mathewhe/aqua_rat huggingface dataset:
Question: A person starting with Rs.64 and making 6 bets, wins three times and loses 3times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, then the final result is?
(A) Rs.37
(B) Rs.40
(C) Rs.45
(D) Rs.47
(E) Rs.50
Rationale: As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order).
The overall resultant will remain same.
So final amount with the person will be (in all cases):
=64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)==64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 2727
Hence the final result is:
64−27=3764−27=37:
A loss of Rs.37
A
Answer: (A) Rs.37
Question: If 2ab - 5c = 2a(b - c), which of the following must be true?
(A)  a=0 and c=0
(B)  a=1/2 and b=2
(C)  b=1 and c=0
(D)  a=1 or b=0
(E)  a=5/2 or c=0
Rationale: 2ab-5c = 2a (b-c)
2ab - 5c = 2ab - 2ac
5c= 2ac
2ac-5c = 0
c(2a-5) = 0
Either c = 0; or a = 5/2
E is the answer
Answer: (E)  a=5/2 or c=0
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
(A) 16 2/3% loss
(B) 16 7/3% loss
(C) 18 2/3% loss
(D) 16 2/9% loss
(E) 26 2/3% loss
Rationale: 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer:A
Answer: (A) 16 2/3% loss
Question: A woman buys two articles for Rs.1980 each and he gains 10% on the first and loses 10% on the next. Find his total gain or loss percent?
(A) 10%
(B) 1%
(C) -1%
(D) -10%
(E) 11%
Rationale: B
Answer: (B) 1%
Question: If 2/a + 3/a + 7/a is an integer, which of the following must also be an integer?
(A) 12/a
(B) 3/a
(C) 6/a
(D) 9/a
(E) 15/a
Rationale: 2/a + 3/a + 7/a
=12/a
Answer A
Answer: (A) 12/a
Question: The average of 30 results is 20 and the average of other 20 results is 30 . what is the average of all the results?
(A) 24
(B) 25
(C) 48
(D) 50
(E) None
Rationale: Answer
Sum of 50 result = sum of 30 result + sum of 20 result.
= 30 x 20 + 20 x 30
= 1200
Correct Option: A
Answer: (A) 24
Question: What will come in place of the x in the following Number series? 2, 7, 10, 22, 18, 37, 26, x
(A) 29
(B) 32
(C) 35
(D) 42
(E) 52
Rationale: There are two series here
2, 10, 18, 26, ... (Increase by 8)
7, 22, 37, ... (Increase by 15)
Hence, next term is 37+15 = 52
E
Answer: (E) 52
Question: Fresh dates contain 90% water while dry dates contain 28% water . How many kg of dry dates can be obtained from 36kg of fresh dates ?
(A) 5Kg
(B) 10Kg
(C) 12 Kg
(D) 16Kg
(E) 26Kg
Rationale: 36 kilograms of fresh dates contain 0.1*36=3.6 kilograms of non-water.
Dry dates obtained from these fresh dates will contain the same amount of non-water and we are told that this amount should be 72% of the dry dates, thus x*0.72=3.6 --> x=5 kilograms.
Answer: A.
Answer: (A) 5Kg
Question: Can you find the smallest non fractional number such that
If the number gets divided by 13 , we get the remainder of 1;
If the number gets divided by 14 , we get the remainder of 2
If the number gets divided by 15 , we get the remainder of 3;
If the number gets divided by 16 , we get the remainder of 4.
(A) 55321
(B) 30238
(C) 58020
(D) 44141
(E) 72033
Rationale: B
30238.
As we know LCM of the numbers 13 14 15 & 16 is 30240
So if i divide 30240 by any of the four number , it gives remainder as 0.
Now to get reminder as desired, is should be 2 short of 30238. (3-1,4-2,5-3,6-4 )
Ans:option B
Answer: (B) 30238
Question: The difference between the place values of 7 and 3 in the number 527435 is
(A) 4
(B) 5
(C) 45
(D) 6970
(E) None
Rationale: Sol.
= (Place value of 7) – (place Value of 3)
= (700 - 30)
= 6970
Answer D
Answer: (D) 6970
Question: In a group of 160 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20?
