[User]
Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
The answer: (C)
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is
Options:
(A) 1/9
(B) 1/7
(C) 1/5
(D) 1/1
(E) 1/2

Rationale: (50/100) * 250 â€“ (25/100) * 400
125 - 100 = 25
The answer: (B)
Question: By how much is 50% of 250 greater than 25% of 400.
Options:
(A) 25
(B) 26
(C) 29
(D) 39
(E) 26

Rationale: 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.
The answer: (C)

[Assistant]
Question: 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


[User]
Rationale: A = 7500(26/25)^5 = 9125
The answer: (D)
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 5 years the amount to be paid is?
Options:
(A) 3377
(B) 2688
(C) 2688
(D) 9125
(E) 1268

Reasoning: S = (90 + 60)/2 = 75 kmph
Ans: (B)
Question: 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) 22
(B) 75
(C) 44
(D) 28
(E) 12

Rationale: Largest 4 digit number is 9999
After doing 9999 ÷ 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
The answer: (C)
Question: Find the largest 4 digit number which isexactly divisible by 88?
Options:
(A) 8765
(B) 9543
(C) 9944
(D) 1012
(E) 2465

Reasoning: The total of twelve numbers = 12X7 = 84
The total of first 9 and last 2 numbers is = 9 X 6+2 X 10 = 74
So, the middle number is (84 - 74 ) = 10
Ans: (B)
Question: The average of twelve numbers is 7. The average of first nine numbers is 6 and the average of last two numbers is 10. What is the middle number?
Options:
(A) A) 9
(B) B) 10
(C) C) 12
(D) D) 7
(E) E) 13

Rationale: On dividing 5474827 by 12 we get the remainder 7, so 7 should be subtracted
The answer: (D)
Question: Find the least number must be subtracted from 5474827 so that remaining no.is divisible by 12?
Options:
(A) 3
(B) 5
(C) 4
(D) 7
(E) 2

Rationale: S = (90 + 60)/2 = 75 kmph
The answer: (B)

[Assistant]
Question: 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


[User]
Given the rationale, provide a reasonable question and answer. Step-by-step reasoning process: The length of cloth painted by one girl in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 girls = 36/ 6 × 6 = 1 day.
 The question and answer:

[Assistant]
If 4 girls can color 48 m long cloth in 2 days, then 6 girls can color 36 m long cloth in
Options:
(A) 1 1/5 days
(B) 1/5 day
(C) 1 day
(D) 2 days
(E) 3 days
The answer is (C)


[User]
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Total distance covered = 495 +240 = 735 m
Required time = 700 * 2/35 = 42 sec
The answer: (D)
Question: A train 495 m long is running at a speed of 63 km/hr. In what time will it pass a bridge 240 m long?
Options:
(A) 39
(B) 40
(C) 41
(D) 42
(E) 43

Rationale: (x + 1)(2x - 2)(3x + 3) = ax3+bx2+cx+dax3+bx2+cx+d
6(x + 1)(x - 1)(x + 1) = ax3+bx2+cx+dax3+bx2+cx+d
6(x2x2 - 1)(x + 1) = ax3+bx2+cx+dax3+bx2+cx+d
⇒6(x3+x2−x−1)⇒6(x3+x2−x−1) = ax3+bx2+cx+dax3+bx2+cx+d
⇒6x3+6x2−6x−6⇒6x3+6x2−6x−6 = ax3+bx2+cx+dax3+bx2+cx+d
Equating the coefficients of like learns on both the sides, a = 6, b = 6, c = -6 and d = -6.
The answer: (C)
Question: (x +1 )(2x - 2)(3x + 3) = ax3+bx2+cx+dax3+bx2+cx+d What are the values of a, b, c and d?
Options:
(A) 2
(B) 7
(C) 6
(D) 1
(E) 9

Rationale: S = 600/20 = 1530 mps
S = 3600/30 = 120 sec = 2 min
The answer: (B)

[Assistant]
Question: A 600 meter long train crosses a signal post in 20 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) 8 min
(D) 9 min
(E) 5 min


[User]
Reasoning: 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: (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

Rationale: A's 1 hour work = 1/6;
(B + C)'s 1 hour work = 1/4;
(A + C)'s 1 hour work = 1/3
(A + B + C)'s 1 hour work = (1/4 + 1/6) = 5/12
B's 1 hour work = (5/12 - 1/3) = 1/12
B alone will take 12 hours to do the work.
The answer: (D)
Question: A can do a piece of work in 6 hours; B and C together can do it in 4 hours, which A and C together can do it in 3 hours. How long will B alone take to do it?
Options:
(A) 8hours
(B) 6hours
(C) 14hours
(D) 12hours
(E) 5hours

Reasoning: ? = 285 + 1895 – 655 – 645 or, ? = 880
Ans: (C)
Question: What approximate value should come in place of question mark (?) in the following equation
287.532 + 1894.029 – 657.48 = 643.095 + ?
Options:
(A) 870
(B) 790
(C) 880
(D) 770
(E) 890

Rationale: Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
The answer: (A)
Question: The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
(A) 49
(B) 88
(C) 25
(D) 18
(E) 11

Reasoning: 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.
Ans: (B)
Question: 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

Reasoning: (800*3*3)/100 = 72
920 + 72 = 992
Ans: (D)

[Assistant]
Question: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
Options:
(A) 299
(B) 277
(C) 266
(D) 992
(E) 188


[User]
Consider the question. Dacid obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Options:
(A) 32
(B) 88
(C) 77
(D) 99
(E) 75
 If the answer is '(E)'; explain the reasoning:

[Assistant] Average = (76 + 65 + 82 + 67 + 85)/5 = 375/5 = 75.


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

[Assistant]
The question is: The average of four results is 222 and that of the first three is 219. The fourth result is?
Options:
(A) 231
(B) 201
(C) 85
(D) 192
(E) 215
Step-by-step reasoning process: 4 * 222 â€“ 3 * 219 = 231


[User]
Sum of 17 even numbers = 17 * 18 = 306
Average = 306/17 = 18
This justifies what answer for what question? Q & A:

[Assistant]
The average of first 17 even numbers is?
Options:
(A) 10
(B) 11
(C) 18
(D) 20
(E) 24
(C)


[User]
Reasoning: Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out.
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

Rationale: Speed downstream = 60 + 30 = 90 kmph
Speed upstream = 60 - 30 = 30 kmph
The answer: (D)
Question: The speed of a boat in still water is 60kmph and the speed of the current is 30kmph. Find the speed downstream and upstream?
Options:
(A) kmph
(B) kmph
(C) kmph
(D) kmph
(E) kmph

Reasoning: 36963 = 111*111*3
Required smallest number = 3
3 is the smallest number which should be multiplied with 36963 to make it a perfect square.
Ans: (D)
Question: Find the smallest number which should be multiplied with 36963 to make it a perfect square.
Options:
(A) 4
(B) 7
(C) 4
(D) 3
(E) 6

Rationale: Cost price of article = 48$
% of overhead cost = 5
Net profit = 12 $
We need to calculate % markup
Net profit as % of cost price = (12/48)*100 = 25%
Total markup should be = 25 + 5 = 30%
The answer: (C)
Question: The purchase price of an article is $48. In order to include 5% of cost for overhead and to provide $12 of net profit, the markup should be
Options:
(A) 15%
(B) 25%
(C) 30%
(D) 40%
(E) 45%

Reasoning: Since average price of a pencil = 2
∴ Price of 75 pencils = 150
∴ Price of 30 pens = (510 – 150) = 360
∴ Average price of a pen = 360⁄60 = 12
Ans: (C)
Question: 30 pens and 75 pencils were purchased for 510. 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: The first letters are in alphabetical order with a letter skipped in between each segment: C, E, G, I, K. The second and third letters are repeated; they are also in order with a skipped letter: M, O, Q, S, U.
Ans: (D)

[Assistant]
Question: CMM, EOO, GQQ, _____, KUU
Options:
(A) MSQ
(B) IPS
(C) IIS
(D) ISS
(E) POL


[User]
Reasoning: Formula = √a×b
A = 64 and B = 81
√64×81 = 8 × 9 = 72
Ans: (D)
Question: Find the mean proportional between 64 & 81?
Options:
(A) A) 59
(B) B) 61
(C) C) 63
(D) D) 72
(E) E) 67

Reasoning: 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
Ans: (C)
Question: 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

Reasoning: Option(B) is correct
P(Both are red), 6C2/13C2 = 5/26
Ans: (B)
Question: An urn contains 6 red, 5 blue and 2 green marbles. If 2 marbles are picked at random, what is the probability that both are red?
Options:
(A) 6/13
(B) 5/26
(C) 6/26
(D) 9/26
(E) 10/27

Reasoning: 1/4: 1/2: 1/1 = 2:4:8
Ans: (A)

[Assistant]
Question: 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


[User]
Q: 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) 20
(B) 40
(C) 45
(D) 25
(E) 60
A: (A)
Explain how we arrive at this answer:

[Assistant]
Explanation: 1: 2/5 = 5: 2
2/7 * 70 = 20


[User]
[Ans] (E)
[Question] Solve:-
222 x 222 x 222 + 555 x 555 x 555 = ?(222 x 222 - 222 x 555 + 555 x 555)
Options:
(A) 888
(B) 333
(C) 555
(D) 988
(E) 777
[CoT] Given Exp. = (a3 + b3) = (a + b) = (222 + 555) = 777(a2 - ab + b2)

[Ans] (C)
[Question] 5,9,16,28,48,__
Options:
(A) 79
(B) 80
(C) 81
(D) 82
(E) 83
[CoT] (9+5) +2 = 16
(16+9) +3 = 28
(28+16)+4 = 48
(48+28)+5 = 81

[Ans] (E)
[Question]

[Assistant]
The edge of a cube is 7a cm. Find its surface?
Options:
(A) 24a8
(B) 24a4
(C) 24a1
(D) 24a2
(E) 294a2
[CoT] 6a2 = 6 * 7a * 7a = 294a2


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

[Assistant]
The question is: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 80 miles per hour. At 2 o’clock the faster train is 20 miles behind the slower one. How far apart are the two trains at 5 o'clock?
Options:
(A) 60 miles
(B) 80 miles
(C) 90 miles
(D) 130 miles
(E) 400 miles
Step-by-step reasoning process: Answer = D. 130 miles
Relational speed = 130 - 80 = 50 miles per hour
In 3 hours, difference = 50 * 3 = 150 miles
Fast train trailing 20 miles, so effective difference = 150 - 20 = 130 miles


