150 m

Reasoning: Sum of 17 even numbers = 17 * 18 = 306
Average = 306/17 = 18
Ans: (C)
Question: The average of first 17 even numbers is?
Options:
(A) 10
(B) 11
(C) 18
(D) 20
(E) 24

Reasoning: Speed downstream = 60 + 10 = 70 kmph
Speed upstream = 60 - 10 = 50 kmph
Ans: (B)

[Assistant]
Question: The speed of a boat in still water is 60kmph and the speed of the current is 10kmph. Find the speed downstream and upstream?
Options:
(A) 40, 68 kmph
(B) 70, 50 kmph
(C) 90, 60 kmph
(D) 40, 60 kmph
(E) 20, 60 kmph


[User]
70 + 60 = 130 * 5/18 = 325/9 mps
D = 150 + 100 = 250 m
T = 250 * 9/325 = 90/13 = 6 12/13 secis the reasoning for what question and answer pair?

[Assistant]
Q: Two trains are moving at 60 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Options:
(A) 6 12/13 sec
(B) 7 1/7 sec
(C) 7 2/2 sec
(D) 8 1/2 sec
(E) 7 1/9 sec
A: (A)


[User]
Reasoning: K + 2K +2 + 3K - 5 + 5K +1 = 11K -2
(11K -2)/4 = 63
11K = 63 * 4 +2 = 252 +2 = 254
K = 254 / 11 = 23 1/11
Ans: (E)
Question: If the average (arithmetic mean) of the four numbers K, 2K + 2, 3K – 5 and 5K + 1 is 63, what is the value of K?
Options:
(A)  11
(B)  15 3/4
(C)  22
(D)  23
(E)  23 1/11

Rationale: 1. Subtract 1 from both sides: 2x + 1 - 1 = -23 - 1 2. Simplify both sides: 2x = -24 3. Divide both sides by 2: 4. Simplify both sides: x = -12
The answer: (C)
Question: Solve below question 2x + 1 = -23
Options:
(A) -8
(B) -9
(C) -12
(D) -4
(E) 12

Reasoning: 125% of 120% of A = 237
125/100 * 120/100 * A = 237
A = 237 * 2/3 = 158.
Ans: (C)
Question: A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $237 for it, the cost price of the Cricket Bat for A is:
Options:
(A) 150
(B) 120
(C) 158
(D) 160
(E) 210

Rationale: Let the average after 7th inning = x
Then average after 16th inning = x - 3
\inline \fn_jvn \therefore 16(x-3)+87 = 17x
\inline \fn_jvn \therefore x = 87 - 48 = 39
The answer: (A)
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?
Options:
(A) 39
(B) 88
(C) 3
(D) 7
(E) 62

Reasoning: 1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/4
15 women's 1 day work = (1/4 - 10/100) = 3/20
1 woman's 1 day work = 1/100
1 woman alone can complete the work in 100 days.
Ans: (A)
Question: 10 men and 15 women together can complete a work in 4 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
Options:
(A) 100 days
(B) 667 days
(C) 177 days
(D) 187 days
(E) 225 days

Reasoning: Must be once on heads and twice on tails
1/2*1/2*1/2 = 1/8
Ans: (D)

[Assistant]
Question: When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land once on heads and twice tails?
Options:
(A) 1/3
(B) 1/6
(C) 1/4
(D) 1/8
(E) 1/5


[User]
Given the rationale, provide a reasonable question and answer. Step-by-step reasoning process: (60/100) * 50 – (40/100) * 30
30 - 12 = 18
 The question and answer:

[Assistant]
How much 60% of 50 is greater than 40% of 30?
Options:
(A) 18
(B) 55
(C) 33
(D) 22
(E) 11
The answer is (A)


[User] Reconstruct a question, answer pair from this explanation: Required time = (6)/3 + (6)/6 = 3 hours.

[Assistant]
Q:A man walks at a speed of 3 km/hr and runs at a speed of 6 km/hr. How much time will the man require to cover a distance of 12 km, if he completes half of the distance, i.e., (6) km on foot and the other half by running?
Options:
(A) 2.6
(B) 2.2
(C) 2.5
(D) 2
(E) 3
A:(E)


[User]
Reasoning: 2
2 × 4 - 1 = 7
7 × 4 - 1 = 27
27 × 4 - 1 = 107
107 × 4 - 1 = 427
427 × 4 - 1 = 1707
Ans: (C)
Question: What will come in place of the x in the following Number series? 2, 7, 27, 107, 427, x
Options:
(A) 1427
(B) 1607
(C) 1707
(D) 2047
(E) 2147

Rationale: 18520. This is the only option with last two digits divisible by 8
The answer: (D)
Question: Which of the following numbers is divisible by 8?
Options:
(A) 10021
(B) 17511
(C) 26778
(D) 18520
(E) 26711

Reasoning: 10th letter from your left is J
7th letter from your right is T
The mid letter between J and T is O.
Ans: (A)
Question: Which letter will come exactly between the tenth letter from your left and the seventh letter from your right. Without changing any order in the original from the alphabet?
Options:
(A) o
(B) p
(C) e
(D) r
(E) s

Rationale: Sum of 10 odd no. = 100
Average = 100/10 = 10
The answer: (B)
Question: The average of first 10 odd numbers is?
Options:
(A) 11
(B) 10
(C) 19
(D) 16
(E) 13

Reasoning: O and P should serve on A
Ans: (D)
Question: In case N is the only individual sewing on committee B, which among the following shouldserve on committee A?
Options:
(A) V and U
(B) V and T
(C) U and S
(D) O and P
(E) T and U

Reasoning: 72nd/75th/83rd/85th/94th
Ans: (B)

[Assistant]
Question: John's grade was 80th percentile of the 100 grades for his class. Of the 60 grades from another class, 20 were higher than John's, and the rest were lower. If no other grade was the same as John's grade, then John's grade was what percentile of the grades of the two classes of two classes combined?
Options:
(A) 72nd
(B) 75th
(C) 83rd
(D) 85th
(E) 94th


[User]
Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12is the reasoning for what question and answer pair?

[Assistant]
Q: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is
Options:
(A) 5/54
(B) 5/12
(C) 5/17
(D) 5/18
(E) 5/14
A: (B)


[User]
## Solution
Others are requal to 4x2 + 9y2 + 12xy.
## What the question and answer could be
Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
Options:
(A) (2x + 3y) 2
(B) (2y – x) 2 + y(16x + 5y)
(C) 4x(x + 2y)  + y(4x + 9y)
(D) (2x + 2y) 2 + y(4x + 5y)
(E) (2x – y) 2 + 8y(2x + y)
(B)

## Solution
(80/100) * 40 â€“ (4/5) * 15
32 - 12 = 20
## What the question and answer could be
How much is 80% of 40 is greater than 4/5 of 15?
Options:
(A) 12
(B) 20
(C) 18
(D) 12
(E) 81
(B)

## Solution
Total = 500(25) + 600(27)
Number of installments = 52
Average = Total/Number of installments = 552 approximately
## What the question and answer could be
A certain debt will be paid in 52 installments from January 1 to December 31 of a certain year. Each of the first 25 payments is to be $500; each of the remaining payments is to be $100 more than each of the first 25 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?
Options:
(A) 500
(B) 450
(C) 552
(D) 600
(E) 400
(C)

## Solution
A = 1600(21/20)3 = 2522
## What the question and answer could be

[Assistant]
Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly?
Options:
(A) 3377
(B) 2889
(C) 2522
(D) 2678
(E) 7111
(C)


[User]
Consider the question. A man collects cigarette stubs and makes one full cigarette with every 8 stubs. If he gets 64 stubs how many full cigarettes can he smoke
Options:
(A) 7
(B) 8
(C) 9
(D) 10
(E) 15
 What is the step-by-step reasoning process to arrive at the answer: (C)?

[Assistant] From 64, he makes 8. From this 8 he makes one more. Total 9.


[User]
Consider the question. A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 85. How many points altogether did the team score?
Options:
(A) 662
(B) 672
(C) 652
(D) 642
(E) 670
 If the answer is '(E)'; explain the reasoning:

[Assistant] 8 * 85 = 680 – 10 = 670


[User]
Stream of consciousness rationale: Sum of 10 odd no. = 100
Average = 100/10 = 10
The question and answer pair are described below.

[Assistant]
Q: The average of first 10 odd numbers is?
Options:
(A) 11
(B) 10
(C) 88
(D) 176
(E) 12
A: (B)


[User]
What was the question for this implicit rationale, and corresponding answer?
D = 72 * 5/18 = 20 = 400 â€“ 250 = 150m
 The answer: (A)

[Assistant]
The question: A train 250 m long running at 72 kmph crosses a platform in 20 sec. What is the length of the platform?
Options:
(A) 150m
(B) 200m
(C) 250m
(D) 270m
(E) 300 m


[User]
Given the rationale, provide a reasonable question and answer. Step-by-step reasoning process: It basically asks for the number of 5s in 150!
150/5 + 150/25 + 150/125 = 30 + 6 + 1. Hence 37
 The question and answer:

[Assistant]
If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ?
Options:
(A) 30
(B) 34
(C) 36
(D) 37
(E) 39
The answer is (D)


[User]
Ques: In Sam's hanger there are 22 boxes, 16 out of the boxes are filled with toys and the rest are filled with electrical appliances. 8 boxes are for sale, 5 of them are filled with toys. How many boxes with electrical appliances are in Sam's hanger that is not for sale?
Options:
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(E) 5.
Ans: (C)
CoT: Total boxes = 22
Filled with toys = 16
Filled with appliance = 6
Total boxes for sale = 8
Toy boxes for sale = 5
Appliance boxes for sale = 3
Appliance boxes not for sale = 6 - 3 = 3

Ques: A football field is 9600 square yards. If 800 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards?
Options:
(A) 450
(B) 600
(C) 750
(D) 2400
(E) 300
Ans: (E)
CoT: Answer E) 9600 yards need 1200 lbs
1 Yard will need 800/9600 = 1/12 lbs
3600 Yards will need 1/12* 3600 Yards = 300lbs

Ques: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
(A) 22 sec
(B) 16 second
(C) 77 sec
(D) 55 sec
(E) 17 sec
Ans: (B)
CoT: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec

Ques: Express 50 mps in kmph?
Options:
(A) 172
(B) 160
(C) 150
(D) 180
(E) 120
Ans: (D)

[Assistant] CoT: 25 * 18/5 = 180 kmph


[User]
Rationale: A = 8000(21/20)3 = 9261
The answer: (A)
Question: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
Options:
(A) 9261
(B) 1261
(C) 9621
(D) 9162
(E) 5000

Reasoning: A = 7500(26/25)2 = 8112
Ans: (D)
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
Options:
(A) Rs.8082
(B) Rs.7800
(C) Rs.8100
(D) Rs.8112
(E) none of these

Rationale: 100 * 100 = 10000
125 * 80 = 10000
The answer: (A)
Question: The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?
Options:
(A) 10000
(B) 18999
(C) 16990
(D) 16007
(E) 16991

Reasoning: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
Ans: (E)
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 4556
(B) 2354
(C) 4576
(D) 6768
(E) 5184

Rationale: The ratio is 2:3 = gym:ride, so (18)(3/2) = 27 minutes at the gym, and 27 + 18 = 45 minutes exercise, so (2/3)(45) = 30 minutes yog
The answer: (A)
Question: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 18 minutes, how much time will she spend doing yoga? (rounded to minutes)
Options:
(A) 30 min.
(B) 41 min.
(C) 17 min.
(D) 23 min.
(E) 25 min.