(A) 0.44
(B) 0.55
(C) 0.65
(D) 0.75
(E) 0.85
Rationale: Number of people whose age is less than 20 is given by
160 - 90 = 70
Probability P that a person selected at random from the group is less than 20 is gieven by
70 / 160 = 0.4375 ~ 0.44
correct answer A
Answer: (A) 0.44
Question: Find the missing couple of letters in the following series:
AZ, GT, MN, ? , YB
(A) SE
(B) SM
(C) SO
(D) SH
(E) SP
Rationale: D
SH
If you look closely, you will see that the first letter of every set is moving 6 alphabets forward while the second one is moving six alphabets backwards.
Answer: (D) SH
Question: The market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 7500, brokerage being 1/4%, is:
(A) 103.92
(B) 114
(C) 114.75
(D) 124
(E) 124.75
Rationale: Face Value = Rs. 7500.
Dividend = 10.5%.
Annual Income = Rs. 756.
Brokerage per Rs. 100 = Rs. 0.25.
Dividend is always paid on the face value of a share.
Face Value * Dividend / (Market Value + Brokerage per Rs. 100) = Annual income.
= 7500 * 10.5 / 756 = Market Value of Rs. 100 stock + Brokerage per Rs. 100.
= Market Value of Rs. 100 stock + Brokerage per Rs. 100 = Rs. 104.17
= Market Value of Rs. 100 stock = Rs. 104.17 - Re. 0.25.
= Market Value of Rs. 100 stock = Rs. 103.92.
answer : A
Answer: (A) 103.92
Question: A man two flats for $675958 each. On one he gains 13% while on the other he loses 13%. How much does he gain or lose in the whole transaction?
(A) 1.69%
(B) 2.56%
(C) 3.12%
(D) 4.65%
(E) 5.12%
Rationale: In such a case there is always a loss
Loss% = (13/10)^2 = 120/71 = 1.69%
Answer is A
Answer: (A) 1.69%
Question: Calculate the HCF of 69, 561, 963
(A) 4
(B) 5
(C) 22
(D) 3
(E) 1
Rationale: Explanation:
Lets solve this question by factorization method.
The factors of 69 are: 1, 3, 23, 69
The factors of 561 are: 1, 3, 11, 17, 33, 51, 187, 561
The factors of 963 are: 1, 3, 9, 107, 321, 963
Then the greatest common factor is 3.
Answer: Option D
Answer: (D) 3
Question: A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 1 students left over. What is the sum of the two smallest possible values of n?
(A) 33
(B) 62
(C) 49
(D) 53
(E) 86
Rationale: 4x+1 = 5y+ 1...........ie: 4x-5y = 2
x,y must be >1 and y is even ie ( 2,4,6,..etc)
if y = 2 thus x = fraction (not possible)
if y = 4 thus x =5 n =21
if y = 6 thus x = not possible fraction
if y =8 thus x = 10 n =41
21+41 = 62.....
B
Answer: (B) 62
Question: The arithmetic mean of the 7 consecutive integers starting with 's' is 'a'. What is the arithmetic mean of 9 consecutive integers that start with s + 3?
(A) 2 + s + a
(B) 22 + a
(C) 2s
(D) 2a + 2
(E) 3 + a
Rationale: (7s+21)/7=s+3=a
(9s+54)/9=s+6=3+a
E
Answer: (E) 3 + a
Question: A pupil's marks were wrongly entered as 73 instead of 65. Due to the average marks for the class got increased by half. The number of pupils in the class is?
(A) 18
(B) 82
(C) 16
(D) 27
(E) 29
Rationale: Let there be x pupils in the class.
Total increase in marks
= (x * 1/2) = x/2
x/2 = (73 - 65) => x/2
= 8 => x = 16.
Answer: C
Answer: (C) 16
Question: Tammy climbed a mountain in two days. She spent a total of 14 hours climbing the mountain. On the second day, she walked at an average speed that was half a kilometer per hour faster, but 2 hours less than what she walked on the first day. If the total distance she climbed during the two days is 52 kilometers, how many R kilometers per hour did Tammy walk on the second day?