[User]
Reasoning: Answer = A
Please refer diagram below
85 - 10 = 75
Ans: (A)
Question: 85 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

Rationale: Distance traveled by Eddy = 540 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 540/3 = 180 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 180/75 = 12/5
The answer: (D)
Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 540 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
Options:
(A) 8/3
(B) 3/8
(C) 8/5
(D) 12/5
(E) 5/3

Reasoning: D 85 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 85 matches were playe
Ans: (D)
Question: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 86 players took part in that tournament. How many matches were played?
Options:
(A) 90 matches
(B) 95 matches
(C) 99 matches
(D) 85 matches
(E) 87 matches

Rationale: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 54 = 378
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 378 - 780 = 25.
The answer: (A)
Question: The average of 13 numbers is 60. Average of the first 7 of them is 54 and that of the last 7 is 61. Find the 8th number?
Options:
(A) 25
(B) 83
(C) 45
(D) 53
(E) 64

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) 37
(C) 32
(D) 39
(E) 28

Reasoning: A’s two day’s work = 2/20 = 1/10
(A + B + C)’s one day’s work = 1/20 + 1/30 + 1/60 = 6/60 = 1/10
Work done in 3 days = (1/10 + 1/10) = 1/5
Now, 1/5 work is done in 3 days
Therefore, Whole work will be done in (3 x 5) = 15 days.
Ans: (C)

[Assistant]
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
Options:
(A) 12 days
(B) 15 days
(C) 18 days
(D) 20 days
(E) 22 days


[User]
The first letters are in alphabetical order with a letter skipped in between each segment: C, E, G, I, K. The second and third letters are repeated; they are also in order with a skipped letter: M, O, Q, S, U.
This justifies what answer for what question? Q & A:

[Assistant]
CMM, EOO, GQQ, _____, KUU
Options:
(A) MSQ
(B) IPS
(C) IIS
(D) ISS
(E) POL
(D)


[User]
Q: Find the least number must be subtracted from 427398 so that remaining no.is divisible by 15?
Options:
(A) 3
(B) 4
(C) 6
(D) 9
(E) 8
A: (A)
Explain how we arrive at this answer:

[Assistant] Explanation: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted


[User]
Rationale: Total = n(A) + n(B) - Both + None
None = Total - n(A) - n(B) + Both
Calculate "none" for each case
None(5+ yrs Line) = 200 - 50 - 40 + 30 = 140
None(5+ yrs Staff) = 160 - 40 - 50 + 20 = 90
Employees not taking either workshop/Total number of employees = (140 + 90)/(200 + 160) = 230/360 = About 64%
The answer: (B)
Question: Approximately what percent of the employees with 5 or more years of employment are NOT taking either workshop?
Options:
(A) 86%
(B) 64%
(C) 50%
(D) 14%
(E) 7%

Reasoning: D = 25 * 60 + 3500 = 5000 m
T = 5000/60 * 18/5 = 300 sec = 5 mins
Ans: (C)
Question: 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 3.5 km long?
Options:
(A) 4
(B) 3
(C) 5
(D) 7
(E) 9

Rationale: Given: x≥−3x≥−3 and x≤2 x≤2
(x+3)≥0(x+3)≥0 and (x−2)≤0(x−2)≤0
(x+3)≥0(x+3)≥0 and (2−x)≥0(2−x)≥0
The answer: (D)
Question: The entire range of values of x is marked by the dark region on the number line, as shown above. Which of the following expressions describes the range of values of x?
Options:
(A) (3+x) (2−x)  ≤ 0
(B) (3−x) (2+x)  ≥ 0
(C) (x−3) (x+2)  ≤ 0
(D) (x+3) (2−x)  ≥ 0
(E) (3−x) (2−x)  ≥ 0

Reasoning: 200/36 * 18/5 = 20 km/hr
Ans: (A)
Question: A boy runs 200 metres in 36 seconds. What is his speed ?
Options:
(A) 20 km/hr
(B) 24 km/hr
(C) 30 km/hr
(D) 32 km/hr
(E) 34 km/hr

Rationale: T = 20/36 * 18/5 = 2 sec
The answer: (E)
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

Rationale: S = 480/16 * 18/5 = 108 kmph
The answer: (B)

[Assistant]
Question: A train 480 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
Options:
(A) 22 kmph
(B) 108 kmph
(C) 54 kmph
(D) 71 kmph
(E) 88 kmph


[User]
Given the stream of consciousness rationale, provide a reasonable question and answer. Rationale: Speed = 117 * 5/18 = 65/2 m/sec
Total distance covered = 650 + 325 = 975 m
Required time = 975 * 2/65 = 30 sec
 The question and answer:

[Assistant]
A train 650 m long is running at a speed of 117 km/hr. In what time will it pass a bridge 325 m long?
Options:
(A) 30
(B) 35
(C) 40
(D) 45
(E) 50
The answer is (A)


[User]
Female students in 2005 = 25% of 40 = 10
Female students in 2007 = 40% of 85 = 34
Percentage increase = [(34- 10)/10] *100 % = 240%
In 2005, 25 percent of the math department’s 40 students were female, and in 2007, 40 percent of the math department’s 85 students were female. What was the percent increase from 2005 to 2007 in the number of female students in the department?
Options:
(A) 15%
(B) 50%
(C) 62.5%
(D) 115%
(E) 240%
(E)

According to the information in the question the maximum range would be between 450 and 650(200). The minimum range would be the greatest range for any one individual, which is listed in the problem as 110. So the difference between these would be 200-110 or 90.
Three people took GMAT practice tests in which the minimum and maximum possible scores are 200 and 800, respectively. They each took a test 4 times, and no one scored below 450 or over 650. If the individual ranges of the three people's scores in those 4 practice tests were 30, 80 and 110, what is the difference between the maximum and minimum possible ranges of all their scores put together.
Options:
(A) 90
(B) 120
(C) 50
(D) 70
(E) 100
(A)

(Place value of 6) - (Face value of 6) = (6000 - 6) = 5994

[Assistant]
The difference between the place value and the face value of 6 in the numeral 856973 is
Options:
(A) 5994
(B) 6973
(C) 973
(D) 1000
(E) 7000
(A)


[User]
Rationale: It is clear that 22 x 45 = 10 x 55 + K + 11 x 40 ⇒⇒ K = 0
The answer: (B)
Question: The average mark obtained by 22 candidates in an examination is 45. The average of the first ten is 55 while the last eleven is 40 .The marks obtained by the 11th candidate is ?
Options:
(A) 2
(B) 0
(C) 9
(D) 8
(E) 6

Reasoning: In 1 kg mixture quantity of iron = 200 gm
Let x gm sand should be added, then
10% of (1000 + x) = 200
\ x = 1000 gm = 1 kg
Ans: (A)
Question: In 1 kg mixture of sand and iron, 20% is iron. How much sand should be added so that the proportion of iron becomes 10%?
Options:
(A) 1 kg
(B) 200 gms
(C) 800 gms
(D) 1.8 kg
(E) None of these

Rationale: Answer = C
Please refer diagram below
95 - 10 = 85
The answer: (C)
Question: 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

Reasoning: In this series, each number is repeated, then 14 is subtracted to arrive at the next number.
Ans: (B)
Question: Look at this series: 53, 53, 39, 39, 25, 25, ... What number should come next?
Options:
(A) A) 12
(B) B) 11
(C) C) 27
(D) D) 53
(E) E) 86

Rationale: B's 1 day work = (1/12 - 1/20) = 1/30
Now, (A + B)'s 1 day work = (1/20 + 1/60) = 1/15
So, A and B together will complete the work in 15 days.
The answer: (C)
Question: A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?
Options:
(A) 11 days
(B) 77 days
(C) 15 days
(D) 18 days
(E) 19 days

Rationale: Speed downstream = d/t = 90/(3) = 30 kmph
Speed upstream = d/t = 51/(3) = 17 kmph
The speed of the stream = (30 - 17)/2 = 7 kmph
The answer: (A)

[Assistant]
Question: A man rows his boat 90 km downstream and 5` km upstream, taking 3 hours each time. Find the speed of the stream?
Options:
(A) 7 kmph
(B) 5 kmph
(C) 2 kmph
(D) 8 kmph
(E) 1 kmph


[User]
Q: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 2234
(B) 4350
(C) 4560
(D) 5132
(E) y=5184
A: (E)
Explain how we arrive at this answer:

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


[User]
Reasoning: P is the maternsl uncle of A
Ans: (B)
Question: A is the son of C; C and Q are sisters; Z is the mother of Q and P is the son of Z. Which of the following statements is true?
Options:
(A) P and A are cousins
(B) P is the maternsl uncle of A
(C) Q is the maternal grandfather of A
(D) C and P are sisters
(E) none

Rationale: 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
The answer: (A)
Question: In wardrobe Marry 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 hiswardrobe in the dark and pick out one shirt trouser 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) 3/5
(D) 3/7
(E) 4/9

Reasoning: Total ways to choose 4 employees from 8 employees = 8C3
Two women = 5C2
Two Men = 3C1
P = (5C2 * 3C1)/8C2 = 5/7 hence
Ans: (D)
Question: A small company employs 3 men and 5 women. If a team of 3 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?
Options:
(A)  1/14
(B)  1/7
(C)  2/7
(D)  5/7
(E)  1/2

Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
The answer: (C)
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is
Options:
(A) 1/9
(B) 1/7
(C) 1/5
(D) 1/6
(E) 1/3

Reasoning: Overall, there can be 73 minuses. Tus, it is
Ans: (C)
Question: A certain league has three divisions. The respective divisions had 10, 12 and 15 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?
Options:
(A)  70
(B)  72
(C)  73
(D)  78
(E)  80

Reasoning: Option 'E'
The total number of arrangements is
3P3 = 3! = 6
Ans: (E)

[Assistant]
Question: In how many different ways can the letters of the word "AIM" be rearrangement?
Options:
(A) 4
(B) 2
(C) 7
(D) 9
(E) 6


