MU-NLPC/Calc-aqua_rat huggingface dataset:
If a man walks at a rate of 5kmph, he misses a train by 7minutes. However, if he walks at the rate of 6kmph, he reaches the station 5minutes before the arrival of the train. Find the distance covered by him to reach the station.	Choose the correct choice from the following choices:  A) 8  B) 4  C) 15  D) 6  E) 12

Solution: Let the required distance x km   difference in the times taken at two speeds = 12min = 1/5 hr   (x/5)-(x/6) = 1/5   x = 6   the required distance is 6 km   Answer is 6
Answer: D
Today is Varun's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today ?  Choose the correct choice from the following choices:
A) 33  B) 98  C) 25  D) 29  E) 27

Solution: Explanation:   Let Varun's age today = x years.   Then, Varun's age after 1 year = (x + 1) years.   Therefore x + 1 = 2 (x - 12) x + 1 = 2x - 24 x = 25   Answer: 25) 25 years
Answer: C
A sum of money becomes double itself in 6 years at simple interest. How many times will it become 10 years at the same rate?
Select:
A) 2 1/3
B) 3 1/3
C) 2 1/4
D) 3 1/4
E) 4

Solution: P ---- 2P ---- 6 years3 1/3 P ---- 10 years Answer: 3 1/3
Answer: B
Pipe A fills a tank in 12 minutes. Pipe B can fill the same tank 3 times as fast as pipe A. If both the pipes are kept open when the tank is empty, how many minutes will it take to fill the tank?
Choose the correct option: A) 4 mins B) 6 mins C) 5 mins D) 3 mins E) 7 mins

Solution: A's rate is 1/12 and B's rate is 1/4.   The combined rate is 1/12 + 1/4 = 1/3   The pipes will fill the tank in 3 minutes.   The answer is 3 mins.
Answer: D
Three pairs of siblings, each pair consisting of one girl and one boy, are randomly seated at a table. What is the probability that all three girls are seated on the left of their boy siblings?
Choose one:
A) 1/2  B) 1/4  C) 1/6  D) 1/8  E) 1/16

Solution: Notice that we need a girl to be to the left of her sibling, but not necessarily right to the left of him (meaning that if B and G are siblings, then GB arrangement as well as for example G*B arrangement is possible).   Now, the probability that one particular sibling is seated that way is 1/2 (a girl can be either to the left of her sibling or to the right), the probability that two siblings are seated that way is 1/2*1/2 and the probability that all three siblings are seated that way is 1/2*1/2*1/2=1/8.   Answer: 1/8.
Answer: D
Holly,Paul,Anne and Jim are rehearsing a dance routine. How many different ways can you arrange the 4 dancers in a line if Anne must be first or second	Choose the correct choice from the following options.
A) 11 B) 12 C) 13 D) 14 E) 15

Solution: Anne first: three others follow in any order; 3P3 = 3! ways = 6   Anne 2nd: three other positions assigned in 3!ways = 6 ways.   TOTAL: 12 possible arrangements   Answer 12
Answer: B
There are 25 students in a class. Find the numbers of ways in which a committee of 3 students is to be formed? Choices
A) 1250 B) 1800 C) 2300 D) 3256 E) 2863

Solution: Required number of ways = 2523003 = 25*24*23 / 6= 
25*24*23 / 6 = 2_300
2300   Answer is 2300
Answer: C
Which of the following options represents an approximate value for the question mark (?) in the following equation? 65.321 + 22.4 × 3.2 + ? = 502.871	Choose one.
A) 509.2  B) 529.2  C) 504.2  D) 549.2  E) 506.2

Solution: 65.321 + 22.4 × 3.2 + ? = 502.871   or, ? = 502.871 – 65.321 + 22.4 × 3.2   ? = 502.871 – 65.321 + 71.68   ≈ 509.2   509.2nswer 509.2
Answer: A
Lisa and Robert have taken the same number of photos on their school trip. Lisa has taken 3 times as many photos as Claire and Robert has taken 12 more photos than Claire. How many photos has Claire taken? Choose the correct option
A) 6	B) 8	C) 10	D) 12	E) 14