Rationale: Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3
All the three pipes together will fill the tank in 3 hours.
The answer: (C)

[Assistant]
Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
(A) 5
(B) 4
(C) 3
(D) 6
(E) 8


[User]
Rationale: Total expenditure = 40 + 25 + 15 + 5 = 85%
Saving = (100 - 85) = 15%
15/100 × Salary = 2700, Salary = 18000 Rs.
The answer: (C)
Question: A person spends 40% of his salary on food, 25% on house rent, 15% on entertainment and 5% on conveyance. If his savings at the end of the month is Rs. 2700, then his salary per month in rupees is:
Options:
(A) 4000
(B) 6000
(C) 18000
(D) 10000
(E) None of these

Rationale: It doesn't matter which type of card you choose, so:
Probability of choosing 1st card: 1
Probability of choosing 2nd card of the same type: 5/17
Probability of choosing 3rd card of the same type: 4/16
Probability of choosing 4th marble of the same type: 3/15
Multiply and you get 1/68
The answer: (A)
Question: A marble shop contains 6 blue marbles, 6 red marbles, and 6 green marbles. If 4 marbles are purchased at random from the shop, what is the probability that the 4 marbles will be the same color?
Options:
(A) 1/68
(B) 60/68
(C) 13/68
(D) 13/48
(E) 1/48

Rationale: ? = 285 + 1895 – 655 – 745 or, ? = 780
The answer: (C)

[Assistant]
Question: What approximate value should come in place of question mark (?) in the following equation
287.532 + 1894.029 – 657.48 = 743.095 + ?
Options:
(A) 870
(B) 790
(C) 780
(D) 770
(E) 890


[User]
Explain simply why (A) is the correct answer to: The average of five numbers is 9. The average of first two numbers is 7 and the average of last two numbers is 12. What is the middle number?
Options:
(A) 7
(B) 8
(C) 5
(D) 10
(E) 6. Explanation:

[Assistant]
The total of five numbers = 5x9 = 45
The total of first 2 and last 2 numbers is = 2 X 7+2 X 12 = 38
So, the middle number is (45 - 38 ) = 7


[User]
Q: What is the % change in the area of a rectangle when its length increases by 20% and its width decreases by 20%?
Options:
(A) 0%
(B) 20% increase
(C) 20% decrease
(D) 4% decrease
(E) Insufficient data
A: (D)
Explain how we arrive at this answer:

[Assistant]
Explanation: (12/10)*(8/10) = 96/100 of original area
96/100 is a 4% decrease from 100/100 ->


[User]
∴ 6x + 3x + 2x = 132 ⇒ x = 12. Second number = 3x = 3×12 = 36.
This justifies what answer for what question? Q & A:

[Assistant]
Let the second number be 3x, so that the first number is 6x and the third number is 2x.
Options:
(A) 22
(B) 77
(C) 98
(D) 27
(E) 36
(E)


[User] Imagine a question and stream-of-consciousness explanation for which this is the answer: (B)

[Assistant]
Question: In a class there are 60% of girls of which 25% poor. What is the probability that a poor girl is selected is leader?
Options:
(A) 22
(B) 15
(C) 77
(D) 17
(E) 11
Stream-of-consciousness: Assume total students in the class = 100
Then Girls = 60% (100) = 60
Poor girls = 25% (60) = 15
So probability that a poor girls is selected leader = Poor girls / Total students = 15/100 = 15%


[User]
Reasoning: (555 + 445) * 2 * 110 + 80 = 220000 + 80 = 220080
Ans: (D)
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 80 as remainder. Find the no. is?
Options:
(A) 220880
(B) 145778
(C) 220081
(D) 220080
(E) 220030

Reasoning: Initial mileage/weight ratio = 38/180 = 190/900
Revised mileage/weight ratio = 43/150 = 258/900
Ans: (C)
Question: A 2015 model car had an average mileage of 38 miles per gallon, when the car wight was 180 kilograms. An upgraded version of the car in 2016 gave a mileage of 43 miles per gallon and the car weight was reduced to 150 kilograms. By approximately what percent did the mileage of the car to the weight of the car improve?
Options:
(A) 28
(B) 43
(C) 36
(D) 19
(E) 37

Reasoning: The sum all three digits comes to 10 except 324
Ans: (A)
Question: Find the odd man out
253, 136, 352, 324, 631, 244
Options:
(A) 324
(B) 136
(C) 352
(D) 631
(E) 531

Reasoning: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
Ans: (B)

[Assistant]
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
(A) 15 sec
(B) 16 sec
(C) 18 sec
(D) 20 sec
(E) 25 sec


[User]
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 455 * 2/35 = 39 sec
The answer: (D)
Question: A train 455 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
(A) 22 sec
(B) 16 sec
(C) 17 sec
(D) 39 sec
(E) 12 sec

Reasoning: (1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2
Ans: (B)
Question: What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23?
Options:
(A) 1
(B) 2
(C) 4
(D) 5
(E) 6

Rationale: Required time = (9)/3 + (9)/9 = 4 hours.
The answer: (A)
Question: A man walks at a speed of 3 km/hr and runs at a speed of 9 km/hr. How much time will the man require to cover a distance of 18 km, if he completes half of the distance, i.e., (9) km on foot and the other half by running?
Options:
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9

Reasoning: If he draws any combination of 3 socks he will definitely have the matching pair of either colour.
Ans: (A)
Question: John has 10pairs of dark blue socks and 10pairs of black socks. He keeps them all in the same bag. If he picks out 3socks at random, then what is the probability thathe will get a matching pair?
Options:
(A) 1
(B) 3
(C) 5
(D) 8
(E) 9

Rationale: 5C4 * 4C2 * 3C2 = 5*6*3 = 90.
The answer: (C)
Question: An analyst will recommend a combination of 4 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 8 stocks are possible?
--
Options:
(A) 12
(B) 19
(C) 90
(D) 180
(E) 720

Rationale: You have 40 multiples of 5, 8 of 25 and 1 of 125. This will give 49 zeros.
The answer: (C)

[Assistant]
Question: How many terminating zeroes Q does 200! have?
Options:
(A)  40
(B)  48
(C)  49
(D)  55
(E)  64


[User]
Reasoning: Required time = (5 1/4)/3 + (5 1/4)/7 = 2 1/2 hours.
Ans: (E)
Question: A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
Options:
(A) 2 1/0
(B) 2 1/8
(C) 2 1/5
(D) 2 1/3
(E) 2 1/2

Rationale: 30 Seconds
Distance travelled = 140 + 360m = 500m
Speed = 60 * 5/8 = 50/3m
Time = 500 * 3/50 = 30 Seconds
The answer: (A)
Question: A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 360 m long?
Options:
(A) 30 Seconds
(B) 22 Seconds
(C) 41 Seconds
(D) 24 Seconds
(E) 29 Seconds

Reasoning: Req percentage = 11628/20400*100 = 57%
Ans: (A)
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
Options:
(A) 57%
(B) 60%
(C) 90%
(D) 65%
(E) 70%

Rationale: T and S should serve on A
The answer: (D)
Question: In case R is the only individual sewing on committee B, which among the following shouldserve on committee A?
Options:
(A) V and U
(B) V and T
(C) U and S
(D) T and S
(E) T and U

Reasoning: C
23
This is an alternating addition and subtraction series. In the first pattern, 10 is added to each number to arrive at the next. In the second, 10 is subtracted from each number to arrive at the next.
Ans: (C)
Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much? Look at this series: 5, 43, 15, 33, 25, ...What number should come next?
Options:
(A) 10
(B) 40
(C) 23
(D) 13
(E) 20

Reasoning: Dollars needed for first 100 copies = d
Dollars needed for each successive copy = e
Cost of 125 copies = cost of 100 copies + cost of 25 copies = d + 25e
Ans: (D)

[Assistant]
Question: If it costs d dollars to make the first 100 copies of a poster and e dollars for each poster after that, what is the total cost of 125 posters?
Options:
(A) 25d + 100e
(B) 100d + 25e
(C) 125de
(D) d + 25e
(E) 125/(de)


[User]
Reasoning: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 50. So, the amount with remaining 6 people = 140 - 50 = Rs. 90
The average amount with them = 90/6 = Rs. 15.
Ans: (C)
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?
Options:
(A) Rs.17
(B) Rs.76
(C) Rs.15
(D) Rs.72
(E) Rs.71

Rationale: Sum of 10 odd no. = 100
Average = 100/10 = 10
The answer: (B)
Question: The average of first 10 odd numbers is?
Options:
(A) 11
(B) 10
(C) 99
(D) 77
(E) 65

Reasoning: T = 192/32 = 6 h
T = 6 - 3 = 3
Time Ratio = 6:3 = 2:1
Speed Ratio = 1:2
Ans: (A)
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) 1:2
(B) 1:9
(C) 1:1
(D) 1:9
(E) 3:2

Rationale: Total number of letters = 8
Using these letters the number of 8 letters words formed is 8P8 = 4.
The answer: (A)
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
Options:
(A) 8!
(B) 1
(C) 7
(D) 6
(E) 5

Reasoning: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 16 = 90
So, the middle number is (126 - 90 ) = 36
Ans: (C)
Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 16. What is the middle number?
Options:
(A) 27
(B) 29
(C) 36
(D) 34
(E) 35

Reasoning: 1/8 + 1/24 = 1/6
6 * 2 = 12
Ans: (B)

[Assistant]
Question: Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
Options:
(A) 22
(B) 12
(C) 88
(D) 99
(E) 27


[User] Come up with a question and stream of consciousness reasoning that would justify this answer: (A)

[Assistant]
The question is: Find the mean proportional between 36 & 49?
Options:
(A) A) 42
(B) B) 61
(C) C) 63
(D) D) 65
(E) E) 67
Stream of consciousness: Formula = √a×b
A = 36 and B = 49
√36×49 = 6 × 7 = 42


[User]
What was the question for this implicit rationale, and corresponding answer?
Time taken for train A = 30 minutes + d1/s1 = 30 minutes + 100 / 100 = 1 hours 30 minutes
Since Train B travels 50 miles / hour ; train A travels twice the speed of B which gives s1 = 100 miles/ hour
Time taken for train B = d2/s2 = 100 / 50 = 2 Hours
So Train A reaches 30 minutes before Train B
 The answer: (A)

[Assistant]
The question: Train A & B leave from same station and reaches same destination but train A leaves half an after Train B & travels 2 times faster than B. Total distance is 100 miles & train B travels 50 miles/hour. Which train reaches the destination first & what is the time difference between the train
Options:
(A) Train A reaches 30 minutes before Train B
(B) Train B reaches 30 minutes before Train A
(C) Train A reaches 60 minutes before Train B
(D) Train B reaches 60 minutes before Train A
(E) None of the above


[User]
Rationale: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
The answer: (B)
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
Options:
(A) 9179
(B) 3000
(C) 2997
(D) 2678
(E) 2682

Reasoning: Number of ways = 5!/2! = 5X4X3X2X1/2X1 = 60
Ans: (C)
Question: In how many different ways can the letters of the word â€˜CASESâ€™ be arranged?
Options:
(A) 250
(B) 280
(C) 60
(D) 310
(E) 360

Rationale: 70 + 50 = 120 * 5/18 = 100/3 mps
D = 150 + 100 = 250 m
T = 250 * 3/100 = 15/2 = 7 Â½ sec
The answer: (A)
Question: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Options:
(A) 7 1/2 sec
(B) 2 sec
(C) 3 sec
(D) 5 sec
(E) 7 sec

Reasoning: A = 1600(21/20)3 = 2522
Ans: (C)
Question: Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly?
Options:
(A) 2528
(B) 2526
(C) 2522
(D) 2722
(E) 2426