[User]
Question: A train 210 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) 12 sec
(E) 25 sec
Ans: (D)
CoT: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 210 * 2/35 = 12 sec
----
Question: The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the odds that it is an ace?
Options:
(A) 1/52
(B) 1/26
(C) 1/13
(D) 1/4
(E) 5/13
Ans: (C)
CoT: There are 13 spades, the probability that the spade we already have is an ace is therefore 1/13.
----
Question: Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?
Options:
(A) 19
(B) 28
(C) 30
(D) 32
(E) 44
Ans: (C)

[Assistant]
CoT: Using Speed Formula: Speed = Distance / Time
Distance to be covered = 51-11 = 40
Speed of approach = 57 + 63 floors/min
Time = 40/120 = 1/3
So Steve will cover 57x 1/3 floors in that time = 19
So he will be in 19 + 11 floor = 30th Floor
----


[User]
Question: How much 60% of 50 is greater than 50% of 30?
Options:
(A) 18
(B) 91
(C) 11
(D) 17
(E) 15
Ans: (E)
CoT: (60/100) * 50 – (50/100) * 30
30 - 15 = 15
----
Question: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 5 (B + G) is ?
Options:
(A) Equal to 3
(B) Less than 3
(C) More than 3
(D) Less than 1/3
(E) none of these
Ans: (E)
CoT: Let number of boys = x
Let number of girls = y
Therefore x/y = B and y/x = G
5(B + G) = 5[(x/y) + (y/x)] = 5[(x2 + y2)/xy] > 5
----
Question: At what rate percent on simple interest will a sum of money double itself in 30 years?
Options:
(A) 3 1/9%
(B) 3 7/3%
(C) 7 1/3%
(D) 5 1/3%
(E) 1 1/3%
Ans: (A)

[Assistant]
CoT: P = (P*30*R)/100
R = 3 1/3%
----


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

Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 210 * 2/35 = 18 sec
The answer: (D)
Question: A train 210 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) 18 sec
(E) 12 sec

Reasoning: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 se
Ans: (C)
Question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
Options:
(A) 18 sec
(B) 77 sec
(C) 48 sec
(D) 28 sec
(E) 12 sec

Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 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 140 m long?
Options:
(A) 40 sec
(B) 11 sec
(C) 88 sec
(D) 19 sec
(E) 10 sec

Reasoning: The total of 15 numbers = 15X11 = 165
The total of first 7 and last 7 numbers is = 7 X 14+7 X 6 = 140
So, the middle number is (165 - 140 ) = 25
Ans: (D)
Question: There are a total of 15 numbers with an average of 11. The average of first seven numbers is 14 and the average of last seven numbers is 6. What is the middle number?
Options:
(A) 31
(B) 24
(C) 29
(D) 25
(E) 21

Reasoning: Clearly, 97 is a prime number.
Ans: (C)

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


[User]
Consider the question. Last year, Company Z made q dollars in profit. Half of the profit went to the company’s founder. The rest was split evenly among his two 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
 If the answer is '(A)'; explain the reasoning:

[Assistant]
Profit = q
Profit to company founder = q/2
Profit to other partners = q/2
Number of other partners = 2
Profit to each partner = (q/2)/2 = q/4


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

[Assistant]
The question is: What is the area of a rectangle whose length is twice its width and whose perimeter is equal to that of a square whose area is 1?
Options:
(A) 1/9 sq units.
(B) 4/9 sq units.
(C) 8/9 sq units.
(D) 7/9 sq units.
(E) 6/9 sq units.
Step-by-step reasoning process: Area will be 2/3 *4/3 = 8/9 sq units.


[User]
Rationale: (800*3*3)/100 = 72
920 + 72 = 992
The answer: (D)
Question: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
Options:
(A) 299
(B) 277
(C) 266
(D) 992
(E) 188

Reasoning: The worst scenario is when she takes 10 red and 4 green, total of 14 jellybeans, and still doesn't have 3 distinct colors. But the next draw (15th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket.
Ans: (E)
Question: Grace has 18 jellybeans in her pocket. She has 10 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
Options:
(A) 4
(B) 8
(C) 12
(D) 13
(E) 15

Rationale: 6a2 = 6 * 2a * 2a = 24a2
The answer: (D)
Question: The edge of a cube is 2a cm. Find its surface?
Options:
(A) 24a8
(B) 24a4
(C) 24a1
(D) 24a2
(E) 24a7

Reasoning: Profit = q
Profit to company founder = 2q/3
Profit to other partners = q/3
Number of other partners = 3
Profit to each partner = (q/3)/3 = q/9
Ans: (A)
Question: Last year, Company X made q dollars in profit. two Thrid 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/9
(B) q/5
(C) q/6
(D) q/7
(E) q/8

Rationale: Work done by X in 1 day = 1/20
Work done by Y in 1 day = 1/15
Work done by Y in 9 days = 9/15 = 3/5
Remaining work = 1 – 3/5 = 2/5
Number of days in which X can finish the remaining work = (2/5) / (1/20) = 8
The answer: (D)
Question: X can finish a work in 20 days. Y can finish the same work in 15 days. Yworked for 9 days and left the job. how many days does X alone need to finish the remaining work?
Options:
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9

Rationale: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 se
The answer: (C)

[Assistant]
Question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
Options:
(A) 66 sec
(B) 46 sec
(C) 48 sec
(D) 65 sec
(E) 64 sec


[User]
Question: A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 6, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created?
Options:
(A) 27
(B) 22
(C) 24
(D) 26
(E) 30
Ans: (A)
CoT: Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes
----
Question: Find the 100th place digit of a number forming from digits 1 to 9 without repeatation and number passes the divisibility test of 11 means difference of sum of alternative digits is 0 or divisible by 11.
Options:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Ans: (D)
CoT: Largest no is 987652413
So digit will be 4
----
Question: 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
Ans: (A)

[Assistant]
CoT: 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]
Given the stream of consciousness rationale, provide a reasonable question and answer. Rationale: (1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2
 The question and answer:

[Assistant]
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) 5
(D) 6
(E) 8
The answer is (B)


[User]
What was the question for this implicit rationale, and corresponding answer?
Since 32P6 = k32C6
⇒ 32/ ( 32-6 ) = k(32/ ( 32-6 )
⇒k = 6! = 720
 The answer: (D)

[Assistant]
The question: If P(32, 6) = kC (32, 6), then what is the value of k?
Options:
(A) 6
(B) 32
(C) 120
(D) 720
(E) None


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

[Assistant]
The question is: A bus travels k miles in n hours. How many miles will it travel in x hours at the same rate?
Options:
(A) knx
(B) k⁄n
(C) x
(D) kx⁄n
(E) kn⁄x
Stream of consciousness: Given Speed = k/n
To Find distance in x hours with same speed
Distance = speed * time
Distance = k/n*x = kx/n


[User]
Rationale: I = (450*8*5)/100 = 180
The answer: (C)
Question: Find the simple interest on Rs.450 for 8 months at 5 paisa per month?
Options:
(A) 277
(B) 270
(C) 180
(D) 266
(E) 121

Reasoning: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 15 = 250 m
Ans: (E)
Question: A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train?
Options:
(A) 120 m
(B) 190 m
(C) 115 m
(D) 110 m
(E) 250 m

Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
The answer: (E)
Question: Find the value of y from given equation: (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 2568
(B) 3468
(C) 4500
(D) 4876
(E) 5184

Reasoning: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 70 * 2/35 = 140 sec
Ans: (A)
Question: A train 70 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
(A) 140 sec
(B) 160 sec
(C) 176 sec
(D) 150 sec
(E) 170 sec

Rationale: 8597 – ? = 7429 – 4358
∴ ? = 5526
The answer: (B)
Question: What should come in place of question mark(?) in the following equation?
8597 – ? = 7429 – 4358
Options:
(A) 5706
(B) 5526
(C) 5426
(D) 5626
(E) None of these

Rationale: Time = (100 x 100)/(500 x 5) years = 4 years.
The answer: (B)

[Assistant]
Question: How much time will it take for an amount of 500 to yield 100 as interest at 5% per annum of simple interest?
Options:
(A) 3 year
(B) 4 year
(C) 6 year
(D) 5 year
(E) 7 year


[User]
D = 110 + 170 = 280 m
S = 36 * 5/18 = 10
T = 280 * 1/10 = 28 sec
How long does a train 110 m long traveling at 36 kmph takes to cross a bridge of 170 m in length?
Options:
(A) 28
(B) 16.0
(C) 16.4
(D) 16.8
(E) 16.1
(A)

1 also gives the remainder of 1 when divided by 4. So, there are total of 15 numbers.
How many positive integers less than 60 have a reminder 01 when divided by 4?
Options:
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
(C)

I got 20/(sqr2 +1) and just forgot to multiply by (sqr2 -1).

[Assistant]
Consider a quarter of a circle of radius 20. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.
Options:
(A) 20*(sqr2 -1)
(B) 8*(sqr3 -1)
(C) 4*(sqr7 - 1)
(D) 12* (sqr7 -1)
(E) None of these
(A)


[User]
What was the question for this implicit rationale, and corresponding answer?
The correct answer should not take the form: 5x + 3. Hence, it is
 The answer: (A)

[Assistant]
The question: People standing in a straight line are wearing alternating colored shirts. The pattern of shirts begins with red, followed by green, blue, white and yellow. This pattern continues (red, green, blue, white and yellow) until it ends with a blue shirt. If there are more than 5 people in line, which of the following cannot be the number of people in the line?
Options:
(A) 27
(B) 38
(C) 53
(D) 63
(E) 78


[User]
Given the rationale, provide a reasonable question and answer. Step-by-step reasoning process: Speed = 90*(5/18) m/sec = 25 m/sec
Length of Train (Distance) = Speed * Time
25 *10 = 250 meter
 The question and answer:

[Assistant]
A train running at the speed of 90 km/hr crosses a pole in 10 seconds. Find the length of the train.
Options:
(A) 150
(B) 180
(C) 250
(D) 200
(E) 225
The answer is (C)


[User]
Rationale: A intersect B intersect C = 4
A intersect B but not C = 1
B intersect C but not A = 1
C intersec A but not B = 1
A only is 2; B only is 2; C only is 2
Therefore, total 13 members serve on one or more boards of directors.
The answer: (B)
Question: Each of three charities in Novel Grove Estates has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors?
Options:
(A) 8
(B) 13
(C) 16
(D) 24
(E) 27