(A) 3
(B) 3.5
(C) 4
(D) 4.5
(E) 6
Rationale: Ans: C
Total time = 14 hrs
Let time traveled during 1st day = x
Let time traveled during 2nd day = x-2
Total time =14
x+x-2 = 14
x=8
speed * time = distance
s*8 + (s+0.5)(8-2) = 52
solving s = 4.5
now speed for 2nd day is 0.5 less than the 1st day which is 4.5
Thus speed for 2nd day = 4
Its simple algebra for s*8 + (s+0.5)(8-2) = 52 but for some reason Im getting 3.5 and not 4.5.
8s+6s+3=52
14s=49
s=3.5
Answer: (C) 4
Question: The three sides of an acute angled triangle (all in cms) are 12, 19 and h. How many integer values can h take?
(A) 23
(B) 22
(C) 15
(D) 8
(E) 7
Rationale: In acute angle triangles all angles in the triangle should be less than 90.
The maximum length of h can be when it is the hypotenuse of the triangle.
So, h= sqrt(12^2 + 19^2) = 22.5 (approx)
The maximum length of h can be when side of length 12 is the hypotenuse of the triangle.
So, h = sqrt (19^2 - 12^2) = 14.7 (approx)
So, h>14.7 and h<22.5.
Hence, possible values for h can be 15,16,17,18,19,20,21 and 22. Total 8 values.
Answer D.
Answer: (D) 8
Question: A boat takes 3 hours to travel from place M to N down stream and back from N to M upstream. If the speed of the boat instill water is 4 km/hr, what is the distance between the two places?
(A) 8 km
(B) 12 km
(C) 6 km
(D) Data inadequate
(E) None of these
Rationale: Let the distance between M and N and the speed of current in still water be d km and x km/hr respectively.
According to the question, d/4+x+d/4−x=3
In the above equation we have only one equation but two variables, hence, can’t be determined.
Answer D
Answer: (D) Data inadequate
Question: The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?
(A) 300 km
(B) 320 km
(C) 360 km
(D) 420 km
(E) 460 km
Rationale: Sol. Average speed of a tractor = 25 km / h
The speed of a bus in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 9/5 * 50 = 90 km
So, the distance covered by car in 4 h is
90 × 4 = 360 km
Ans.(C)
Answer: (C) 360 km
Question: The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?
(A) 5
(B) 8
(C) 10
(D) 12
(E) 15
Rationale: Lets say T = 10 ---> S = 300 ---> 350/15 = a bit less than 25 (A and B will only make this ratio lesser, eliminate A and B)
Go for T = 12 --> S = 30*12 = 360 ---> 360+50 / 12+5 = less than 25. Either you can now go further with T = 15 or mark E as the answer .
Check: T = 15 ---> S = 30*15=450 ---> 450+50/20 = 25.
ANSWER:E
Answer: (E) 15
Question: A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3300, A will get:
(A) Rs.1200
(B) Rs.1500
(C) Rs. 1980
(D) Rs.2000
(E) None of these
Rationale: Explanation:
Ratio of working days of A : B = 10 : 15
Therefore, their wages ratio = reverse ratio = 15 : 10
Therefore, A will get 15 units of ratio
Total ratio = 25
1 unit of ratio =3000/25 = 132
So, A’s amount = 120 × 15 = Rs.1980.
Answer: Option C
Answer: (C) Rs. 1980
Question: Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 12 minutes more to walk to work than to ride his bike to work, then x equals?
(A) 4
(B) 7
(C) 10
(D) 15
(E) 18
Rationale: Please follow posting guidelines, link is in my signatures.
As for your question, x/60 = blocks/time/block = block^2/time . This is not what you want. You are given x blocks and 60 seconds PER BLOCK. Thus you need to put it as 60*x to give you units of seconds as you are equating this to 720 (which is TIME in seconds.).
Thus the correct equation is : 60*x-20*x=7200 ----> 40x=720--> x = 18.
option E
Answer: (E) 18
Question: Find the missing figures: 0.75% of ? = 0.06
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: Let 0.75% of x = 0.06. Then , 0.75*x/100 = 0.06
X= [(0.06*100)/0.75] = 8.
Answer is C.