Rationale: 90 * 20/60 = 30 kmph
The answer: (D)
Question: The speed of a train is 90 kmph. What is the distance covered by it in 20 minutes?
Options:
(A) 15
(B) 66
(C) 77
(D) 30
(E) 42

Rationale: Cost price of article = 48$
% of overhead cost = 30
Net profit = 12 $
We need to calculate % markup
Net profit as % of cost price = (12/48)*100 = 25%
Total markup should be = 25 + 30 = 55%
The answer: (E)

[Assistant]
Question: The purchase price of an article is $48. In order to include 30% of cost for overhead and to provide $12 of net profit, the markup should be
Options:
(A) 15%
(B) 25%
(C) 35%
(D) 40%
(E) 55%


[User]
Given the stream of consciousness rationale, provide a reasonable question and answer. Rationale: K + 2K +3 + 3K - 4 + 5K +1 = 11K
(11K -1)/4 = 63
11K = 63 * 4 = 252
K = 252 / 11 = 22 10/11
 The question and answer:

[Assistant]
If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 4 and 5K + 1 is 63, what is the value of K?
Options:
(A)  22 10/11
(B)  15 3/4
(C)  22
(D)  23
(E)  25 3/10
The answer is (A)


[User]
[Ans] (A)
[Question] he population of a city is 110,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence?
Options:
(A) 123596
(B) 1237723
(C) 123776
(D) 123728
(E) 123718
[CoT] Population after n years = P [1 + (R/100)]2
Population after 2 years = 110000 * [1 + 6/100]2 = (110000 x 53/50 x 53/50) = 123596

[Ans] (C)
[Question] A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 83. How many points altogether did the team score?
Options:
(A) 662
(B) 672
(C) 654
(D) 642
(E) 721
[CoT] 8 * 83 = 664 – 10 = 654

[Ans] (A)
[Question]

[Assistant]
A river 2m deep and 45 m wide is flowing at the rate of 3 kmph the amount of water that runs into the sea per minute is?
Options:
(A) 4500 M3
(B) 27000 M3
(C) 3000 M3
(D) 2700 M3
(E) 3700 M3
[CoT] (3000 * 2 * 5)/60 = 4500 M3


[User]
What was the question for this implicit rationale, and corresponding answer?
Say May income = 100
L's income = 60 and rest of the family = 40
In June L's income = 60 * 120 /100 = 72
So 72 /72 + 40 = 64%
 The answer: (A)

[Assistant]
The question: In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?
Options:
(A) 64%
(B) 68%
(C) 72%
(D) 76%
(E) 80%


[User]
Q: The average length of the sides of triangle ABC is 12. What is the perimeter of triangle ABC?
Options:
(A) 4
(B) 6
(C) 12
(D) 24
(E) 36
A: (E)
Explain how we arrive at this answer:

[Assistant]
Explanation: (average) = (perimeter)/3;
12 = (perimeter)/3;
(perimeter) = 36.


[User]
Reasoning: 1/2 * 10 * 5 = 25 m2
Ans: (B)
Question: The area of a triangle is with base 10m and height 5m?
Options:
(A) 11
(B) 25
(C) 787
(D) 122
(E) 12

Rationale: Ordering the data from least to greatest, we get:
87, 88, 88, 90, 92, 93, 95, 96, 98
The median score is 92.
The answer: (C)
Question: What is the median from the below series
90, 92, 93, 88, 95, 88, 97, 87, and 98
Options:
(A) 85
(B) 89
(C) 92
(D) 98
(E) 100

Reasoning: Each of the numbers is odd number except 22. The number 22 is the only even number.
Ans: (C)
Question: Find the odd man out? 3, 7, 15, 17, 22, 27, 29
Options:
(A) 15
(B) 17
(C) 22
(D) 27
(E) 0

Rationale: Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 * 20/11 = 6/11
The answer: (B)
Question: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
Options:
(A) 6/17
(B) 6/11
(C) 6/18
(D) 6/19
(E) 6/10

Reasoning: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 3 = 50 m
Ans: (D)
Question: A train running at the speed of 60 km/hr crosses a pole in 3 sec. What is the length of the train?
Options:
(A) 85 m
(B) 70 m
(C) 115 m
(D) 50 m
(E) 150 m

Reasoning: Maximum points of intersection between n different circles = n*(n - 1) = 20*19 = 380
Ans: (A)

[Assistant]
Question: There are different 20 circles. What is the number of the greatest possible points with which the circles intersect?
Options:
(A) 380
(B) 200
(C) 110
(D) 180
(E) 200


[User]
Question: A corporation triples its annual bonus to 50 of its employees. What percent E of the employees’ new bonus is the increase?
Options:
(A) 50%
(B) 662⁄3%
(C) 100%
(D) 200%
(E) 300%
Ans: (B)
CoT: E of the employees’ new bonus is the increase Hence
----
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
(A) 6 kmph
(B) 5 kmph
(C) 2 kmph
(D) 8 kmph
(E) 1 kmph
Ans: (D)
CoT: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph
----
Question: How many seconds will a train 100 meters long take to cross a bridge 250 meters long if the speed of the train is 36 kmph?
Options:
(A) 54 sec
(B) 35 sec
(C) 25 sec
(D) 45 sec
(E) 24 sec
Ans: (B)

[Assistant]
CoT: D = 100 + 250 = 350
S = 36 * 5/18 = 10 mps
T = 350/10 = 35 sec
----


[User]
[Ques]: 10, 14, 16, 18, 21, 24, 26
Options:
(A) 17
(B) 20
(C) 21
(D) 25
(E) 26
*Ans*: (C)
--CoT--: Each of the numbers except 21 is an even number

[Ques]: The speed of a car is 80 km in the first hour and 60 km in the second hour. What is the average speed of the car?
Options:
(A) 50 kmph
(B) 60 kmph
(C) 70 kmph
(D) 80 kmph
(E) 85 kmph
*Ans*: (C)
--CoT--: S = (80 + 60)/2 = 70 kmph

[Ques]: A password for a computer is six digits from 0 and 9. The six digit number is a prime number. What is the approximate probability that the last digit is a 3?
Options:
(A) 1/4
(B) 1/6
(C) 1/10
(D) 1/20
(E) 1/50
*Ans*: (A)
--CoT--: If the last digit is 0, 2, 4, 6, or 8, the number is even and therefore not prime. If the last digit is 5, the number is divisible by 5 and therefore not prime. The only possibilities are 1, 3, 7, and 9. So the probability is approximately 1/4 (answer A). We say approximately because there is a certain degree of randomness in the distribution of prime numbers.

[Ques]: A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 28 minutes. When both pipes are opened, find when the cistern will be full?
Options:
(A) 76 minutes
(B) 29 minutes
(C) 70 minutes
(D) 17 minutes
(E) 98 minutes
*Ans*: (C)

[Assistant]
--CoT--: 1/20 - 1/28 = 1/70
70 minutes


[User]
Consider the question. Find the third proportional to 3 and 9?
Options:
(A) 10
(B) 12
(C) 27
(D) 19
(E) 20
 If the answer is '(C)'; explain the reasoning:

[Assistant]
Formula = Third proportional = (b × b)/a
A = 3 and B = 9
(9 x 9)/ 3 = 81/3 = 27


[User]
[Ques]: One copy machine can make 15 copies a minute, and a second copy machine makes 10 copies a minute. If the two copiers work together, how long would it take them to make 1,000 copies?
Options:
(A) 20 minutes
(B) 30 minutes
(C) 40 minutes
(D) 50 minutes
(E) 60 minutes
*Ans*: (C)
--CoT--: Total work done by both machines in a minute = 15 + 10 = 25 copies
Total number of copies required = 1000
Time = 1000/25 = 40 mins

[Ques]: In a particular year, the month of january had exactly 4 thursdays, and 4 sundays. On which day of the week did january 1st occur in the year.
Options:
(A) 33
(B) Monday
(C) 299
(D) 299
(E) 277
*Ans*: (B)
--CoT--: Ans: If a month has 31 days, and it starts with sunday, Then Sundays, Mondays, tuesdays are 5 for that month. If this month starts with monday, then mondays, tuesdays, and wednesdays are 5 and remaining days are 4 each. so this month start with Monday.

[Ques]: Find the mean proportional between 81 & 100?
Options:
(A) A) 59
(B) B) 61
(C) C) 63
(D) D) 65
(E) E) 90
*Ans*: (E)
--CoT--: Formula = √a×b
A = 81 and B = 100
√81×100 = 9 × 10 = 90

[Ques]: Find the value of y from (12)^3 x 6^4÷432 =y?
Options:
(A) 4363
(B) 4765
(C) 4879
(D) 6789
(E) 5184
*Ans*: (E)

[Assistant]
--CoT--: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62


[User]
Reasoning: Whenever you are asked to find the number of digits, try to bring the number in multiples of 10. This way, we can wasily calculate the umber of 0's through the powers of 10
50^8 × 8^3 × 11 = (5^2*2)^8*2^9*11 = 5^16*2^17*11 = 2*11*10^16 = 22*10^16
Hence we would have 16 trailing 0's and the three digits from 22
Total digits = 2 + 16 = 18
Ans: (A)
Question: How many digits are in the number 50^8 × 8^3 × 11?
Options:
(A) 18
(B) 20
(C) 19
(D) 22
(E) 17

Rationale: K + 2K +3 + 3K - 5 + 5K +1 = 11K -1
(11K -1)/4 = 85
11K = 85 * 4 +1 = 340 +1 = 341
K = 253 / 11 = 31.
The answer: (C)
Question: If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 5 and 5K + 1 is 85, what is the value of K?
Options:
(A)  11
(B)  15 3/4
(C)  31
(D)  23
(E)  25 3/10

Reasoning: 30 m/s = 30 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 30 * 18/5 * 15/4 km = 405 km.
Ans: (E)
Question: If a man can cover 30 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
(A) 118 km
(B) 162 km
(C) 1767 km
(D) 1887 km
(E) 405 km

Rationale: Any number multiplied by 2 has to be an even number
The answer: (B)
Question: If c and d are unique prime integers, which of the following must be even?
Options:
(A) c−d
(B) 2c−2d
(C) c−2d
(D) 2c−d
(E) cd^2

Reasoning: {Total} = {finance} + {marketing} - {both} + {neither}
100 = 25 + 50 - {both} + 40
{both} = 15%.
Ans: (D)
Question: Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 50% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
Options:
(A) 60%
(B) 50%
(C) 25%
(D) 15%
(E) 10%

Reasoning: Distance covered by the car = 50 × 10 = 500 km
\ Speed = 500⁄5 = 100 km/hr
\ Speed gain = 100 – 50 = 50 km/hr
Ans: (E)

[Assistant]
Question: A car finishes a journey in ten hours at the speed of 50 km/hr. If the same distance is to be covered in five hours how much more speed does the car have to gain?
Options:
(A) 8 km/hr
(B) 10 km/hr
(C) 12 km/hr
(D) 16 km/hr
(E) 50 km/hr


[User]
Given the rationale, provide a reasonable question and answer. Step-by-step reasoning process: T = 60/36 * 18/5 = 6 sec
 The question and answer:

[Assistant]
In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
(A) 3
(B) 5
(C) 4
(D) 6
(E) 7
The answer is (D)


[User]
## Solution
(Local value of 7) - (Face value of 7) = (70000 - 7) = 69993
## What the question and answer could be
The difference between the local value and the face value of 7 in the numeral 32675149 is
Options:
(A) 69950
(B) 69993
(C) 69997
(D) 70000
(E) 01000
(B)

## Solution
(1-(1/16))(1-(1/15))(1-(5/7)) of Income = 50
Hence income = 200
## What the question and answer could be
A person deposits 1/16 of his income as Provident Fund and 1/15 of the remaining as insurance premium. If he spends 5/7 of the balance on domestic needs and deposits an amount of Rs. 50 in the bank, his total income would be
Options:
(A) 150
(B) 200
(C) 250
(D) 300
(E) 350
(B)

## Solution
(80/100) * 40 – (4/5) * 25
32 - 20 = 12
## What the question and answer could be
How much is 80% of 40 is greater than 4/5 of 25?
Options:
(A) 17
(B) 19
(C) 11
(D) 12
(E) 10
(D)

## Solution
5C4 * 4C2 * 3C2 = 5*6*3 = 90.
## What the question and answer could be

[Assistant]
An analyst will recommend a combination of 4 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 8 stocks are possible?
--
Options:
(A) 12
(B) 19
(C) 90
(D) 180
(E) 720
(C)


[User]
(Ans). (C)
(Question). For some integer m, m^2 - 5 is divisible by all of the following EXCEPT
Options:
(A) 38
(B) 41
(C) 30
(D) 31
(E) 29
(CoT). Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out.