Reasoning: 23m - n = p
Add n to both sides:
23m = n + p
Add m to both sides:
24m = n + p + m
Now, divide both sides by 3
8m = (n + p + m)/3 = the average of n, p, and m
Ans: (E)
Question: If 23m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
Options:
(A) 2m −1
(B) 4m
(C) 6m
(D) m/5
(E) 8m

Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 18 = 300 m
The answer: (C)
Question: A train running at the speed of 60 km/hr crosses a pole in 18 sec. What is the length of the train?
Options:
(A) 118
(B) 150
(C) 300
(D) 258
(E) 191

Reasoning: Maximum points of intersection between n different circles = n*(n - 1) = 10*9 = 90
Ans: (A)
Question: There are different 10 circles. What is the number of the greatest possible points with which the circles intersect?
Options:
(A) 90
(B) 100
(C) 110
(D) 180
(E) 200

Rationale: Sum of 13 even numbers = 13 * 14 = 110
Average = 182/13 = 14
The answer: (E)
Question: The average of first 13 even numbers is?
Options:
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14

Rationale: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.
The answer: (C)

[Assistant]
Question: Find the invalid no.from the following series 13, 18, 25, 30, 37, 40
Options:
(A) 23
(B) 25
(C) 40
(D) 46
(E) 48


[User]
Given the stream of consciousness rationale, provide a reasonable question and answer. Rationale: 1/30 + 1/40 = 7/120
120/7 = 17 1/7 days
 The question and answer:

[Assistant]
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) 17 1/7 days
(B) 17 1/8 days
(C) 17 5/7 days
(D) 17 3/7 days
(E) 13 1/7 days
The answer is (A)


[User]
P(1 + 20/100)n > 2P or (6/5)n > 2
Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years.
This justifies what answer for what question? Q & A:

[Assistant]
The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is?
Options:
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
(B)


[User]
Suppose the amount in the beginning was Rs ’x’
Money spent on clothes = Rs 1x/3 Balance = Rs 2x/3
Money spent on food = 1/5 of 2x/3 = Rs 2x/15
Balance = 2x/3 - 2x/15 = Rs 8x/15
Money spent on travel = 1/4 of 8x/15 = Rs 2x/15 = 8x/15 - 2x/15 = 6x/15 = Rs2x/5
Therefore 2x/5 = 500 = 1250
A person spends 1/3rd of the money with him on clothes, 1/5th of the remaining on food and 1/4th of the remaining on travel. Now, he is left with Rs 500. How much did he have with him in the beginning?
Options:
(A) s 200
(B) s 1250
(C) s 300
(D) s 450
(E) s 550
(B)

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
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) 5 kmph
(B) 7 kmph
(C) 9 kmph
(D) 8 kmph
(E) 1 kmph
(D)

Six members can be selected from ten members in
10C6 = 10C4 ways.

[Assistant]
in how many ways can six members be selected from a group of ten members?
Options:
(A) 10C6
(B) 10C4
(C) 10C9
(D) 10C2
(E) 10C1
(B)


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

[Assistant]
The question is: What is the smallest positive integer x, such that 1,152x is a perfect cube?
Options:
(A) 4
(B) 6
(C) 8
(D) 12
(E) 18
Stream of consciousness: We need to make 1152x a perfect cube, hence we need to have the powers a multiple of 3
1152 = 2^7*3^2
The minimum value of x for which 1152x is a perfect cube = 2^2*3 = 12


[User]
For this chain-of-thought reasoning and answer, what was the question?
Number of ways of selecting 2 fiction books = 7C2
Number of ways of selecting 2 non fiction books = 6C2
7C2 * 6C2 = 21 * 15 = 315
 A: (C)

[Assistant]
Q: There are 7 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them?
Options:
(A) 90
(B) 120
(C) 315
(D) 180
(E) 200


[User]
Rationale: 5 * 46 – 4 * 45 = 50
The answer: (D)
Question: The average of five results is 46 and that of the first four is 45. The fifth result is?
Options:
(A) 29
(B) 27
(C) 29
(D) 50
(E) 81

Reasoning: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
Ans: (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) 2277
(B) 3000
(C) 2682
(D) 7222
(E) 2682

Rationale: 10 because after 10 wickets, the innings is complet
The answer: (E)
Question: A BOWLER CAN TAKE MAX. 3WICKETS IN A OVER.IF HE BOWLS 6OVERS IN AN INNINGS, HOW MANY MAXIMUM WICKETS CAN HE TAKE?
Options:
(A) 8
(B) 9
(C) 11
(D) 7
(E) 10

Reasoning: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 18 = 300 m
Ans: (C)
Question: A train running at the speed of 60 km/hr crosses a pole in 18 sec. What is the length of the train?
Options:
(A) 356
(B) 278
(C) 300
(D) 279
(E) 150

Rationale: 4/9 P = (P*R*R)/100
R = 20/3 = 6 2/3%
The answer: (A)
Question: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
Options:
(A) 6 2/3%
(B) 6 2/7%
(C) 6 2/2%
(D) 6 3/3%
(E) 6 5/3%

Rationale: Since the man can go in 4 ways and can back in 3 ways. Therefore total number of ways are 4 x3 = 12ways.
The answer: (C)

[Assistant]
Question: 4 buses runs between Chennai and Mysore. If a man goes from Chennai to Mysore by a bus and comes back to Mysore by another bus, then the total possible ways are
Options:
(A) 4
(B) 8
(C) 12
(D) 16
(E) None of these


[User]
Rationale: If deepak can only choose one of each, there are 5*3 = 15 possible combinations.
The answer: (C)
Question: if deepak has 5 pants and 3 shirts how many combinations can deepak make?
Options:
(A) 10
(B) 9
(C) 15
(D) 20
(E) 25

Reasoning: 21-12 < no of hrs < 21-5
9< no of hrs < 16.
Ans: (D)
Question: Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 5 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week?
Options:
(A) 30
(B) 20
(C) 18
(D) 12
(E) 6

Rationale: The probability of selecting girl is: 25/100 = 1/4
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 10/100 = 1/10
Three are independent;probability of rich and fair complexioned girl is:
(1/4) Ã—(1/5) Ã— (1/10) = 1/200
The answer: (A)
Question: A class consists of 100 students, 25 of them are girls and 75 boys; 20 of them are rich and remaining poor; 10 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
Options:
(A) 1/200
(B) 1/59
(C) 1/56
(D) 1/54
(E) 1/53

Reasoning: 16 m/s = 16 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 16 * 18/5 * 15/4 km = 216 km.
Ans: (E)
Question: If a man can cover 16 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
(A) 180km
(B) 190km
(C) 200km
(D) 210km
(E) 216km

Rationale: 220 + 43 = 263/17 = 8 (Remainder)
The answer: (B)
Question: A no.when divided by 220 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
Options:
(A) 2
(B) 8
(C) 9
(D) 11
(E) 15

Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
The answer: (E)

[Assistant]
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 1234
(B) 2343
(C) 4546
(D) 3435
(E) 5184


[User]
Given the stream of consciousness rationale, provide a reasonable question and answer. Rationale: Work done by X in 1 day = 1/21
Work done by Y in 1 day = 1/15
Work done by Y in 5 days = 5/15 = 1/3
Remaining work = 1 – 1/3 = 2/3
Number of days in which X can finish the remaining work = (2/3) / (1/21) = 14
 The question and answer:

[Assistant]
X can finish a work in 21 days. Y can finish the same work in 15 days. Y worked for 5 days and left the job. how many days does X alone need to finish the remaining work?
Options:
(A) 12
(B) 13
(C) 16
(D) 14
(E) 18
The answer is (D)


[User]
What was the question for this implicit rationale, and corresponding answer?
Distance covered in first two hours = 10 Ã— 2 = 20 km
Distance covered in next two hours = 12 Ã— 2 = 24 km
Distance covered in next two hours = 14 Ã— 2 = 48 km
Distance covered in first six hours
20 + 24 + 48 = 92 km
Remaining distance = 8 km
92 + 8 = 100 km
 The answer: (B)

[Assistant]
The question: A woman begins bicycling with a pace of 10 kmph and she increases her pace every two hours by 2 kmph. She rests from bicycling 2 hours after her pace reaches her maximum speed of 14 kmph. She does a cool-down for the final 8 km at a pace of 2 kmph. How far in km did she bicycle?
Options:
(A) 96 km
(B) 100 km
(C) 106 km
(D) 116 km
(E) 126 km


[User]
Explain simply why (E) is the correct answer to: 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.9880. Find the share of A?
Options:
(A) 3002
(B) 3000
(C) 3018
(D) 3019
(E) 4000. Explanation:

[Assistant]
60*5:36*6:75*3
100: 72: 75
100/247 * 9880 = 4000


[User]
Given the rationale, provide a reasonable question and answer. Step-by-step reasoning process: 1/30 + 1/40 = 7/120
120/7 = 17 1/7 days
 The question and answer:

[Assistant]
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) 17 1/7
(B) 17 1/9
(C) 17 1/2
(D) 17 1/7
(E) 17 1/5
The answer is (A)


[User]
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%is the reasoning for what question and answer pair?