Answer: (C) 8
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 20 sec
(B) 10 sec
(C) 30 sec
(D) 40 sec
(E) 50 sec
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer:C
Answer: (C) 30 sec
Question: Two clocks begin to strike 12 together. One strikes in 33 seconds and the other in 22 secs. What is the interval between the 6th
stroke of the first and the 8th
stroke of the second?
(A) 11 secs
(B) 12 secs
(C) 10 secs
(D) 13 secs
(E) 14 secs
Rationale: Time of 6th strike of first clock = 5*33= 165 secs after 1200 hrs
Time of 8th strike of 2nd clock = 7*22= 154 secs after 1200 hrs
Time interval between the 6th stroke of the first and the 8th stroke of the second = 165-154=11 secs
ANSWER:A
Answer: (A) 11 secs
Question: A courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $1.85?
(A) 1680
(B) 1420
(C) 1120
(D) 970
(E) 740
Rationale: The charge is 65 cents for the first 250 grams.
This leaves a charge of $1.85 - $0.65 = $1.20
The charge for the next 1100 grams is $1.10 which leaves a charge of $0.10
The weight is somewhere between 1350 and 1450.
The answer is B.
Answer: (B) 1420
Question: The sector of a circle has radius of 35 cm and central angle 135o. Find its perimeter?
(A) 91.5 cm
(B) 92.2 cm
(C) 152.5 cm
(D) 29.2 cm
(E) 98.2 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 35) + 2(35)
= 82.5 + 70 = 152.5 cm
Answer:C
Answer: (C) 152.5 cm
Question: The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 28 years. The ratio of their ages after 5 years will be
(A) 22 : 17
(B) 9 : 11
(C) 5 : 4
(D) 4 : 5
(E) 8 : 11
Rationale: Let Mini’s age = 4x and Minakshi’s age = 3x
Then 4x + 3x = 28
x = 4
Mini’s age = 16 years
And Minakshi’s age = 12 years
Ratio of their ages after 8 years = (16 + 5) : (12 + 5) = 22 : 17
ANSWER:A
Answer: (A) 22 : 17
Question: If x = |-x| , then which one of the following statements could be true?
I. x = 0
II. x < 0
III. x > 0
(A)  None
(B)  I only
(C) C) III only
(D)  I and II
(E)  I and II and III
Rationale: Answer copied from NOVA guide
Statement I could be true because ± 0 = −(+0) = −(0) = 0 .
Statement II could be true because the right side of the equation is always negative [ ± x = –(a positive number) = a negative number].
Now, if one side of an equation is always negative, then the other side must always be negative,
otherwise the opposite sides of the equation would not be equal.
Since Statement III is the opposite of Statement II, it must be true. But let’s show this explicitly:
Suppose x were positive. Then x = x, and the equation x = |-(± x) |becomes x = x. Dividing both sides of this equation by x yields 1 = –1. This is contradiction.
Hence, x cannot be positive. The answer is (E).
Answer: (E)  I and II and III
Question: Today Katherine, who is 40 years old, and her daughter, who is 10 years old, celebrate their birthdays. How many years will pass before Katherine’s age is twice her daughter’s age?
(A) 22
(B) 20
(C) 23
(D) 24
(E) 25
Rationale: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
After x years passes Katherine’s age will be (40+x) years old, and her daughter’s age will be (10+x) years old. Since the Katherine’s age is twice her daughter’s age (40+x)= 2 * (10+x) ---> 40+x=20+2x ---> x= 20.
The answer is (B).
Answer: (B) 20
Question: A Coach is filling out the starting lineup for his indoor soccer team. There are 10 boys on the team, and he must assign 6 starters to the following positions: 1 goalkeeper, 2 on defence, 2 in midfield, and 1 forward. Only 2 of the boys can play goalkeeper, and they cannot play any other positions. The other boys can each play any of the other positions. How many different groupings are possible?
(A) 60
(B) 210
(C) 2580
(D) 3360
(E) 151200
Rationale: 2C1 select 1 goalkeeper from 2 boys;
8C2 select 2 defense from 8 boys (as 2 boys can only play goalkeeper 10-2=8);
6C2 select 2 midfield from 6 boys (as 2 boys can only play goalkeeper and 2 we've already selected for defense 10-2-2=6);
4C1 select 1 forward from 4 boys (again as 2 boys can play only goalkeeper, 4 we've already selected for defense and midfield 10-2-4=4)
Total # of selection=2C1*8C2*6C2*4C1=3360
Answer: D.