(Ans). (B)
(Question). A pipe can fill a cistern in 18 minutes whereas the cistern when fill can be emptied by a leak in 36 minutes. When both pipes are opened, find when the cistern will be full?
Options:
(A) 17
(B) 36
(C) 70
(D) 13
(E) 12
(CoT). 1/18 - 1/36 = 1/36
36 minutes

(Ans). (B)
(Question). In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 200 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
Options:
(A) 140
(B) 146
(C) 152
(D) 162
(E) 170
(CoT). Number of newborns that can die in first month = 1/10 * 200 = 20
Survived = 180
Number of newborns that can die in second month = 1/10 * 180 = 18
Survived = 162
Number of newborns that can die in third month = 1/10 * 162 = 16
Survived = 146

(Ans). (D)
(Question).

[Assistant]
A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 4.5 km long?
Options:
(A) 4
(B) 3
(C) 5
(D) 6
(E) 9
(CoT). D = 25 * 60 + 4500 = 6000 m
T = 6000/60 * 18/5 = 360 sec = 6 mins


[User]
Stream of consciousness rationale: Given Speed = k/n
To Find distance in x hours with same speed
Distance = speed * time
Distance = k/n*x = kx/n
The question and answer pair are described below.

[Assistant]
Q: A racng car travels k kilometres in n hours. How many miles will it travel in x hours at the same rate?
Options:
(A) knx
(B) k⁄n
(C) kn⁄x
(D) kx
(E) kx⁄n
A: (E)


[User]
Reasoning: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
Ans: (E)
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 6434
(B) 4673
(C) 7684
(D) 7658
(E) 5184

Reasoning: 400*(90/100)*(95/100) = 342
Ans: (C)
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
Options:
(A) 39
(B) 37
(C) 342
(D) 288
(E) 261

Reasoning: 221 + 43 = 264/17 = 9 (Remainder)
Ans: (C)
Question: A no.when divided by 221 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
Options:
(A) 2
(B) 7
(C) 9
(D) 11
(E) 15

Reasoning: Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 * 20/11 = 6/11
Ans: (B)

[Assistant]
Question: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
Options:
(A) 5/11
(B) 6/11
(C) 7/11
(D) 8/11
(E) 9/11


[User]
Rationale: Speed downstream = d/t = 78/(4) = 20 kmph
Speed upstream = d/t = 56/(4) = 14 kmph
The speed of the stream = (20 - 14)/2 = 3 kmph
The answer: (E)
Question: A man rows his boat 78 km downstream and 56 km upstream, taking 4 hours each time. Find the speed of the stream?
Options:
(A) 6
(B) 5
(C) 7
(D) 8
(E) 3

Rationale: For example, if there were 4 carrot rows, the garden would have a 4x4 arrangement. If each carrot attracts 4 bunnies, the number of bunnies would be (4*4)*4 = 64 pieces, which is a cube of 4.
The answer: (D)
Question: In a garden, carrots are planted in rows. In each row there are as many carrots as the number of rows in the garden. If each plant attracts as many bunnies as the number of carrots in each row and if the total number of bunnies is n, then :
Options:
(A) n is a perfect square
(B) n is an odd number
(C) n is an even number
(D) n is a perfect cube
(E) none

Rationale: 1: 2/5 = 5: 2
2/7 * 70 = 20
The answer: (B)

[Assistant]
Question: A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
(A) 21
(B) 20
(C) 17
(D) 12
(E) 18


[User]
Rationale: I will go with C (pending elements to match is 2^2*3^2*10^1 = 360
The answer: (C)
Question: If 2^4, 3^3, and 10^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w?
Options:
(A) 198
(B) 288
(C) 360
(D) 396
(E) 484

Reasoning: The time they take will be what the 1st friend takes to complete one circumference as he is the slowest and that is the point all 3 of them will be together at the end of 7 mins.
Ans: (E)
Question: Three friends-whose walking rates are 1 ft./sec., 3ft./sec.,and 6ft./sec. start together walking in the same direction around a circular track that is 420 feet in circumference.After how many minutes are the three of them together again?
Options:
(A) 5 mins
(B) 10 mins
(C) 15 mins
(D) 3 mins
(E) 7 mins

Rationale: |15 - 8n| represents the distance between 15 and 8n on the number line. Now, the distance will be minimized when 8n, which is multiple of 8, is closest to 15. Multiple of 8 which is closest to 15 is 16 (for n = 2), so the least distance is 1: |15 - 16| = 1.
The answer: (C)
Question: If n is an integer, then the least possible value of |15 - 8n| is?
Options:
(A) 0
(B) 2
(C) 1
(D) 3
(E) 5

Reasoning: Answer: Option A
Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Ans: (A)
Question: A train 360 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 sec
(B) 32 sec
(C) 12 sec
(D) 85 sec
(E) 56 sec

Rationale: Speed = 27 * 5/18 = 15/2 m/sec
Total distance covered = 250 + 200 = 450 m
Required time = 450 * 2/15 = 60 sec
The answer: (E)
Question: A train 250 m long is running at a speed of 27 km/hr. In what time will it pass a bridge 200 m long?
Options:
(A) 40
(B) 45
(C) 50
(D) 55
(E) 60

Rationale: 12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km.
The answer: (B)

[Assistant]
Question: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
(A) 228
(B) 162
(C) 5528
(D) 256
(E) 191


[User]
Answer: (A)
Question: How much 60% of 50 is greater than 40% of 30?
Options:
(A) 18
(B) 99
(C) 66
(D) 55
(E) 71
[CoT]: [(60/100) * 50 – (40/100) * 30
30 - 12 = 18]

Answer: (A)
Question: Find the largest 2 digit number which is exactly divisible by 88?
Options:
(A) 88
(B) 89
(C) 99
(D) 54
(E) 90
[CoT]: [Largest 2 digit number is 99
After doing 99 ÷ 88 we get remainder 11
Hence largest 2 digit number exactly divisible by 88 = 99 - 11 = 88]

Answer: (A)
Question: In wardrobe Karan has 3 trousers. One of them is grey the 2nd blue and the 3rd brown. In his wardrobe he also has 4 shirts. One of them is grey and the other 3are white. He opens his wardrobein the dark and pick out one shirttrouser pair without examination the color. What is the likelihood that neither the shirt nor the trouser is grey?
Options:
(A) 1/2
(B) 2/3
(C) 4/5
(D) 6/11
(E) 4/5
[CoT]: [Probability that trouser is not grey = 2/3
Probability that shirt is not grey = 3/4
∴ Required probability = 2/3 x 3/4 = 1/2]

Answer: (D)
Question:

[Assistant]
In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Options:
(A) 3
(B) 4
(C) 5
(D) 8
(E) 9
[CoT]: [Speed in still water = (11 + 5)/2 kmph = 8 kmph.]


[User]
P(A|B) = P(A ∪ B)/P(B)
P(A|B) = (6/15)/(4/15) = 3/2.
If P(A) = 2/15, P(B) = 4/15, and P(A ∪ B) = 6/15 Find P(A|B)
Options:
(A) 1/2
(B) 2/3
(C) 3/2
(D) 4/5
(E) 4/7
(C)

Total number of balls = 9 + 3 + 4
Two balls can be drawn from 16 balls in ¹⁶C₂ ways.
A bag contains nine black balls, three red balls and four red balls. In how many ways can two balls be drawn from the bag?
Options:
(A) ¹⁶C₂
(B) ⁹C₂
(C) ³C₂
(D) ¹²C₂
(E) ¹⁴C₂
(A)

1. Subtract 1 from both sides: 6x - 1 + 1 = -13 + 1 2. Simplify both sides: 6x = -12 3. Divide both sides by 6: 4. Simplify both sides: x = -2

[Assistant]
Solve below question 6x - 1 = -13
Options:
(A) -8
(B) -2
(C) -5
(D) -4
(E) 1
(B)


[User]
Reasoning: (1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2
Ans: (B)
Question: What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23?
Options:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Rationale: Distance covered by the car = 80 × 9 = 720 km
\ Speed = 720⁄6 = 120 km/hr
\ Speed gain = 120 – 80 = 40 km/hr
The answer: (B)
Question: A car finishes a journey in nine hours at the speed of 80 km/hr. If the same distance is to be covered in six hours how much more speed does the car have to gain?
Options:
(A) 8 km/hr
(B) 40 km/hr
(C) 12 km/hr
(D) 16 km/hr
(E) None of these

Reasoning: (555 + 445) * 2 * 110 + 25 = 220000 + 25 = 220025
Ans: (E)
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 25 as remainder. Find the no. is?
Options:
(A) 145646
(B) 236578
(C) 645353
(D) 456546
(E) 220025

Rationale: 400*(80/100)*(95/100) = 304
The answer: (E)
Question: The sale price sarees listed for Rs.400 after successive discount is 20% and 5% is?
Options:
(A) 338
(B) 277
(C) 342
(D) 882
(E) 304

Reasoning: To arrange them as described I did as follows on my scratch paper (see the file attached), where I counted 4 sides
Ans: (A)
Question: Suppose you have three identical prisms with congruent equilateral triangles as the end-polygons. Suppose you attach them by the rectangular faces so they are perfectly aligned. There will be some large faces created by two or more co-planar faces of the individual prisms: count each such large face as one. Given that, how many faces does the resultant solid have
Options:
(A)  4
(B)  6
(C)  9
(D)  10
(E)  12

Reasoning: Work done by X in 1 day = 1/18
Work done by Y in 1 day = 1/15
Work done by Y in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which X can finish the remaining work = (1/3) / (1/18) = 6
Ans: (C)

[Assistant]
Question: X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work?
Options:
(A) 1
(B) 3
(C) 6
(D) 8
(E) 9


[User]
Rationale: 10 * 10 * 100 = 10000
The answer: (C)
Question: In digging a hole 10 m * 10 m * 100 m the volumes of the sand extracted will be?
Options:
(A) 100 cu.m
(B) 1000 cu.m
(C) 10000 cu.m
(D) 2000 cu.m
(E) 4000 cu.m

Rationale: (80/100) * 40 – (4/5) * 25
32 - 20 = 12
The answer: (D)
Question: How much is 80% of 40 is greater than 4/5 of 25?
Options:
(A) 15
(B) 57
(C) 16
(D) 12
(E) 73

Rationale: Let the length E of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence
The answer: (D)