[Assistant]
Q: 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%
A: (E)


[User]
What was the question for this implicit rationale, and corresponding answer?
D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 se
 The answer: (C)

[Assistant]
The question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
Options:
(A) 287 sec
(B) 288 sec
(C) 48 sec
(D) 16 sec
(E) 17 sec


[User]
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
The answer: (C)
Question: If six persons sit in a row, then the probability that three particular persons are always together is?
Options:
(A) 1/9
(B) 1/6
(C) 1/5
(D) 1/2
(E) 1/3

Rationale: Let the bill be x. Then
90% of x = 45
⇒ x = 45×100/90 = 50
The answer: (A)
Question: If 10 % of an electricity bill is deducted, 45 is still to be paid. How much was the bill?
Options:
(A) 50
(B) 60
(C) 55
(D) 70
(E) None of these

Rationale: Speed downstream = 50 + 20 = 70 kmph
Speed upstream = 50 - 20 = 30 kmph
The answer: (C)

[Assistant]
Question: The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
(A) 40, 68 kmph
(B) 40, 30 kmph
(C) 70, 30 kmph
(D) 40, 60 kmph
(E) 20, 60 kmph


[User]
Rationale: (1-(1/16))(1-(1/15))(1-(5/7)) of Income = 50
Hence income = 200
The answer: (B)
Question: 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

Reasoning: (60/100) * 50 – (40/100) * 30
30 - 12 = 18
Ans: (A)
Question: How much 60% of 50 is greater than 40% of 30?
Options:
(A) 18
(B) 27
(C) 26
(D) 29
(E) 21

Rationale: Average of 20 numbers = 0
Sum of 20 numbers = (0 * 20) = 0
It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a).
The answer: (D)
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
Options:
(A) 7
(B) 4
(C) 12
(D) 19
(E) 28

Reasoning: Female students in 2005 = 30% of 40 = 12
Female students in 2007 = 40% of 65 = 26
Percentage increase = [(26 - 12)/12] *100 % = 116%
Ans: (B)
Question: In 2005, 30 percent of the math department’s 40 students were female, and in 2007, 40 percent of the math department’s 65 students were female. What was the percent increase from 2005 to 2007 in the number of female students in the department?
Options:
(A) 15%
(B) 116%
(C) 136%
(D) 155%
(E) 160%

Rationale: Increase = (30/50)*100 = (3/5)*100 = 60%.
The answer: (E)
Question: John makes $50 a week from his job. He earns a raise and now makes $80 a week. What is the % increase?
Options:
(A) 16%
(B) 16.66%
(C) 17.9%
(D) 18.12%
(E) 60%

Rationale: (12/170)/(4/50) = 15/17 = 88% it means that 12/170 represents only 88%. Therefore a decrease of 12%.
The answer: (A)

[Assistant]
Question: A pharmaceutical company received $4 million in royalties on the first $50 million in sales of and then $12 million in royalties on the next $170 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $50 million in sales to the next $170 million in sales?
Options:
(A) 12%
(B) 15%
(C) 45%
(D) 52%
(E) 56%


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

[Assistant]
The question is: If 4 men can reap 40 acres of land in 15 days, how many acres of land can 16 men reap in 30 days?
Options:
(A) 320
(B) 240
(C) 369
(D) 489
(E) 125
Step-by-step reasoning process: 4 men 40 acres 15 days
16 men ? 30 days
40 * 16/4 * 30/15
40 * 4 * 2
40 * 8 = 320


[User]
Ques: When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder X when N is divided by 30?
Options:
(A) (a)  4
(B) (b)  7
(C) (c)  11
(D) (d)  13
(E) (e)  17
Ans: (C)
CoT: N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder X when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.

Ques: A 21 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) 6
(C) 88
(D) 77
(E) 14
Ans: (B)
CoT: 1: 2/5 = 5: 2
2/7 * 21 = 6

Ques: In his room, Dumbo has three trousers. One of them is black, the second is blue, and the third is brown. In his room, he also has four shirts. One of them is black and the other 3 are white. He opens his room in the dark and picks out one shirt and one trouser pair without examining the colour. What is the likelihood that neither the shirt nor the trouser is black?
Options:
(A) 1/12
(B) 1/6
(C) 1/2
(D) 1/4
(E) 1/3
Ans: (C)
CoT: Probability that trouser is not black = 2/3
Probability that shirt is not black = 3/4
Required probability = 2/3 x 3/4 = 1/2

Ques: Rs.600 amounts to Rs.900 in 3 years at simple interest. If the interest is increased by 4%, it would amount to how much?
Options:
(A) 672
(B) 246
(C) 258
(D) 856
(E) 653
Ans: (A)

[Assistant]
CoT: (600*3*4)/100 = 72
600 + 72 = 672


[User]
What was the question for this implicit rationale, and corresponding answer?
On first wheel there can be 10 digits. On the second wheel there will be one of the 9 digits and on the third wheel there will be 8 digits. Therefore, the number of numbers is
10 x 9 x 8 = 720
 The answer: (A)

[Assistant]
The question: A number lock on a suitcase has 3 wheels each labelled with 10 digits from 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?
Options:
(A) 720
(B) 760
(C) 680
(D) 780
(E) 880


[User]
Distance traveled by Eddy = 480 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 480/3 = 160 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 160/75 = 32/15
This justifies what answer for what question? Q & A:

[Assistant]
Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 480 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
Options:
(A) 32/15
(B) 3/8
(C) 8/5
(D) 5/8
(E) 5/3
(A)


[User]
Given the rationale, provide a reasonable question and answer. Step-by-step reasoning process: 64000* 9/8 * 9/8 = 81000
 The question and answer:

[Assistant]
Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?
Options:
(A) Rs.81000
(B) Rs.80000
(C) Rs.75000
(D) Rs.64000
(E) Rs.68000
The answer is (A)


[User]
Consider the question. A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is?
Options:
(A) 124432
(B) 145366
(C) 157768
(D) 178432
(E) 220030
 If the answer is '(E)'; explain the reasoning:

[Assistant] (555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030


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

[Assistant]
Question: There are 10 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them?
Options:
(A) 90
(B) 120
(C) 675
(D) 180
(E) 200
Stream-of-consciousness: Number of ways of selecting 2 fiction books = 10C2
Number of ways of selecting 2 non fiction books = 6C2
10C2 * 6C2 = 45 * 15 = 675


[User] Reconstruct a question, answer pair from this explanation: Age of B = Age of (A + B + C) â€“ Age of (A + C) = 29 Ã— 3 â€“ 32 Ã— 2 = 87 â€“ 64 = 23 years

[Assistant]
Q:The average age of A, B and C is 29 years. If the average age of A and C is 32 years, what is the age of B in years ?
Options:
(A) 19
(B) 35
(C) 20
(D) 32
(E) 23
A:(E)


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

[Assistant]
The question is: During a sale, the price of a pair of shoes is marked down 15% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?
Options:
(A) 9%
(B) 10%
(C) 11%
(D) 18%
(E) 90%
Stream of consciousness: Assume the price = 100
Price during sale = 85
Price after sale = 100
Percent increase = 15/85*100 = 18% approx.


[User]
For this chain-of-thought reasoning and answer, what was the question?
Present age of total members = 6 X 28 = 168
7 yrs back their ages were = 6 x 7 = 42
Ages at the birth of youngest member = 168 - 42 = 126
Therefore, avg age at the birth of youngest member = 126/6 = 21.
 A: (C)

[Assistant]
Q: The average age of a family of 6 members is 28 years.If the age of the youngest member is 7 years,what was the average age of the family at the birth of the youngest member?
Options:
(A) 15
(B) 18
(C) 21
(D) 12
(E) 19


[User]
(Ans). (E)
(Question). If 21 WOMen and 12 men can finish the work in 42 days.How many men should accompany 42 women to that the work will be completed in ten and half days???
Options:
(A) 40
(B) 45
(C) 50
(D) 60
(E) 15
(CoT). 15 men using chain rul

(Ans). (A)
(Question). The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
Options:
(A) 6 2/3%
(B) 6 2/8%
(C) 6 9/3%
(D) 6 2/3%
(E) 6 2/1%
(CoT). 4/9 P = (P*R*R)/100
R = 20/3 = 6 2/3%

(Ans). (A)
(Question). There are 23 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) 51
(D) 58
(E) 63
(CoT). {Total} = {M} + {N} - {Both}
{Total} = 23 + 28 - 12 = 39.

(Ans). (B)
(Question).

[Assistant]
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) 3
(C) 3.5
(D) 4
(E) 4.5
(CoT). 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.


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

[Assistant]
Question: The average of seven numbers is 26. 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) 83
(C) 29
(D) 32
(E) 34
Stream-of-consciousness: The total of seven numbers = 7X26 = 182
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (182 - 99 ) = 83


[User]
Given the rationale, provide a reasonable question and answer. Step-by-step reasoning process: 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 question and answer:

[Assistant]
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
The answer is (E)


[User]
Given the following reasoning and answer, what was the question? 31 + 37 + 41 + 43 = 152/4 = 38
 The answer: (A)

[Assistant]
The question The average of first four prime numbers greater than 30 is?
Options:
(A) 38
(B) 20
(C) 30
(D) 40
(E) 50


[User]
Consider the question. 45 pupil,out of them 12 in debate only and 22 in singing only.then how many in both?
Options:
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
 If the answer is '(C)'; explain the reasoning:

[Assistant] The intersection for two = 45 - 12 - 22 = 11 play both games.


[User]
Question: 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) 22 minutes
(B) 88 minutes
(C) 70 minutes
(D) 77 minutes
(E) 48 minutes
Ans: (C)
CoT: 1/20 - 1/28 = 1/70
70 minutes
----
Question: Two persons A and B can complete a piece of work in 15 days and 30 days respectively. If they work together, what part of the work will be completed in 5 days?
Options:
(A) 1/8
(B) 1/3
(C) 1/6
(D) 1/2
(E) 5/3
Ans: (D)
CoT: A's one day's work = 1/15
B's one day's work = 1/30
(A + B)'s one day's work = 1/15 + 1/30 = 1/10
The part of the work completed in 5 days = 5 (1/10) = 1/2.
----
Question: Find the smallest number which should be divided with 3872 to make it a perfect square.
Options:
(A) 8
(B) 6
(C) 2
(D) 4
(E) 1
Ans: (C)

[Assistant]
CoT: 3872 = 11*11*2*2*2*2*2
Required smallest number = 2
2 is the smallest number which should be divided with 3872 to make it a perfect square.
----


[User]
Rationale: S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
The answer: (A)
Question: A 600 meter long train crosses a signal post in 40 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) 8 min
(D) 9 min
(E) 5 min

Reasoning: Simple interest = (18000 * 5 * 15)/100 = Rs. 13500
Amount = P + I = 18000 + 13500 = Rs. 31500
Ans: (A)
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for five years?
Options:
(A) 31500
(B) 27773
(C) 29989
(D) 28800
(E) 29883

Rationale: Correct average = [( 50 x 36) - 73 + 37 )]/36 = 1764/36 = 49 kg.
The answer: (A)
Question: The average weight of 36 men is 50 kg. It was found later that the figure of 37 kg was misread as 73 kg. What is the correct average?
Options:
(A) 49 kg
(B) 51 kg
(C) 50.5 kg
(D) 51.5 kg
(E) None of these

Reasoning: Work done by X in 1 day = 1/24
Work done by Y in 1 day = 1/16
Work done by Y in 10 days = 10/16 = 5/8
Remaining work = 1 – 5/8 = 3/8
Number of days in which X can finish the remaining work = (3/8) / (1/24) = 9
Ans: (E)
Question: X can finish a work in 24 days. Y can finish the same work in 16 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work?
Options:
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9

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 answer: (E)
Question: 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

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)

[Assistant]
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


[User]
[Ques]: The no. of girls in a class are 7times the no. of boys, which value cannever be the of total students?
Options:
(A) 20
(B) 35
(C) 30
(D) 40
(E) 42
*Ans*: (C)
--CoT--: Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.