Answer: (D) 3360
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
(A) 6
(B) 6.25
(C) 6.5
(D) 7
(E) 7.5
Rationale: equired run rate = 282 - (3.2 x 10)/40 =	250/40 = 6.25
ANSWER A
Answer: (A) 6
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
(A) 22 days
(B) 20 days
(C) 67 days
(D) 17 days
(E) 18 days
Rationale: C = 1/2 - 1/4 - 1/5 = 1/20
=> 20 days
Answer:B
Answer: (B) 20 days
Question: The ratio of investments of two partners A and B is 7:5 and the ratio of their profits is 7:10. If A invested the money for 5 months, find for how much time did B invest the money ?
(A) 25 months
(B) 11 months
(C) 16 months
(D) 10 months
(E) 12 months
Rationale: 7x5: 5xk = 7:10
k = 10 months
Answer: D
Answer: (D) 10 months
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 15000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) 13.8
(B) 77
(C) 18
(D) 99
(E) 88
Rationale: Total CP = Rs. 42000 + Rs. 15000 = Rs. 57000 and SP = Rs. 64900
Profit(%) = (64900 - 57000)/57000 * 100 = 13.8%
Answer: A
Answer: (A) 13.8
Question: Two pipes A and B can separately fill a tank in 8 and 10 minutes respectively. A third pipe C can drain off 15 liters of water per minute. If all the pipes are opened, the tank can be filled in 10 minutes. What is the capacity of the tank?
(A) 590 liters
(B) 160 liters
(C) 740 liters
(D) 560 liters
(E) 120 liters
Rationale: 1/8 + 1/10 - 1/x
= 1/10
x = 8
8 * 15 = 120
Answer:E
Answer: (E) 120 liters
Question: John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $60. What is the percent decrease?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%
Rationale: The is always the difference between our starting and ending points. In this case, it’s 100 – 60 = 40. The “original” is our starting point; in this case, it’s 100. (40/100)*100 = (0.4)*100 = 40%.
C
Answer: (C) 40%
Question: A number when divided by 221 gives a remainder 43, what remainder will be obtained by dividing the same number 17?
(A) 7
(B) 6
(C) 9
(D) 2
(E) 3
Rationale: Explanation:
221 + 43 = 264/17 = 9 (Remainder)
Answer: C
Answer: (C) 9
Question: The sum of 3 hours 45 minutes and 2 hours 55 minutes is approximately what percent of a day?
(A) 14%
(B) 16%
(C) 24%
(D) 28%
(E) 72%
Rationale: Since the question is asking for an approximate percentage
3:45+2:55 ~ 7 hours
% of day = 7*100/24 ~ 7*100/25= 28%
Answer is D.
Answer: (D) 28%
Question: Current ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.3 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomas’s current age in years?
(A) 24 years
(B) 44 years
(C) 34 years
(D) 64 years
(E) 84 years
Rationale: A
24 years
If current ages of Rahim and Thomas be 5A years and 4A years correspondingly
Then, 5A + 3 = 11
4A + 3 = 9
9(5A + 3)=11(4A + 3)
A = 6
Thomas’s current age = 4A
= 24 years.
Answer: (A) 24 years
Question: Three years ago the average age of a class of six members was 21 years. A boy have been added, the average age of the class is the same today. What is the age of the boy?
(A) A)1
(B) B)2
(C) C)3
(D) D)4
(E) E)5
Rationale: 6 * 24 = 144
7 * 21 = 147
`3
C
Answer: (C) C)3
Question: A number of 55 marbles is to be divided and contain with boxes. If each box is to contain 3, 4, or 5 marbles, what is the largest possible number of boxes?
(A) 10
(B) 12
(C) 15
(D) 16
(E) 19
Rationale: To maximize # of boxes we should minimize marbles per box: 17*3+1*4+1*5=50 --> 17+1+1=19.
Answer: E.