[Assistant]
Question: The length E of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
Options:
(A) Decreases by 19%
(B) Decreases by 25%
(C) Increases by 6%
(D) Increases by 19%
(E) Increases by 25%


[User]
## Solution
Money paid in cash = Rs. 1000
Balance payment = (60000 - 1000) = Rs. 59000
## What the question and answer could be
The price of a T.V. set worth Rs. 60000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
Options:
(A) 22678
(B) 59000
(C) 26788
(D) 19000
(E) 26711
(B)

## Solution
A = 7500(26/25)^4 = 8774
## What the question and answer could be
If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 4 years the amount to be paid is?
Options:
(A) 3377
(B) 2688
(C) 2688
(D) 8774
(E) 1268
(D)

## Solution
Must be once on heads and twice on tails
1/2*1/2*1/2 = 1/8
## What the question and answer could be
When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land once on heads and twice tails?
Options:
(A) 1/3
(B) 1/6
(C) 1/4
(D) 1/8
(E) 1/5
(D)

## Solution
1: 2/5 = 5: 2
2/7 * 28 = 8
## What the question and answer could be

[Assistant]
A 28 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
(A) 12
(B) 8
(C) 88
(D) 77
(E) 14
(B)


[User]
Q: How much is 70% of 40 is greater than 4/5 of 25?
Options:
(A) 12
(B) 27
(C) 18
(D) 12
(E) 8
A: (E)
Explain how we arrive at this answer:

[Assistant]
Explanation: (70/100) * 40 â€“ (4/5) * 25
28- 20 = 8


[User]
Reconstruct a question, answer pair from this explanation: Profit = q
Profit to company founder = q/2
Profit to other partners = q/2
Number of other partners = 3
Profit to each partner = (q/2)/3 = q/6

[Assistant]
Q:Last year, Company M made q dollars in profit. Half of the profit went to the company’s founder. The rest was split evenly among his Three other partners. In terms of q, how much did each of the other partners receive?
Options:
(A) q/4
(B) q/5
(C) q/6
(D) q/7
(E) q/8
A:(C)


[User]
Question: In what time will a railway train 20 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
(A) 5 sec
(B) 4 sec
(C) 3 sec
(D) 6 sec
(E) 2 sec
Ans: (E)
CoT: T = 20/36 * 18/5 = 2 sec
----
Question: An design manager has 10patterns of chairs & 8patterns of tables. In how many ways can he make a pair of table & chair?
Options:
(A) 20
(B) 40
(C) 80
(D) 90
(E) 100
Ans: (C)
CoT: He has has ten patterns of chairs and eight patterns of tables
Hence, A chair can be arranged in 10 ways and
A table can be arranged in 8 ways
Hence one chair and one table can be arranged in 10 x 8 ways = 80 ways
----
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) kmph
(B) kmph
(C) kmph
(D) kmph
(E) kmph
Ans: (D)

[Assistant]
CoT: Speed downstream = 70 + 20 = 90 kmph
Speed upstream = 70 - 20 = 50 kmph
----


[User]
Rationale: 1/2:1/3:1/4 = 6:4:3
3/13*1300 = 300
The answer: (A)
Question: Rs. 1300 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?
Options:
(A) 300
(B) 992
(C) 772
(D) 552
(E) 312

Reasoning: Let the time taken be = x
One way distance = 51x
Total distance traveled = 2 * 51x = 102x
Total time taken = x + 2x = 3x
Average speed = 102x/3x = 34
Ans: (B)
Question: A car traveled from San Diego to San Francisco at an average speed of 51 miles per hour. If the journey back took twice as long, what was the average speed of the trip?
Options:
(A) 24.
(B) 34.
(C) 36.
(D) 42.
(E) 44.

Rationale: T = (100 * 16500)/(15 * 5000) = 22 years
The answer: (A)
Question: In how many years does a sum of Rs. 5000 yield a simple interest of Rs. 16500 at 15% p.a.?
Options:
(A) 22
(B) 20
(C) 25
(D) 30
(E) 35

Reasoning: I will go with D (pending elements to match is 2^2*3^2*10^1 = 360
Ans: (D)
Question: If 2^4, 3^3, and 10^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w?
Options:
(A) 198
(B) 288
(C) 363
(D) 360
(E) 484

Rationale: The prompt is essentially asking for the maximum number of 5 x 5 squares that can be cut from a larger 15 by 15 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 3 'pieces' each, we have (3)(3) = 9 total smaller squares (at maximum).
The answer: (E)
Question: What is the maximum number of pieces of birthday cake of size 5” by 5” that can be cut from a cake 15” by 15”?
Options:
(A) 5
(B) 10
(C) 16
(D) 20
(E) 9

Rationale: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted
The answer: (A)

[Assistant]
Question: Find the least number must be subtracted from 427398 so that remaining no.is divisible by 15?
Options:
(A) 3
(B) 5
(C) 7
(D) 8
(E) 9


[User]
Answer: (B)
Question: A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $222 for it, the cost price of the Cricket Bat for A is:
Options:
(A) 150
(B) 148
(C) 130
(D) 160
(E) 210
[CoT]: [125% of 120% of A = 222
125/100 * 120/100 * A = 222
A = 222 * 2/3 = 148.]

Answer: (A)
Question: Find the largest 2 digit number which is exactly divisible by 88?
Options:
(A) 88
(B) 89
(C) 99
(D) 54
(E) 90
[CoT]: [Largest 2 digit number is 99
After doing 99 ÷ 88 we get remainder 11
Hence largest 2 digit number exactly divisible by 88 = 99 - 11 = 88]

Answer: (E)
Question: 10 men and 15 women together can complete a work in 8 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
Options:
(A) 127 days
(B) 667 days
(C) 177 days
(D) 187 days
(E) 600 days
[CoT]: [1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/8
15 women's 1 day work = (1/8 - 10/100) = 1/40
1 woman's 1 day work = 1/600
1 woman alone can complete the work in 600 days.]

Answer: (E)
Question:

[Assistant]
What is the greatest positive integer x such that 5^x is a factor of 125^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
[CoT]: [125^10 = (5^3)^10 = 5^30]


[User]
Explain simply why (A) is the correct answer to: The inverse ratio of 4: 2: 1 is?
Options:
(A) 2:4:8
(B) 2:3:9
(C) 2:3:2
(D) 2:3:6
(E) 2:3:1. Explanation:

[Assistant] 1/4: 1/2: 1/1 = 2:4:8


[User]
Consider the question. The edge of a cube is 6a cm. Find its surface?
Options:
(A) 116a2 cm2
(B) 126a2 cm2
(C) 256a2 cm2
(D) 150a2 cm2
(E) 216a2 cm2
 What is the step-by-step reasoning process to arrive at the answer: (E)?

[Assistant] 6a2 = 6 * 6a * 6a = 216a2


[User]
Given the stream of consciousness rationale, provide a reasonable question and answer. Rationale: S = (90 + 60)/2 = 75 kmph
 The question and answer:

[Assistant]
The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?
Options:
(A) 228
(B) 75
(C) 299
(D) 267
(E) 312
The answer is (B)


[User]
[Ans] (E)
[Question] Calculate the circumference of a circular field whose radius is 7 centimeters.
Options:
(A) 11 π cm
(B) 15 π cm
(C) 1 π cm
(D) 4 π cm
(E) 14 π cm
[CoT] Circumference C is given by
C = 2πr = 2π*7 = 14 π cm

[Ans] (D)
[Question] Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together?
Options:
(A) 19 1/7 days
(B) 16 1/7 days
(C) 14 1/7 days
(D) 17 1/7 days
(E) 13 1/7 days
[CoT] 1/30 + 1/40 = 7/120
120/7 = 17 1/7 days

[Ans] (E)
[Question]

[Assistant]
Which of the following is equal to the average (arithmetic mean) of (y+4)^2 and (y-4)^2?
Options:
(A) x^2
(B) x^2+2
(C) x^2 +12
(D) x^2+21
(E) y^2+16
[CoT] Avg = [(y+4)^2 + (y-4)^2] / 2
Expanding and simplifying, (y^2 + 8y + 16 + y^2 - 8y + 16 ) / 2 = y^2 + 16


[User]
Rationale: I = (620*10*10)/100 = 620
The answer: (B)
Question: Find the simple interest on Rs.620 for 10 months at 10 paisa per month?
Options:
(A) 277
(B) 620
(C) 640
(D) 678
(E) 121

Reasoning: 315is divisible by 3 which is odd number where as all others are even numbers divisible by 3.
Ans: (C)
Question: Find the odd man out
36, 315, 612, 810, 966, 1362
Options:
(A) 966
(B) 612
(C) 315
(D) 36
(E) 1362

Rationale: 7g/30 tells us that g is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3.
The answer: (B)
Question: In g is a positive integer smaller than 200 and (14g)/60 is an integer, then g has how many different positive prime factors?
Options:
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8

Reasoning: 1 to 11 = 11 * 50 = 550
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 550 = 56
Ans: (B)
Question: The average of 11 results is 50, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
(A) 21
(B) 56
(C) 18
(D) 25
(E) 23

Rationale: Final number = Initial number + 25%(original number) = 80 + 25%(80) = 80 + 20 = 100.
The answer: (E)
Question: A light has a rating of 80 watts, it is replaced with a new light that has 25% higher wattage. How many watts does the new light have?
Options:
(A) 105
(B) 95
(C) 80
(D) 60
(E) 100

Rationale: The smallest prime number is 2.
The answer: (B)

[Assistant]
Question: The smallest prime number is:
Options:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5


[User]
Rationale: Final number = Initial number + 12%(original number) = 60 + 12%(60) = 60 + 7 = 67
The answer: (B)
Question: A light has a rating of 60 watts, it is replaced with a new light that has 12% higher wattage. How many watts does the new light have?
Options:
(A) 105
(B) 67
(C) 80
(D) 60
(E) 100

Reasoning: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Ans: (A)
Question: A train 360 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) 14

Rationale: (30*30)/100 = 9%loss
The answer: (A)
Question: A man sells two articles for Rs.3600 each and he gains 30% on the first and loses 30% on the next. Find his total gain or loss?
Options:
(A) 9% loss
(B) 400
(C) 4000
(D) 324
(E) 200

Reasoning: Local value of 4 = 4 x 100 = 400
Place value of 4 = 4
There fore = 4 x 400 = 1600
Ans: (E)
Question: Find the product of the localvalue and absolutevalue of 4 in 20468?
Options:
(A) 1000
(B) 1100
(C) 1200
(D) 1300
(E) 1600

Rationale: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 2 chairs to sit. The remaining 4 people can sit in 4! ways. Thus the # of arrangements is 2*4! = 48.
The answer: (A)
Question: In how many ways can you seat 5 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
Options:
(A) 48
(B) 1720
(C) 2880
(D) 5040
(E) 10080

Rationale: S = 600/60 = 10 mps
S = 3600/10 = 360 sec = 6 min
The answer: (C)

[Assistant]
Question: A 600 meter long train crosses a signal post in 60 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
Options:
(A) 4 min
(B) 2 min
(C) 6 min
(D) 9 min
(E) 5 min


[User]
Reasoning: Total number of votes polled = (6136 + 7636 + 11628) = 25400
So, Required percentage = 11628/25400 * 100 = 46%
Ans: (A)
Question: 3 candidates in an election and received 6136, 7636 and 11628 votes respectively. What % of the total votes did the winning candidate got in that election?
Options:
(A) 46%
(B) 49%
(C) 57%
(D) 59%
(E) 61%

Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 50. So, the amount with remaining 6 people = 140 - 50 = Rs. 90
The average amount with them = 90/6 = Rs. 15.
The answer: (C)
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?
Options:
(A) 22
(B) 27
(C) 15
(D) 77
(E) 16