[Ques]: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
(A) 23
(B) 27
(C) 28
(D) 29
(E) 31
*Ans*: (B)
--CoT--: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27

[Ques]: A train 420 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
(A) 36 sec
(B) 16 sec
(C) 17 sec
(D) 88 sec
(E) 12 sec
*Ans*: (A)
--CoT--: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 420 * 2/35 = 36 sec

[Ques]: Find the area of a parallelogram with base 24 cm and height 16 cm.
Options:
(A) 384 cm^2
(B) 200 cm^2
(C) 250 cm^2
(D) 350 cm^2
(E) 400 cm^2
*Ans*: (A)

[Assistant] --CoT--: Area of a parallelogram = base * height = 24 * 16 = 384 cm2


[User]
Given the rationale, provide a reasonable question and answer. Step-by-step reasoning process: If he draws any combination of 3 socks he will definitely have the matching pair of either colour.
 The question and answer:

[Assistant]
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) 6
(E) 9
The answer is (A)


[User]
Consider the question. How many terminating zeroes Q does 200! have?
Options:
(A)  40
(B)  48
(C)  49
(D)  55
(E)  64
 If the answer is '(C)'; explain the reasoning:

[Assistant] You have 40 multiples of 5, 8 of 25 and 1 of 125. This will give 49 zeros.


[User]
Consider the question. How much is 80% of 40 is greater than 4/5 of 25?
Options:
(A) 17
(B) 19
(C) 11
(D) 12
(E) 10
 What is the step-by-step reasoning process to arrive at the answer: (D)?

[Assistant]
(80/100) * 40 – (4/5) * 25
32 - 20 = 12


[User]
46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
What will come in place of the x in the following Number series? 46080, 3840, 384, x
Options:
(A) 48
(B) 3
(C) 4
(D) 5
(E) 6
(A)

Number of times wheel moves in 1 hour = 15 * 60 = 900
:. Distance moves = (900 *35) cms = 31500 cms
In metres = 315 metre
A wheel rotates 15 times every minute and moves 35 cm during each rotation. How many metres does the wheel move in one hour?
Options:
(A) 6 metre
(B) 12 metre
(C) 120 metre
(D) 315 metre
(E) 130 metre
(D)

Increase = (20/40)*100 = 50%.

[Assistant]
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%
(E)


[User]
Stream of consciousness rationale: Area of the outer rectangle = 23 Ã— 16 = 368 m2
Area of the inner rectangle = 19 Ã— 12 = 228 m2
Required area = (368 â€“ 228) = 140 m2
The question and answer pair are described below.

[Assistant]
Q: The floor of a rectangular room is 19 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is :
Options:
(A) 144 m2
(B) 140 m2
(C) 108 m2
(D) 158 m2
(E) None of these
A: (B)


[User]
[Ques]: In how many different ways can the letters of the word â€˜EXTENTâ€™ be arranged?
Options:
(A) 250
(B) 180
(C) 300
(D) 310
(E) 360
*Ans*: (B)
--CoT--: Number of ways = 6!/2!2! = 6X5X4X3X2X1/2X1X2X1 = 180

[Ques]: How much 60% of 50 is greater than 40% of 30?
Options:
(A) 18
(B) 28
(C) 26
(D) 27
(E) 23
*Ans*: (A)
--CoT--: (60/100) * 50 – (40/100) * 30
30 - 12 = 18

[Ques]: The average age of a family of 6 members is 22 years.If the age of the youngest member is 7 years,what was the average age of the family at the birth of the youngest member?
Options:
(A) 15
(B) 18
(C) 21
(D) 12
(E) 19
*Ans*: (A)
--CoT--: Present age of total members = 6 X 22 = 132
7 yrs back their ages were = 6 x 7 = 42
Ages at the birth of youngest member = 132 - 42 = 90
Therefore, avg age at the birth of youngest member = 90/6 = 15.

[Ques]: There are 25 balls in a jar. You take out 5 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/5. How many blue balls were there in the beginning?
Options:
(A) 12.
(B) 9.
(C) 8.
(D) 7.
(E) 6.
*Ans*: (B)

[Assistant] --CoT--: 9 = 5 blue balls + 20/ 5


[User]
[Ans] (A)
[Question] The number N is H,284, where H represents the ten's digit. If N is divisible by 6, what is the value of H?
Options:
(A) 1
(B) 2
(C) 3
(D) 5
(E) 8
[CoT] If the number is divisible by 6, then the sum of the digits must also be divisible by both 3 and 2. Only 1 yields such a number.

[Ans] (A)
[Question] The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
(A) 49
(B) 88
(C) 25
(D) 18
(E) 11
[CoT] Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs

[Ans] (B)
[Question]

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


[User]
[Ques]: The average of 7 consecutive numbers is 33. The highest of these numbers is:
Options:
(A) 28
(B) 30
(C) 33
(D) 36
(E) 28
*Ans*: (D)
--CoT--: The average of 7 consecutive numbers will be the 4th number which is given to be = 33 5th number = 34, 6th number = 35, 7th number = 36

[Ques]: 60 is increased by 50%. Find the final number.
Options:
(A) 100
(B) 110
(C) 90
(D) 30
(E) 160
*Ans*: (C)
--CoT--: Final number = Initial number + 50%(original number) = 60 + 50%(60) = 60 + 30 = 90.

[Ques]: 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
*Ans*: (C)
--CoT--: 1
1 × 2 + 2 = 4
4 × 2 + 2 = 10
10 × 2 + 2 = 22
22 × 2 + 2 = 46
46 × 2 + 2 = 94

[Ques]: The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is?
Options:
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
*Ans*: (B)

[Assistant]
--CoT--: P(1 + 20/100)n > 2P or (6/5)n > 2
Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years.


[User]
[Ques]: A dice is thrown. What is the probability that the number shown in the dice is divisible by 3?
Options:
(A) 5/5
(B) 5/9
(C) 5/1
(D) 1/3
(E) 5/2
*Ans*: (D)
--CoT--: Total number of outcomes possible when a die is rolled, n(S) = 6 (∵ 1 or 2 or 3 or 4 or 5 or 6)
E = Event that the number shown in the dice is divisible by 3 = {3, 6}
The probability = 2/6 = 1/3.

[Ques]: Let p be a prime number greater than 2 and let N = 14p. How many even numbers divide N?
Options:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
*Ans*: (A)
--CoT--: Answer: A. There is exactly one. The prime factorization of 14 is 14 = 2*7, so N = 2*7*p = 7*2*p = 7*2p, so 2p is the only even number that divides N.

[Ques]: Lisa's grade was 75th percentile of the 40 grades for her class. Of the 50 grades from another class, 8 were higher than Lisa's, and the rest were lower. If no other grade was the same as Lisa's grade, then Lisa's grade was what percentile of the grades of the two classes of two classes combined?
Options:
(A) 62nd
(B) 74th
(C) 80th
(D) 87th
(E) 92nd
*Ans*: (C)
--CoT--: 62nd/74th/80th/87th/92nd

[Ques]: 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)
*Ans*: (D)

[Assistant]
--CoT--: 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


[User]
Given the rationale, provide a reasonable question and answer. Step-by-step reasoning process: 12
12 × 4 + 2 = 50
50 × 4 + 2 = 202
202 × 4 + 2 = 810
810 × 4 + 2 = 3242
3242 × 4 + 2 = 12970
 The question and answer:

[Assistant]
What number comes next in the following number series? 12, 50, 202, 810, 3242, _____
Options:
(A) 12400
(B) 12800
(C) 12970
(D) 13015
(E) 16000
The answer is (C)


[User]
Answer: (B)
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
[CoT]: [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.]

Answer: (B)
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, 4 transportation stocks, and 4 utility stocks, how many different combinations of 7 stocks are possible?
--
Options:
(A) 12
(B) 360
(C) 60
(D) 180
(E) 720
[CoT]: [5C3 * 4C2 * 4C2 = 10*6*6 = 360.]

Answer: (D)
Question: Anmol can eat 27 pastries in a hour.
Aakriti can eat 2 pastries in 10 minutes.
Divya can eat 7 pastries in 20 minutes.
How long will it take them to eat a 240 pastries ?
Options:
(A) 2 hours.
(B) 1 hours.
(C) 5 hours.
(D) 4 hours.
(E) 3 hours.
[CoT]: [In one hour, Anmol eats 27 pastries, Aakriti eats 12, and Divya eats 21. A total of 60 pastries. Therefore 240 pastries would take 240 ÷ 60 = 4 hours.]

Answer: (A)
Question:

[Assistant]
A pharmaceutical company received $4 million in royalties on the first $50 million in sales of and then $12 million in royalties on the next $170 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $50 million in sales to the next $170 million in sales?
Options:
(A) 12%
(B) 15%
(C) 45%
(D) 52%
(E) 56%
[CoT]: [(12/170)/(4/50) = 15/17 = 88% it means that 12/170 represents only 88%. Therefore a decrease of 12%.]