Answer: (E) 19
Question: The average runs scored by a batsman in 20 matches is 40. In the next 30 matches the batsman scored an average of 20 runs. Find his average in all the 50 matches?
(A) 31
(B) 46
(C) 28
(D) 13
(E) 12
Rationale: Total score of the batsman in 20 matches = 800.
Total score of the batsman in the next 30 matches = 600.
Total score of the batsman in the 50 matches = 1400.
Average score of the batsman = 1400/50 = 28.
Answer:C
Answer: (C) 28
Question: What is the least value of p, so that 123p578 is divisible by 11
(A) 7
(B) 8
(C) 6
(D) 5
(E) 4
Rationale: Explanation:
123p578
1 + 3 + 5 + 8 = 17
2 + p + 7 = 17
=> 9 + p = 17
=> p = 17 - 9
=> p = 8
Answer: Option B
Answer: (B) 8
Question: A firm has 4 senior partners and 6 junior partners. How many different groups F of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)
(A) 48
(B) 100
(C) 120
(D) 288
(E) 600
Rationale: What seems to work as well, though its tougher to come up with this solution:
(10*9*8) * 2/3 + (10*9*4)*1/3 = 600. Divided by all possible permutations (=3!) yields 100.
Explanation: For the first spot you have 10 possible canditates, for the 2nd 9. For the 3rd spot you need to differentiate if a senior partner has been picked for one of the first 2 spots or not. If yes, then you can pick one of the 8 remaining guys, so 10*9*8. If no senior partner has been picked yet, you need 10*9*4.
Now you need to weight the 2 cases with the corresponding probabilities: probability of no senior partner being picked in the first 2 draws = 6/10*5/9=1/3, so you weight 10*9*4 with 1/3. For the complementary case (senior partner was picked in the first 2 draws) you just take the complementary prob (1-1/3)= 2/3 and weight 10*9*8 with it.
Now you just need to divide the answer (600) by the number of different positions (=3!) and get F=600/6=100.B
Answer: (B) 100
Question: In how many ways can you sit 6 people on a bench if 3 of them must sit together?
(A) 144
(B) 160
(C) 400
(D) 320
(E) 420
Rationale: In such questions, always tie the person that have to sit together. So we have effectively 3+1= 4 persons to arrange.
They can be arranged in 4! ways.
Now the 3 persons can themselves be arranged in 3! ways.
Total ways: 4!*3! = 144.
A is the answer.
Answer: (A) 144
Question: A train 300 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 72
(B) 67
(C) 54
(D) 26
(E) 27
Rationale: Length = Speed * time
Speed = L/T
S = 300/20
S = 15 M/Sec
Speed= 15*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 54 Kmph
Answer:C
Answer: (C) 54
Question: By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
(A) 228
(B) 267
(C) 287
(D) 480
(E) 811
Rationale: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480
Answer: D
Answer: (D) 480
Question: A 100-litre mixture of milk and water contains 36 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 25%. What is the value of x?
(A) 17.5 litres
(B) 16.67 litres
(C) 17.67 litres
(D) 16.5 litres
(E) 16 litres
Rationale: In 100L mixture we have 36 L milk and 64 L water.
Hence M and W are in the ratio of 9:16.
x L of solution has been removed.
Hence we have 36-9/25x of milk and 64- 16/25x of water.
FOR CALCULATION SIMPLICITY multiply and divide 9/25x by 4 WE GET 36/100x
Since this procedure is repeated 2 times.
This was my equation
25=36*(36-36/100x)^2)/(36)^2
By solving it.
We get x=100/6 OR 50/3 OR 16.67
ANSWER:B
Answer: (B) 16.67 litres
Question: he difference between the compound and simple interest on a certain sum for 2 years at the rate of 8% per annum is Rs.80,What is the sum?
(A) 23798
(B) 27789
(C) 27889
(D) 12,500
(E) 27081
Rationale: ifference in simple and compound interest at the end of 2 years occurs because there is interest on first year interest. So Difference = P×(R100)2P×(R100)2
⇒ 80 = P×(8100)2P×(8100)2
⇒ P=80×(1008)2P=80×(1008)2 = 12,500
Answer:D
Answer: (D) 12,500