Reasoning: A's 1 hour work = 1/4;
(B + C)'s 1 hour work = 1/3;
(A + B)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/4 + 1/3) = 7/12
C's 1 hour work = (7/12 - 1/2) = 1/12
C alone will take 12 hours to do the work.
Ans: (A)
Question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, which A and B together can do it in 2 hours. How long will C alone take to do it?
Options:
(A) 12hours
(B) 10hours
(C) 6hours
(D) 8hours
(E) 4hours

Rationale: 6a2 = 6 * 5a * 5a = 150a2
The answer: (A)
Question: The edge of a cube is 5a cm. Find its surface?
Options:
(A) 150a2 cm2
(B) 170a2 cm2
(C) 125a2 cm2
(D) 175a2 cm2
(E) 120a2 cm2

Reasoning: (Local value of 7) - (Face value of 7) = (70000 - 7) = 69993
Ans: (B)
Question: The difference between the local value and the face value of 7 in the numeral 32675149 is
Options:
(A) 69950
(B) 69993
(C) 69997
(D) 70000
(E) 01000

Reasoning: 5C3 * 4C2 * 3C2 = 10*6*3 = 180.
Ans: (A)

[Assistant]
Question: An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 3 transportation stocks, and 4 utility stocks, how many different combinations of 7 stocks are possible?
--
Options:
(A) 180
(B) 19
(C) 60
(D) 12
(E) 720


[User]
Given the stream of consciousness rationale, provide a reasonable question and answer. Rationale: Plug in an odd integer; in this case 3
(2*3) = 6 Even
(3*3)-1 = 8 Even
(5*3)+6 = 15 + 6 = 21 Odd
3+3^2 = 3 + 9 = 12 Even
(6*3)-6 = 18 - 6 = 12 Even
 The question and answer:

[Assistant]
If x is an odd integer, which of the following is an odd integer?
Options:
(A) 2x
(B) 3x-1
(C) 5x+6
(D) x+x^2
(E) 6x-6
The answer is (C)


[User]
Rationale: 10 m/s = 10 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 10 * 18/5 * 15/4 km = 135 km.
The answer: (D)
Question: If a man can cover 10 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
(A) 288
(B) 162
(C) 145
(D) 135
(E) 130

Reasoning: First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
We can see the patterns here, so the sum of first 100 positive even integers minus the sum of first 100 positive odd integers will be 100.
Ans: (E)
Question: If X is the sum of first 100 positive even integers and Y is the sum of first 100 positive odd integers, what is the value of x-y?
Please try to explain your answers
Options:
(A) 0
(B) 25
(C) 50
(D) 75
(E) 100

Rationale: Fix the third coin as H. The remaining 14 coins have 2^14 outcomes.
The answer: (B)
Question: Fifteen coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
Options:
(A) 2^9
(B) 2^14
(C) 3 * 2^8
(D) 3 * 2^9
(E) 3 * 2^10

Reasoning: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
Ans: (E)
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 2567
(B) 3589
(C) 3789
(D) 4890
(E) 5184

Rationale: Answer A) 10800 yards need 1200 lbs
1 Yard will need 1200/10800 = 1/9 lbs
3600 Yards will need 1/9* 3600 Yards = 400lbs
The answer: (A)
Question: A football field is 10800 square yards. If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards?
Options:
(A) 400
(B) 600
(C) 750
(D) 2400
(E) 3200

Rationale: Circumference C is given by
C = 2πr = 2π*9 = 18 π cm
The answer: (A)

[Assistant]
Question: Calculate the circumference of a circular field whose radius is 8 centimeters.
Options:
(A) 18 π cm
(B) 1 π cm
(C) 8 π cm
(D) 19 π cm
(E) 28 π cm


[User]
Rationale: (1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2
The answer: (B)
Question: What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23?
Options:
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6

Reasoning: This is a simple alternating subtraction and addition series; The first series begins with 6 and adds 8; the second begins with 45 and subtracts 5, and so on.
Ans: (B)
Question: Fill in the blank with the correct number in this number series: 6, 45, 14, 40, __, 35, 30, ?
Options:
(A) 13
(B) 22
(C) 24
(D) 27
(E) 18

Rationale: ? ≈ 18⁄5 × 160 + 40⁄1000 × 1850 + 450
≈ 576 + 740 + 450 ≈ 1760 ≈ 1800
The answer: (D)
Question: What approximate value should come in place of the question mark (?) in the following equation’?
3 3⁄5 of 157.85 + 39% of 1847 = ? – 447.30
Options:
(A) 1200
(B) 1500
(C) 1600
(D) 1800
(E) 2100

Reasoning: Both Dice addition result is 13 = (6+7)
Probability that the number on first die is 6 = 1/6
Probability that the number on Second die is 7 = 1/7
Probability that Both Dice addition result is 13 = 1/6 * 1/7 = 1/42
Ans: (D)
Question: Jack has two dice, one has six equally probable sides, labeled 1, 2, 3, 4, 5, 6, and the other has seven equally probable sides, labeled 1, 2, 3, 4, 5, 6, 7. If Jack rolls both dice what is the probability that both of the number's sum will be 13?
Options:
(A) 3/14
(B) 2/7
(C) 1/3
(D) 1/42
(E) 12/21

Rationale: The lattice points that are in the circle that lie on the perspective axes is as follows: since the diameter is 8, 9 points lie on the horizontal axis (8 + center), but the end points are not in the circle, so 9 - 2 (the same for the vertical axis, but don't count center again), 7 - 1. The lattice points in the circle and not on the horizontal and vertical axes is as follows: lattice points can be found at 45, 45/2 and 30 degrees of axes (30 and 45/2 degrees from horizontal and vertical axes), so same numbers as before, but don't count center again. So, 13 + 5 * 12 = 73
There are a total of 73 lattice points in the circle.
The answer: (C)
Question: In the x-y plane, point (x, y) is a lattice point if both x and y are integers. Circle C has a center at (-2, -2) and a diameter of 8. Some points, such as the center (-2, -2), are inside the circle, but a point such as (-2, 2) is on the circle but not in the circle. How many lattice points are in circle C?
Options:
(A) 40
(B) 10
(C) 73
(D) 60
(E) 63

Rationale: D = 72 * 5/18 = 50 = 1000 â€“ 250 = 750m
The answer: (D)

[Assistant]
Question: A train 250 m long running at 72 kmph crosses a platform in 50 sec. What is the length of the platform?
Options:
(A) 150m
(B) 200m
(C) 250m
(D) 750m
(E) 300 m


[User] Come up with a question and reasoning that would justify this answer: (A)

[Assistant]
The question is: Two trains are moving at 75 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Options:
(A) 6 6/29 sec
(B) 7 1/7 sec
(C) 7 2/2 sec
(D) 8 1/2 sec
(E) 7 1/19 sec
Step-by-step reasoning process: 70 + 75 = 145 * 5/18 = 725/18 mps
D = 150 + 100 = 250 m
T = 250 * 18/725 = 180/29 = 6 6/29 sec


[User] Creatively image a question and justification for this answer: (E)

[Assistant]
The question is: From among the 38 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
Options:
(A) 1360
(B) 1260
(C) 1060
(D) 1160
(E) 1406
Step-by-step reasoning process: There are 38 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 38 ways. When one person is appointed as leader, we are left with 35 students. Out of these 37 teachers, we can select one class representative. So, a class representative can be selected in 37 ways. Hence, the number of ways in which a leader and class representative can be selected = 38 x 37 = 1406


[User]
Given the rationale, provide a reasonable question and answer. Step-by-step reasoning process: Given Exp. = (a3 + b3) = (a + b) = (333 + 555) = 888(a2 - ab + b2)
 The question and answer:

[Assistant]
Solve:-
333 x 333 x 333 + 555 x 555 x 555 = ?(333 x 333 - 333 x 555 + 555 x 555)
Options:
(A) 888
(B) 333
(C) 555
(D) 988
(E) 889
The answer is (A)


[User]
Reasoning: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 6 of them = 6 * 57 = 342
Sum of the last 8 of them = 8 * 61 = 488
So, the 8th number = 342 + 488 - 780 = 50.
Ans: (C)
Question: The average of 13 numbers is 60. Average of the first 6 of them is 57 and that of the last 8 is 61. Find the 8th number?
Options:
(A) 46
(B) 48
(C) 50
(D) 52
(E) 54

Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 160 + 140 = 300 m
Required time = 300 * 2/25 = 24 sec
The answer: (D)
Question: A train 160 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 sec
(B) 50 sec
(C) 44 sec
(D) 24 sec
(E) 60 sec

Reasoning: Answer: Option C
The letters decrease by 1; the numbers are multiplied by 2.
Ans: (C)
Question: Look at this series: F2, __, D8, C16, B32, ... What number should fill the blank?
Options:
(A) A16
(B) G4
(C) E4
(D) E3
(E) F2

Rationale: Present age of total members = 6 X 24 = 144
8 yrs back their ages were = 6 x 8 = 48
Ages at the birth of youngest member = 144 - 48 = 96
Therefore, avg age at the birth of youngest member = 96/6 = 16.
The answer: (B)
Question: The average age of a family of 6 members is 24 years.If the age of the youngest member is 8 years,what was the average age of the family at the birth of the youngest member?
Options:
(A) 15
(B) 16
(C) 21
(D) 12
(E) 19

Reasoning: {Total} = {M} + {N} - {Both}
{Total} = 39 + 28 - 12 = 55.
Ans: (C)
Question: There are 39 distinct numbers in set M, there are 28 distinct numbers in set N, and there are 12 distinct numbers that are in both sets M and N. Set H is the set containing the elements that are in at least one of sets M and N. How many elements are in set H?
Options:
(A) 39
(B) 40
(C) 55
(D) 58
(E) 63

Reasoning: To get Rs. 10, Investment is 96
To get Rs. 650, investment is (96/10)*650 = 6240
Ans: (B)

[Assistant]
Question: In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of:
Options:
(A) Rs. 3100
(B) Rs. 6240
(C) Rs. 6500
(D) Rs. 9600
(E) Rs. 8600


[User]
For this chain-of-thought reasoning and answer, what was the question?
{Total} = {finance} + {marketing} - {both} + {neither}
100 = 25 + 54 - {both} + 40
{both} = 19%.
 A: (D)

[Assistant]
Q: Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 54% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
Options:
(A) 60%
(B) 50%
(C) 25%
(D) 19%
(E) 10%


[User]
For this chain-of-thought reasoning and answer, what was the question?
D = 72 * 5/18 = 50 = 1000 â€“ 250 = 750m
 A: (D)

[Assistant]
Q: A train 250 m long running at 72 kmph crosses a platform in 50 sec. What is the length of the platform?
Options:
(A) 150m
(B) 200m
(C) 250m
(D) 750m
(E) 300 m


[User]
Given the rationale, provide a reasonable question and answer. Step-by-step reasoning process: Largest 4 digit number is 999
After doing 999 ÷ 89 we get remainder 20
Hence largest 3 digit number exactly divisible by 89 = 999 - 20 = 979
 The question and answer:

[Assistant]
Calculate the largest 3 digit number which is exactly divisible by 89?
Options:
(A) 911
(B) 969
(C) 979
(D) 977
(E) 971
The answer is (C)


[User]
Explain simply why (B) is the correct answer to: A die is thrown. If G is the event 'the number appearing is a multiple of 3' and H be the event
'the number appearing is even' then find whether G and H are independent ?
Options:
(A) G and H are not independent events.
(B) G and H are independent events.
(C) Only G independent event
(D) Only H independent event
(E) None. Explanation:

[Assistant]
We know that the sample space is S = {1, 2, 3, 4, 5, 6}
Now G = { 3, 6}, F = { 2, 4, 6} and E n F = {6}
Then P(G) = 2/6 = 1/3
P(H) = 3/6 = 1/2 and P(G ∩ H) = 1/6
P(G n H) = P(G). P (H)
G and H are independent events.