[User]
Rationale: This is a simple multiplication series. Each number is 6 times greater than the previous number.
The answer: (C)
Question: Look at this series: 1.25, 7.5, ____, 270, 1620, ... What number should fill the blank?
Options:
(A) 50
(B) 65
(C) 45
(D) 55
(E) 40

Reasoning: Denise beat Jim
Jack beat Jim
Sam beat Jack
So Sam is the winner
Ans: (A)
Question: In marathon Sam was faster than Jack. Denise beat Jim but lost to Jack. Who is the winner?
Options:
(A) Sam
(B) Jack
(C) Denise
(D) Jim
(E) none

Rationale: 223 + 43 = 266/17 = 11 (Remainder)
The answer: (D)
Question: A no.when divided by 223 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: B's 1 day work = (1/12 - 1/20) = 1/30
Now, (A + B)'s 1 day work = (1/20 + 1/60) = 1/15
So, A and B together will complete the work in 15 days.
Ans: (C)
Question: A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?
Options:
(A) 22
(B) 88
(C) 15
(D) 66
(E) 81

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

Rationale: (555 + 445) * 2 * 110 + 60 = 220000 + 60 = 220060
The answer: (E)

[Assistant]
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 60 as remainder. Find the no. is?
Options:
(A) 145646
(B) 236578
(C) 645353
(D) 456546
(E) 220060


[User]
Q: 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
A: (B)
Explain how we arrive at this answer:

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


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

[Assistant]
The question is: 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
Stream of consciousness: Volume of prism = Area of base * height = 1/2* (square root of 5) * (square root of 5)*10 = 25


[User]
## Solution
Work done by A in 2 days = 2/5
Remaining work = 3/5
Work done by both A and B in one day = 1/5 + 1/10 = 3/10
Remaining work = 3/5 * 10/3 = 2 days.
## What the question and answer could be
A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work?
Options:
(A) 6 days
(B) 2 days
(C) 8 days
(D) 3 days
(E) 9 days
(B)

## Solution
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
## What the question and answer could be
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
(C)

## Solution
Speed = 162*(5/18) m/sec = 45m/sec
Length of Train (Distance) = Speed * Time
45 * 12 = 540 meter
## What the question and answer could be
A train running at the speed of 142 km/hr crosses a pole in 12 seconds. Find the length of the train.
Options:
(A) 540
(B) 288
(C) 200
(D) 340
(E) 712
(A)

## Solution
Simple interest = (16000 * 4 * 15)/100 = Rs. 9600
Amount = P + I = 16000 + 9600 = Rs. 25600
## What the question and answer could be

[Assistant]
What amount does Kiran get if he invests Rs. 16000 at 15% p.a. simple interest for four years?
Options:
(A) 29893
(B) 27773
(C) 25600
(D) 28800
(E) 29883
(C)


[User]
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) 5 kmph
(B) 6 kmph
(C) 7 kmph
(D) 8 kmph
(E) 9 kmph

Reasoning: 6 * 15 â€“ 5 * 13 = 25
Ans: (B)
Question: The average of six results is 15 and that of the first five is 13. The sixth result is?
Options:
(A) 20
(B) 25
(C) 15
(D) 22
(E) 18

Rationale: Distance covered by the car = 100 × 5 = 500 km
\ Speed = 500⁄2 = 250 km/hr
\ Speed gain = 250 – 100 = 150 km/hr
The answer: (C)
Question: A car finishes a journey in five hours at the speed of 100 km/hr. If the same distance is to be covered in two hours how much more speed does the car have to gain?
Options:
(A) 8 km/hr
(B) 10 km/hr
(C) 150 km/hr
(D) 16 km/hr
(E) None of these

Reasoning: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
Ans: (B)
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
(A) 11
(B) 16
(C) 18
(D) 10
(E) 14

Rationale: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144
3x/100 + 200 – 5x/100 = 144
2x/100 = 56 è x = 2800
The answer: (C)
Question: 4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?
Options:
(A) 2277
(B) 2882
(C) 2800
(D) 2677
(E) 2211

Rationale: 25/100*1/5*(total) = 10
1/20*(total) = 10
(total) = 10*20 = 200
The answer: (C)

[Assistant]
Question: Twenty five percent of Country Y's yearly exports come from fruit exports. One-fifth of all fruit exports from Country Y are orange exports. If country Y generates $10 million from its orange exports, how much money does it generate from its yearly total of exports?
Options:
(A) $2125m
(B) $25m
(C) $200m
(D) $300m
(E) $153m


[User]
Answer: (E)
Question: Two persons A and B can complete a piece of work in 40 days and 60 days respectively. If they work together, what part of the work will be completed in 6 days?
Options:
(A) 1/8
(B) 1/3
(C) 1/6
(D) 1/2
(E) 1/4
[CoT]: [A's one day's work = 1/40
B's one day's work = 1/60
(A + B)'s one day's work = 1/40 + 1/60 = 1/24
The part of the work completed in 6 days = 6 (1/24) = 1/4.]

Answer: (A)
Question: The average of 13 numbers is 58. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
Options:
(A) 72
(B) 83
(C) 45
(D) 53
(E) 64
[CoT]: [Sum of all the 13 numbers = 13 * 58 = 754
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 - 754 = 72.]

Answer: (A)
Question: A train 250 m long running at 72 kmph crosses a platform in 40 sec. What is the length of the platform?
Options:
(A) 450m
(B) 200m
(C) 250m
(D) 270m
(E) 300 m
[CoT]: [D = 72 * 5/18 = 40 = 800 â€“ 250 = 450m]

Answer: (E)
Question:

[Assistant]
There are 11 person among whom 2 are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1 person sit between the brothers, is equal to?
Options:
(A) 4!*2!
(B) 7!*2!
(C) 6!*1!
(D) 2!*1!
(E) 8!*2!
[CoT]: [Total number of ways = 8!*2!.]


[User]
Reasoning: The ratio is 2:3 = gym:ride, so (12)(3/2) = 18 minutes at the gym, and 18 + 12 = 30 minutes exercise, so (2/3)(30) = 20 minutes yoga.
Ans: (E)
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 12 minutes, how much time will she spend doing yoga? (rounded to minutes)
Options:
(A) 10 min.
(B) 41 min.
(C) 17 min.
(D) 23 min.
(E) 20 min.

Rationale: (70/100) * 40 â€“ (4/5) * 25
28- 20 = 8
The answer: (E)
Question: How much is 70% of 40 is greater than 4/5 of 25?
Options:
(A) 12
(B) 27
(C) 18
(D) 12
(E) 8

Reasoning: Simple interest = (16000 * 4 * 15)/100 = Rs. 9600
Amount = P + I = 16000 + 9600 = Rs. 25600
Ans: (E)
Question: What amount does Kiran get if he invests Rs. 16000 at 15% p.a. simple interest for four years?
Options:
(A) Rs. 25800
(B) Rs. 15600
(C) Rs. 21600
(D) Rs. 24800
(E) Rs. 25600

Rationale: Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.
The answer: (C)
Question: The no. of girls in a class are seven times the no. of boys, which value cannever be the of total students?
Options:
(A) 10
(B) 15
(C) 30
(D) 34
(E) 36

Reasoning: Divisibility rule for 3 also same as 9. so from the above discussion sum of the digits = 380 and remainder = 380/3 = 2.
Ans: (A)
Question: A number is 101102103104...150. As 101 102 103 103.... 150. What is reminder when divided by 3?
Options:
(A) 2
(B) 5
(C) 6
(D) 7
(E) 8

Reasoning: Number of ways of choosing 5 stocks = 10C5
Number of ways of ranking the chosen stocks = 5!
Hence total ways of chosing and ranking = 10C5 * 5! = 30240
Ans: (D)

[Assistant]
Question: An equity analyst needs to select 5 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 10, in how many ways can she choose and rank her top 5 picks?
Options:
(A) 21548
(B) 31502
(C) 21250
(D) 30240
(E) 84045


[User]
Answer: (D)
Question: The length T 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%
[CoT]: [Let the length T 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]

Answer: (A)
Question: Is 2 a prime number or a composite number?
Options:
(A) prime number
(B) composite number
(C) both prime composite number
(D) Not prime composite number
(E) Don't Know
[CoT]: [A Prime Number can be divided evenly only by 1 or itself
So 2 is prime number]

Answer: (B)
Question: In Sam's hanger there are 23 boxes, 18 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.
[CoT]: [Total boxes = 23
Filled with toys = 18
Filled with appliance = 5
Total boxes for sale = 8
Toy boxes for sale = 5
Appliance boxes for sale = 3
Appliance boxes not for sale = 5 - 3 = 2]

Answer: (D)
Question:

[Assistant]
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
Options:
(A) 22
(B) 28
(C) 29
(D) 20
(E) 21
[CoT]: [Average of 20 numbers = 0
Sum of 20 numbers = (0 * 20) = 0
It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a).]


[User]
Rationale: (1056 / 27) gives remainder 3
24 + 3 = 27, So we need to add 24
The answer: (D)
Question: What is the least number should be added to 1056, so the sum of the number is completely divisible by 27?
Options:
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25

Reasoning: In Cricket game Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1:
P(win) = 1- P(not win) = 1 - 4/6*4/6 = 5/9.
Ans: (C)
Question: In Cricket game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once?
Options:
(A) 1/3
(B) 4/9
(C) 5/9
(D) 2/3
(E) 3/4

Rationale: Ratio of time taken by A & B = 160:100 = 8:5 Suppose B alone takes x days to do the job. Then, 8:5::12:x = > 8x = 5*12 = > x = 15 days.
The answer: (B)
Question: A can do a certain work in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job ?
Options:
(A) 19
(B) 15
(C) 16
(D) 17
(E) 18

Reasoning: 222 + 43 = 265/17 = 10 (Remainder)
Ans: (D)
Question: A no.when divided by 222 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
Options:
(A) 2
(B) 7
(C) 9
(D) 10
(E) 15

Rationale: 1/2 * 20(9 + 6) = 150 cm2
The answer: (B)
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
Options:
(A) 288
(B) 150
(C) 77
(D) 166
(E) 1812

Rationale: Speed = 30*(5/18) m/sec = 25/3 m/sec
Length of Train (Distance) = Speed * Time
(25/3) * 9 = 75 meter
The answer: (A)

[Assistant]
Question: A train running at the speed of 30 km/hr crosses a pole in 9 seconds. Find the length of the train?
Options:
(A) 75
(B) 65
(C) 25
(D) 288
(E) 212


[User]
Reasoning: 40 + 28 + 10 = 78%
100 – 78 = 22%
850 * 22/100 = 187
Ans: (C)
Question: In a school of 850 boys, 40% of Muslims, 28% 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) 187
(D) D) 721
(E) E) 159

Rationale: 144 is square of 12 which is even number where as all others are squares of odd numbers.
The answer: (C)
Question: Find the odd man out
25, 49, 81, 121, 144, 169
Options:
(A) 49
(B) 121
(C) 144
(D) 169
(E) 25

Reasoning: (30*30)/100 = 9%loss
Ans: (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
(B) 8
(C) 7
(D) 5
(E) 3

Rationale: 1/18 + 1/24 = 7/72
72/7 = 72/7 *2 = 20 4/7 days
The answer: (C)
Question: A can do a job in 18 days and B can do it in 24 days. A and B working together will finish twice the amount of work in days?
Options:
(A) 22 1/6
(B) 22 1/2
(C) 20 4/7
(D) 22 1/9
(E) 22 1/1

Reasoning: Answer = C) One
Two digit numbers giving remainder 2 when divided by 9 = 11, 20, 29, 38, 47, 56, 65, 74, 83, 92
Two digit numbers giving remainder 5 when divided by 8 = 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93
Common Numbers = 29 = 1
Ans: (C)
Question: How many common two-digit whole numbers are there which gives a remainder of 2 when divided by 9 and gives a remainder of 5 when divided by 8?
Options:
(A) Five
(B) Three
(C) One
(D) Two
(E) Four

Reasoning: All are even natural numbers except 87.
Ans: (B)

[Assistant]
Question: Find the odd man out
444, 300, 200, 136, 87, 84, 80
Options:
(A) 80
(B) 87
(C) 136
(D) 200
(E) 444


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

[Assistant]
Question: A train 650 m long is running at a speed of 81 km/hr. In what time will it pass a bridge 340 m long?
Options:
(A) 42
(B) 43
(C) 44
(D) 45
(E) 46
Stream-of-consciousness: Speed = 81 * 5/18 = 45/2 m/sec
Total distance covered = 650 + 340 = 990 m
Required time = 990 * 2/45 = 44 se


[User]
Stream of consciousness rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
The question and answer pair are described below.