[User]
What was the question for this implicit rationale, and corresponding answer?
Area of a Rectangle: A = w × h
D) 60 square meters
 The answer: (D)

[Assistant]
The question: A rectangular garden is 12m by 5m, what is its area?
Options:
(A) 12 square meters
(B) 5 square meters
(C) 44 square meters
(D) 60 square meters
(E) 22 square meters


[User]
[Ans] (D)
[Question] The price of a T.V. set worth Rs. 40000 is to be paid in 20 installments of Rs. 2500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
Options:
(A) 29997
(B) 28088
(C) 27098
(D) 37500
(E) 2799
[CoT] Money paid in cash = Rs. 2500
Balance payment = (40000- 2500) = Rs. 37500.

[Ans] (E)
[Question] In a school of 850 boys, 44% of Muslims, 14% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
Options:
(A) A) 125
(B) B) 627
(C) C) 153
(D) D) 721
(E) E) 272
[CoT] 44 + 14 + 10 = 68%
100 – 68 = 32%
850 * 32/100 = 272

[Ans] (A)
[Question]

[Assistant]
There are different 5 circles. What is the number of the greatest possible points with which the circles intersect?
Options:
(A) 20
(B) 10
(C) 15
(D) 22
(E) 21
[CoT] Maximum points of intersection between n different circles = n*(n - 1) = 5*4 = 20


[User]
Rationale: 4C1 + 4C2+ 4C3+4C4 = 15.
The answer: (A)
Question: Jade has 4 flavors of ice cream in his parlor. How many options are there for James to pick a one-flavor, two-flavor, three-flavor or four-flavor order?
Options:
(A) 15
(B) 13
(C) 14
(D) 17
(E) 18

Reasoning: T = 70/36 * 18/5 = 7 sec
Ans: (D)
Question: In what time will a railway train 70 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
(A) 5 sec
(B) 4 sec
(C) 3 sec
(D) 7 sec
(E) 1 sec

Rationale: Fix the third coin as H. The remaining 11 coins have 2^11 outcomes.
The answer: (B)
Question: Twelve coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
Options:
(A) 2^9
(B) 2^11
(C) 3 * 2^8
(D) 3 * 2^9
(E) 3 * 2^10

Reasoning: Work done by X in 1 day = 1/18
Work done by Y in 1 day = 1/15
Work done by Y in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which X can finish the remaining work = (1/3) / (1/18) = 6
Ans: (C)
Question: X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work?
Options:
(A) 2
(B) 3
(C) 6
(D) 7
(E) 8

Rationale: At least one of U and V is odd
The answer: (A)
Question: For integers U and V, when U is divided by V, the remainder is odd. Which of the following must be true?
Options:
(A) At least one of U and V is odd
(B) The sum U + V is odd
(C) U and V share no common factors other than 1
(D) UV is odd.
(E) U is odd

Rationale: Final number = Initial number + 40%(original number) = 150 + 40%(150) = 150 + 60 = 210.
The answer: (B)

[Assistant]
Question: 150 is increased by 40%. Find the final number.
Options:
(A) 200
(B) 210
(C) 180
(D) 190
(E) 220


[User]
Given the following reasoning and answer, what was the question? P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2)^3 = 7/8.
 The answer: (D)

[Assistant]
The question The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?
Options:
(A)  1/8
(B)  1/2
(C)  3/4
(D)  7/8
(E)  15/16


[User]
Rationale: Answer = D = 8
If least = -4, then largest = 9
Range = 9 - 1 = 8
The answer: (D)
Question: List K consists of 14 consecutive integers. If -4 is the least integer in list K, what is the range of the positive integers in list K?
Options:
(A) 5
(B) 6
(C) 7
(D) 8
(E) 12

Rationale: Speed downstream = 40 + 20 = 60 kmph
Speed upstream = 40 - 20 = 20 kmph
The answer: (B)
Question: The speed of a boat in still water is 40kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
(A) kmph
(B) kmph
(C) kmph
(D) kmph
(E) kmph

Rationale: Clearly, 97 is a prime number.
The answer: (C)

[Assistant]
Question: Which of the following is a prime number ?
Options:
(A) 27
(B) 45
(C) 97
(D) 98
(E) 100


[User]
Rationale: P = (P*7*R)/100
R = 14 2/7%
The answer: (C)
Question: In what time a sum of money double itself at 7% per annum simple interest?
Options:
(A) 33 1/8%
(B) 33 1/3%
(C) 14 2/7%
(D) 32 1/3%
(E) 23 1/3%

Reasoning: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
Ans: (E)
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 2345
(B) 3456
(C) 2334
(D) 3456
(E) 5184

Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2
The answer: (C)
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
Options:
(A) 225 cm2
(B) 275 cm2
(C) 285 cm2
(D) 315 cm2
(E) None of these

Reasoning: (Grade 1 + Grade 2) - (Grade 2 + Grade 5) = 30
Grade 1 - Grade 5 = 30
Ans: (B)
Question: The total number of students in Grades 1 and 2 is 30 more than the total number of students in grades 2 and 5. How much lesser is the number of students in Grade 5 as compared to Grade 1?
Options:
(A) 20
(B) 30
(C) 10
(D) 40
(E) 15

Rationale: Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3
All the three pipes together will fill the tank in 3 hours.
The answer: (C)
Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
(A) 2
(B) 2.2
(C) 3
(D) 3.5
(E) 4

Rationale: Speed downstream = d/t = 95/(2 1/2) = 38 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (38 - 18)/2 = 10 kmph
The answer: (A)

[Assistant]
Question: A man rows his boat 95 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
(A) 10 kmph
(B) 6 kmph
(C) 5 kmph
(D) 8 kmph
(E) 7 kmph


[User]
Given the rationale, provide a reasonable question and answer. Step-by-step reasoning process: A + B = 1/20 + 1/15 = 7/60
A + C = 1/20 + 1/12 = 8/60
7/60 + 8/60 = 15/60 = 1/4
4 days * 2 = 8 days
 The question and answer:

[Assistant]
A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?
Options:
(A) 9 days
(B) 8 days
(C) 5 days
(D) 54 days
(E) 2 days
The answer is (B)


[User]
Reasoning: 5C4 * 4C3 * 5C4 = 5*4*5 = 100.
Ans: (D)
Question: An analyst will recommend a combination of 4 industrial stocks, 3 transportation stocks, and 4 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 5 utility stocks, how many different combinations of 11 stocks are possible?
Options:
(A) 12
(B) 19
(C) 60
(D) 100
(E) 720

Rationale: Since average price of a pencil = 2
∴ Price of 75 pencils = 150
∴ Price of 30 pens = (450 – 150) = 300
∴ Average price of a pen = 360⁄60 = 10
The answer: (A)
Question: 30 pens and 75 pencils were purchased for 450. If the average price of a pencil was 2.00, find the average price of a pen.
Options:
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14

Reasoning: Work done by A in 3 days = 3/10
Remaining work = 7/10
Work done by both A and B in one day = 1/10 + 1/15 = 5/30 = 1/6
Remaining work = 7/10 * 6/1 = 21/5 = 4 1/5 days.
Ans: (D)
Question: A and B can do a work in 10 days and 15 days respectively. A starts the work and B joins him after 3 days. In how many days can they complete the remaining work?
Options:
(A) 6 days
(B) 2 days
(C) 8 days
(D) 4 1/5 days
(E) 9 days

Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph
The answer: (D)
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
(A) 2 kmph.
(B) 4 kmph.
(C) 5 kmph.
(D) 8 kmph.
(E) 7 kmph.

Reasoning: 8 * 86 = 688 – 10 = 678
Ans: (B)
Question: A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 86. How many points altogether did the team score?
Options:
(A) 662
(B) 678
(C) 652
(D) 642
(E) 721

Reasoning: Volume of prism = Area of base * height = 1/2* (square root of 5) * (square root of 5)*10 = 25
Ans: (E)

[Assistant]
Question: Right triangle PQR is the base of the prism in the figure above. If PQ=PR=âˆš5 and the height of the prism is 10, what is the volume of the prism?
Options:
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25


[User]
Given the stream of consciousness rationale, provide a reasonable question and answer. Rationale: Since average price of a pencil = 2
∴ Price of 75 pencils = 150
∴ Price of 30 pens = (570 – 150) = 360
∴ Average price of a pen = 420⁄60 = 14
 The question and answer:

[Assistant]
30 pens and 75 pencils were purchased for 570. If the average price of a pencil was 2.00, find the average price of a pen.
Options:
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
The answer is (E)


[User] Come up with a question and reasoning that would justify this answer: (C)

[Assistant]
The question is: Joey is planning to throw a small party and for that he needs to do the following tasks:
I. Decide guest list
II. Send invites
III. Arrange catering
IV. Decide the venue
V. Rent a music system
The tasks can be done in any order as long as the invites are sent after the guest list is decided. In how many ways can Joey do the five tasks listed above?
Options:
(A) 24
(B) 48
(C) 60
(D) 120
(E) 240
Step-by-step reasoning process: These 5 tasks can be arranged in 5! = 120 ways. In half of them invites are sentafterthe guest list is decided and in half of them before. So, there are total of 120/2 = 60 ways to arrange the task so that the invites are sent after the guest list is decided.


[User]
Given the stream of consciousness rationale, provide a reasonable question and answer. Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
 The question and answer:

[Assistant]
Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 4556
(B) 2354
(C) 4576
(D) 6768
(E) 5184
The answer is (E)


[User]
Reasoning: Initial no of students + 3 * (1 + No of possible 3 minute intervals between 15:03 and 15:44) -
8 *(1 + No of possible 10 minute intervals between 15:10 and 15:44)
20 + 3*14 -8 * 4 = 25
Ans: (C)
Question: At 15:00 there were 20 students in the computer lab. At 15:03 and every three minutes after that, 3 students entered the lab. If at 15:10 and every ten minutes after that 7 students left the lab, how many students were in the computer lab at 15:44 ?
Options:
(A) 7
(B) 14
(C) 25
(D) 27
(E) 30

Rationale: 8/15 + 6/x = 1
X = 12 6/7days
The answer: (B)
Question: A can do a piece of work in 15 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
Options:
(A) 11 6/7days
(B) 12 6/7days
(C) 13 6/7days
(D) 14 6/7days
(E) 15 6/7days

Reasoning: D = 72 * 5/18 = 15 = 300 â€“ 250 = 50m
Ans: (A)
Question: A train 250 m long running at 72 kmph crosses a platform in 15 sec. What is the length of the platform?
Options:
(A) 50m
(B) 200m
(C) 250m
(D) 270m
(E) 300 m

Rationale: Saving = (42-32)% of 42400 = 4240.
The answer: (C)
Question: If the personal income tax rate is lowered from 42% to 32%, what is the differential savings for a tax payer having an annual income before tax to the tune of $42400?
Options:
(A) $3500
(B) $5000
(C) $4240
(D) $7000
(E) $10000

Reasoning: 224 + 43 = 267/17 = 12 (Remainder)
Ans: (E)
Question: A no.when divided by 224 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
Options:
(A) 2
(B) 7
(C) 9
(D) 11
(E) 12

Reasoning: Number of ways = 5!/2! = 5X4X3X2X1/2X1 = 60
Ans: (C)

[Assistant]
Question: In how many different ways can the letters of the word â€˜CASESâ€™ be arranged?
Options:
(A) 250
(B) 280
(C) 60
(D) 310
(E) 360


[User] Come up with a question and stream of consciousness reasoning that would justify this answer: (C)

[Assistant]
The question is: The average age of a family of 6 members is 26 years.If the age of the youngest member is 10 years,what was the average age of the family at the birth of the youngest member?
Options:
(A) 15
(B) 18
(C) 16
(D) 12
(E) 19
Stream of consciousness: Present age of total members = 6 X 26 = 156
10 yrs back their ages were = 6 x 10 = 60
Ages at the birth of youngest member = 156 - 60 = 96
Therefore, avg age at the birth of youngest member = 96/6 = 16.


[User]
For this chain-of-thought reasoning and answer, what was the question?
Sum of all the 13 results = 13 * 60 = 780
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 780 = 46.
 A: (C)

[Assistant]
Q: The average of 13 result is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th result?
Options:
(A) 35
(B) 37
(C) 46
(D) 48
(E) 50


[User]
Given the stream of consciousness rationale, provide a reasonable question and answer. Rationale: Let the length Q of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence
 The question and answer:

[Assistant]
The length Q of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
Options:
(A) Decreases by 19%
(B) Decreases by 25%
(C) Increases by 6%
(D) Increases by 19%
(E) Increases by 25%
The answer is (D)


[User]
[Ques]: At a meeting of the 8 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 8 Chiefs of Staff be seated around a circular table?
Options:
(A) 120
(B) 480
(C) 960
(D) 2520
(E) 5080
*Ans*: (E)
--CoT--: Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer E (5080), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect?

[Ques]: 10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
Options:
(A) 2267
(B) 287
(C) 268
(D) 228
(E) 225
*Ans*: (E)
--CoT--: 1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/6
15 women's 1 day work = (1/6 - 10/100) = 1/15
1 woman's 1 day work = 1/225
1 woman alone can complete the work in 225 days.

[Ques]: In what time a sum of money double itself at 3% per annum simple interest?
Options:
(A) 33 1/8%
(B) 33 1/3%
(C) 33 3/3%
(D) 33 1/7%
(E) 32 1/3%
*Ans*: (B)
--CoT--: P = (P*3*R)/100
R = 33 1/3%

[Ques]: A motorcyclist goes from Bombay to Pune, a distance of 256 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) 1:2
(B) 1:5
(C) 1:4
(D) 1:1
(E) 5:8
*Ans*: (E)

[Assistant]
--CoT--: T = 256/32 = 8 h
T = 8 - 3 = 5
Time Ratio = 8:5
Speed Ratio = 5:8


[User]
Explain simply why (E) is the correct answer to: Find the value of y from (12)^3 x 6^4÷432 =y?
Options:
(A) 4363
(B) 4765
(C) 4879
(D) 6789
(E) 5184. Explanation:

[Assistant]
Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62


[User]
Given the stream of consciousness rationale, provide a reasonable question and answer. Rationale: Since the coin is a fair coin, every toss is independent of any other toss. Hence, the probability of appearance of tail on the fifth toss is = 1/2
 The question and answer:

[Assistant]
A fair coin is tossed repeatedly. If head appears on the first four tosses, then the probability of appearance of tail on the fifth toss is.
Options:
(A) 1/7
(B) 1/2
(C) 3/7
(D) 2/3
(E) 1/3
The answer is (B)


[User] Creatively image a question and justification for this answer: (E)

[Assistant]
The question is: What is the are of an equilateral triangle of side 24 cm?
Options:
(A) 66âˆš3 cm2
(B) 74âˆš3 cm2
(C) 64âˆš3 cm2
(D) 64âˆš5 cm2
(E) 144âˆš3 cm2
Step-by-step reasoning process: Area of an equilateral triangle = âˆš3/4 S2
If S = 24, Area of triangle = âˆš3/4 * 24 * 24 = 144âˆš3 cm2;


[User]
Question. There are different 5 circles. What is the number of the greatest possible points with which the circles intersect?
Options:
(A) 20
(B) 10
(C) 15
(D) 22
(E) 21
Answer. (A)
What step-by-step reasoning justifies that answer?

[Assistant] Reasoning: Maximum points of intersection between n different circles = n*(n - 1) = 5*4 = 20


[User]
Answer = C
Please refer diagram below
95 - 10 = 85
This justifies what answer for what question? Q & A:

[Assistant]
95 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?
Options:
(A) 75
(B) 80
(C) 85
(D) 90
(E) 95
(C)


[User]
Stream of consciousness rationale: Required time = (5 1/4)/3 + (5 1/4)/7 = 2 1/2 hours.
The question and answer pair are described below.

[Assistant]
Q: A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
Options:
(A) 2 1/0
(B) 2 1/8
(C) 2 1/5
(D) 2 1/3
(E) 2 1/2
A: (E)


[User] Creatively image a question and justification for this answer: (E)

[Assistant]
The question is: John makes $40 a week from his job. He earns a raise and now makes $60 a week. What is the % increase?
Options:
(A) 16%
(B) 16.66%
(C) 18%
(D) 21%
(E) 50%
Step-by-step reasoning process: Increase = (20/40)*100 = 50%.


[User]
Reasoning: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 12 = 200 m
Ans: (E)
Question: 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) 287
(B) 699
(C) 677
(D) 168
(E) 200

Rationale: (9+5) +2 = 16
(16+9) +3 = 28
(28+16)+4 = 48
(48+28)+5 = 81
The answer: (C)
Question: 5,9,16,28,48,__
Options:
(A) 79
(B) 80
(C) 81
(D) 82
(E) 83

Reasoning: Local value of 7 = 7 x 100 = 700
Place value of 7 = 7
There fore = 7 x 700 = 4900
Ans: (C)
Question: Find the product of the localvalue and absolutevalue of 7 in 20768?
Options:
(A) 9200
(B) 1100
(C) 4900
(D) 3200
(E) 1600

Rationale: 10 * 162 = 1620
3 * 100 + 5 * 150 = 1050
1620 – 1050 = 570
The answer: (D)
Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.162. Find the unknown rate of two blankets?
Options:
(A) 420
(B) 550
(C) 490
(D) 570
(E) 457

Reasoning: 16+31+23 = 70
100-70 = 30
Ans: (E)
Question: In an examination, 47% failed in English and 54% failed in Mathematics. Find the pass percentage in both the subjects if 31% failed in both the subjects?
Options:
(A) 70
(B) 50
(C) 40
(D) 20
(E) 30

Reasoning: Denote X as the sum of the heights of the two new people. From the stem it follows that (700+X)6>175. This reduces to X>350. Only the heights from B add up to 350 cm. All other pairs add up to more than 350 cm.
Ans: (B)

[Assistant]
Question: The average height in a group of 4 people is 175 cm. If the average height increased when 2 more people were added to the group, which of the following cannot be the heights of the two new people?
Options:
(A) 179 cm and 172 cm
(B) 181 cm and 169 cm
(C) 173 cm and 178 cm
(D) 176 cm and 176 cm
(E) 174 cm and 177 cm


[User]
For this chain-of-thought reasoning and answer, what was the question?
The total distance D traveled by John is given by
D = 45 * 2 + 3 * 50 = 240 miles.
 A: (C)

[Assistant]
Q: John left home and drove at the rate of 45 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 50 mph to reach his destination. How many miles did John drive?
Options:
(A) 235 miles.
(B) 245 miles.
(C) 240 miles.
(D) 265 miles.
(E) 275 miles.


[User]
Reasoning: A's one day's work = 1/30
B's one day's work = 1/45
(A + B)'s one day's work = 1/30 + 1/45 = 1/18
The part of the work completed in 5 days = 5 (1/18) = 5/18.
Ans: (A)
Question: Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 5 days?
Options:
(A) 5/18
(B) 1/6
(C) 1/4
(D) 1/9
(E) 2/6

Rationale: The total of seven numbers = 7X22 = 154
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (154 - 99 ) = 55
The answer: (E)
Question: The average of seven numbers is 22. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
(A) 25
(B) 27
(C) 29
(D) 32
(E) 55

Reasoning: S = 180/6 * 18/5 = 108 kmph
Ans: (B)
Question: A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
Options:
(A) 228
(B) 108
(C) 1266
(D) 188
(E) 211

Rationale: Required sum = (53 + 59 + 61 + 67 ) = 240
Note: 1 is not a prime number
The answer: (D)
Question: What is the sum of all the prime numbers greater than 50 but less than 70?
Options:
(A) 249
(B) 248
(C) 246
(D) 240
(E) 241

Reasoning: Initial price/weight ratio = 75 / 100 = 225/300
Revised price/weight ratio = 40 / 30 = 400/300
Ans: (B)
Question: At a supermarket, a variety of cookies was priced at 75 cents per 100 grams. Subsequently, the price was revised to 40 cents for 30 grams of the same cookies. By approximately what percent did the ratio of price to weight increase from the initial price of 75 cents per pound?
Options:
(A) 65
(B) 78
(C) 44
(D) 18
(E) 36

Reasoning: (80/100) * 40 – (10/100) * 15
32 - 15 = 17
Ans: (E)

[Assistant]
Question: How much 80% of 40 is greater than 10% of 15?
Options:
(A) 18
(B) 99
(C) 19
(D) 18
(E) 17


[User]
As per the question, let a = 2, b = 6, c = 5, and d = 10. Plugging these into the answer choices, only A does not yield an integer.
This justifies what answer for what question? Q & A:

[Assistant]
a, b, c, and d are positive integers where a is a factor of b and c is a factor of d. Which of the following is NOT necessarily an integer?
Options:
(A) (ac) /(bd)
(B) (bd) /(ac)
(C) (bcd) /a
(D) d/c + b/a
(E) (a + b) d/c
(A)


[User]
Given the stream of consciousness rationale, provide a reasonable question and answer. Rationale: L and M should serve on A
 The question and answer:

[Assistant]
In case K is the only individual sewing on committee B, which among the following shouldserve on committee A?
Options:
(A) V and U
(B) V and T
(C) U and S
(D) L and M
(E) T and U
The answer is (D)


[User]
(Ans). (C)
(Question). What will come in place of the x in the following number series? 1, 4, 10, 22, 46, x
Options:
(A) 84
(B) 92
(C) 94
(D) 98
(E) 104
(CoT). 1
1 × 2 + 2 = 4
4 × 2 + 2 = 10
10 × 2 + 2 = 22
22 × 2 + 2 = 46
46 × 2 + 2 = 94

(Ans). (E)
(Question). A light has a rating of 80 watts, it is replaced with a new light that has 25% higher wattage. How many watts does the new light have?
Options:
(A) 105
(B) 95
(C) 80
(D) 60
(E) 100
(CoT). Final number = Initial number + 25%(original number) = 80 + 25%(80) = 80 + 20 = 100.

(Ans). (E)
(Question). Rajani has to read a book of 445 pages. She has already read the first 157 pages of the book and if she reads 24 pages of the book everyday then how long will she take now to complete the book?
Options:
(A) 25 days
(B) 20 days
(C) 46 days
(D) 21 days
(E) None of these
(CoT). Remaining pages to read = 445 – 157 = 288
∴ Reqd. number of days = 288⁄24 = 12

(Ans). (A)
(Question).

[Assistant]
How much 60% of 50 is greater than 40% of 30?
Options:
(A) 18
(B) 28
(C) 29
(D) 11
(E) 12
(CoT). (60/100) * 50 – (40/100) * 30
30 - 12 = 18