[Assistant]
Q: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
(A) 22 sec
(B) 16 sec
(C) 77 sec
(D) 55 sec
(E) 17 sec
A: (B)


[User]
Explain simply why (D) is the correct answer to: K-numbers are positive integers with only 2's as their digits. For example, 2, 22, and 222 are K-numbers. The K-weight of a number n is the minimum number of K-numbers that must be added together to equal n. For example, the K-weight of 50 is 5, because 50 = 22 + 22 + 2 + 2 + 2. What is the K-weight of 650?
Options:
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14. Explanation:

[Assistant]
650 = 2*222 + (22*9) + 4*2
K weight of 600 = 2 +9+2 = 13


[User]
Rationale: Final number = Initial number + 40%(original number) = 150 + 40%(150) = 150 + 60 = 210.
The answer: (B)
Question: 150 is increased by 40%. Find the final number.
Options:
(A) 200
(B) 210
(C) 180
(D) 190
(E) 220

Reasoning: 125^10 = (5^3)^10 = 5^30
Ans: (E)
Question: 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

Rationale: Area of an equilateral triangle = √3/4 S2
If S = 2, Area of triangle = √3/4 * 2 * 2 = √3 cm2;
The answer: (A)
Question: What is the are of an equilateral triangle of side 2 cm?
Options:
(A) √3
(B) 64√9
(C) 64√4
(D) 64√3
(E) 64√2

Reasoning: Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes only the product of 555 will be odd, the remaining 26 will have either 2 or 4 in them, which ensures that their product will be even. Therefore the number of codes where the product of the digits is even = (total) - (restriction) = 27 - 26 = 1.
Ans: (D)
Question: A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 5, which can be repeated. If the product of the digits in the area code must be odd, how many different codes can be created?
Options:
(A) 20
(B) 22
(C) 24
(D) 1
(E) 30

Rationale: 10^2 - 20 = 80
20^2 - 30 = 370
30^2 - 40 = 860
40^2 - 50 = 1550
50^2 - 60 = 2440
60^2 - 70 = 3530.
The answer: (D)
Question: 80 370 ? 1550 2440 3530
Options:
(A) 900
(B) 840
(C) 750
(D) 860
(E) 960

Rationale: Avg = [(x+2)^2 + (x-4)^2] / 2
Expanding and simplifying, (x^2 + 4x + 4 + x^2 - 8x + 16 ) / 2 = x^2 - 2x +10
The answer: (C)

[Assistant]
Question: Which of the following is equal to the average (arithmetic mean) of (x+2)^2 and (x-4)^2?
Options:
(A) x^2
(B) x^2+2
(C) x^2-2x+10
(D) x^2+2x+10
(E) x^2+4x+5


[User]
Rationale: S = (200 + 300)/45 = 500/45 * 18/5 = 40
The answer: (D)
Question: A train 200 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
Options:
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50

Reasoning: (555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030
Ans: (E)
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is?
Options:
(A) 122443
(B) 154546
(C) 165454
(D) 186545
(E) 220030

Rationale: 35 * 18/5 = 126 kmph
The answer: (C)
Question: Express 35 mps in kmph?
Options:
(A) 122
(B) 188
(C) 126
(D) 140
(E) 124

Reasoning: 10p4 = 10 X 9 X 8 X 7 = 5040
Ans: (E)
Question: In how many different number of ways 7 men and 3 women can sit on a shopa which can accommodate persons?
Options:
(A) 200
(B) 230
(C) 240
(D) 250
(E) 5040

Rationale: 221 + 43 = 264/17 = 9 (Remainder)
The answer: (C)
Question: A no.when divided by 221 gives a remainder 43, what remainder will beobtained by dividing the same number19?
Options:
(A) 3
(B) 6
(C) 9
(D) 11
(E) 15

Rationale: 5C4 * 4C2 * 3C2 = 5*6*3 = 90.
The answer: (C)

[Assistant]
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


[User]
Money paid in cash = Rs. 1000
Balance payment = (40000 - 1000) = Rs. 39000is the reasoning for what question and answer pair?

[Assistant]
Q: The price of a T.V. set worth Rs. 40000 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) 26699
(C) 26788
(D) 19000
(E) 39000
A: (E)


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

[Assistant]
The question is: If x is a positive integer, which of the following could NOT be the square of x?
Options:
(A) 5,008,644
(B) 5,004,169
(C) 4,999,696
(D) 4,995,225
(E) 4,990,752
Stream of consciousness: A perfect square will never end in 2, 3, 7 or 8. (last digit cannot be 2, 3, 7 or 8)
Here E is the odd one out.


[User]
Given the following reasoning and answer, what was the question? Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
 The answer: (B)

[Assistant]
The question 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


[User]
What was the question for this implicit rationale, and corresponding answer?
The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.
 The answer: (C)

[Assistant]
The question: Find the invalid no.from the following series 13, 18, 25, 30, 37, 40
Options:
(A) 13
(B) 18
(C) 40
(D) 37
(E) 25


[User] Reconstruct a question, answer pair from this explanation: Divisibility rule for 3 also same as 9. so from the above discussion sum of the digits = 380 and remainder = 380/3 = 2.

[Assistant]
Q:A number is 101102103104...150. As 101 102 103 103.... 150. What is reminder when divided by 3?
Options:
(A) 2
(B) 5
(C) 6
(D) 7
(E) 8
A:(A)


[User]
[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
[CoT] 2
2 × 4 - 1 = 7
7 × 4 - 1 = 27
27 × 4 - 1 = 107
107 × 4 - 1 = 427
427 × 4 - 1 = 1707

[Ans] (D)
[Question] Which one of the following is not a prime number?
Options:
(A) 31
(B) 61
(C) 71
(D) 73
(E) 91
[CoT] 91 is divisible by 7. So, it is not a prime number.

[Ans] (C)
[Question]

[Assistant]
The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary?
Options:
(A) 910% increase
(B) 10% increase
(C) 9% decrease
(D) 12% decrease
(E) 15% increase
[CoT] (30 * 30)/100 = 9% decrease


[User]
[Ques]: The average marks of a Suresh in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest?
Options:
(A) 55
(B) 60
(C) 62
(D) 52
(E) Cannot be determined
*Ans*: (B)
--CoT--: Total marks of 10 papers = 80 x 10 = 800
Total marks of 8 papers = 81 x 8 = 648
Total marks of two papers = (800 - 648) = 152
If highest total is 92, then the lowest total is
(152 - 92) = 60.

[Ques]: 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
*Ans*: (A)
--CoT--: To arrange them as described I did as follows on my scratch paper (see the file attached), where I counted 4 sides

[Ques]: 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%
*Ans*: (D)
--CoT--: 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

[Ques]: There are 23 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) 51
(D) 58
(E) 63
*Ans*: (A)

[Assistant]
--CoT--: {Total} = {M} + {N} - {Both}
{Total} = 23 + 28 - 12 = 39.


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

[Assistant]
The question is: If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 5 and 5K + 1 is 41, what is the value of K?
Options:
(A)  41
(B)  15 3/4
(C)  22
(D)  23
(E)  25 3/10
Stream of consciousness: K + 2K +3 + 3K - 5 + 5K +1 = 11K -1
(11K -1)/4 = 41
11K = 41 * 4 +1 = 164 +1 = 165
K = 165 / 11 = 15.


[User]
Answer: (C)
Question: Joel sailed for 3 hours at a speed of 20 miles per hour, then for 6 hours at 30 miles per hour and finally, 1 more hour at 40 miles per hour. What was the average speed of Joel during the whole sail?
.
Options:
(A) 25
(B) 27.5
(C) 28
(D) 30
(E) 32
[CoT]: [3 hours at a speed of 20 miles per hour gives us Distance = 20*3 = 60 miles
6 hours at a speed of 30 miles per hour gives us Distance = 30*6 = 180 miles
1 more hour at 40 miles per hour gives us Distance = 40*1 = 40 miles
Total Distance = 60+180+40 = 280 miles
Total Time = 3+6+1 = 10 Hours
Average Speed = 280 / 10 = 28 Miles per hour]

Answer: (C)
Question: Find the simple interest on Rs.450 for 8 months at 5 paisa per month?
Options:
(A) 277
(B) 270
(C) 180
(D) 266
(E) 121
[CoT]: [I = (450*8*5)/100 = 180]

Answer: (D)
Question: If 10 crates have 98 apples each and how many apples more is required in order to make 100 apples in each crate?
Options:
(A) 5
(B) 10
(C) 15
(D) 20
(E) 0
[CoT]: [Each crate requires 2 apples and totally there are 10 crates so required apples = 10 * 2 = 20]

Answer: (C)
Question:

[Assistant]
The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
(A) 45 Years
(B) 46 Years
(C) 49 Years
(D) 52 Years
(E) 54 Years
[CoT]: [Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
There is a shortcut for these type of problems
Teacher's age is 16+(33X1) = 49 Years]