Solution: Explanation:   L = R   L = 3C   R = C + 12   We can substitute R for L in the second equation: R = 3C. If R is equal to both 3C and C + 12, we can say 3C = C + 12, and solve for C.   3C = C + 12   2C = 12   C = 6   6nswer : (6)
Answer: A
A red ant is sitting on one side of a table (point X) and a black ant is sitting on the opposite side of the table (point Y). Now both of them decides to exchange their places and starts crawling. On the way, both of the ants meet and after that, it takes 20 seconds for the Red ant to move to point Y and it takes 5 seconds for the Black ant to reach point X.
Find out the total time taken by the Red and the Black ant to make the journey.
Choose the correct choice from the following answers.
A) 30 and 15 seconds
B) 10 and 15 seconds
C) 20 and 15 seconds
D) 25 and 15 seconds
E) 5 and 15 seconds

Solution: Solution:   Let the speed of red ant be R.   Speed of Black ant be B.   Time at which they cross their paths be T.   Now we will apply the basic formula of distance   Distance = Speed * Time   The Red ant travels R * T distance before meeting and R * 20 after meeting.   The Black ant travels B * T distance before meeting and B * 5 after meeting.   Now as per the question,   The distance traveled by red ant before they both meet will be equal to the distance covered by black ant after they meet. We can say the same for the vice versa case as well.   Thus   R * T = B * 5 and B * T = R * 20   Using both the quations   T = 10   Thus the red ant will require 10 + 20= 
10 + 20 = 30
30 seconds to travel the distance.   And the black ant will take  10 + 5= 
 10 + 5 = 15
15 seconds to travel the distance.   30 and 15 secondsnswer 30 and 15 seconds
Answer: A
The sum of the ages of 5 children born at the intervals of 1 year each is 50 years. what is the age of the youngest child ?  Choose one:
A) 22
B) 8
C) 10
D) 99
E) 38

Solution: Let x = the youngest child. Each of the other four children will then be x+1, x+2, x+3, x+4.   We know that the sum of their ages is 50 .   so, x+(x+1)+(x+2)+(x+3)+(x+4) = 50   therefore The youngest child is 8 years old   Answer: 8
Answer: B
In the recent, religious conference in India, out of 1100 men, 900 women, 600 children present inside the building premises, 50% of the men, 40% of the women and 30% of the children were Christian. Find the percentage of people who were not Christian? Choose the most appropriate option:
A) 58.08%
B) 59.23%
C) 55.23%
D) 63.25%
E) 61.45%

Solution: Solution: Number of Christian men present there = 1100*50/100= 
1100*50/100 = 550
550   Christian women= 900*40/100= 
900*40/100 = 360
360   Christian children= 600*30/100= 
600*30/100 = 180
180.   Total member present in religious conference= 1100+900+600= 
1100+900+600 = 2_600
2600   Total Christian= 550+360+180= 
550+360+180 = 1_090
1090   Hence, % of Christian present there= 1090*100/2600 = 41.92%   % of people who were not Christian = 100-41.92= 
100-41.92 = 58.08
58.08%.   58.08%nswer 58.08%
Answer: A
Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 12% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit? Choose the correct choice from the following answers.
A) 117%
B) 120%
C) 121%
D) 133%
E) 140%

Solution: Since Michelle earns 12% interest compounded semiannually, then she earns 6% interest every 6 months.   Now, the simple interest earned in 5 periods (30 months = 5*6 months) would be 6%*5=30%. But, since the interest iscompoundedevery 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 30%, only answer choice D fits.   Answer: 133% 6 *5= 
 6 *5 = 30
30%. But, since the interest iscompoundedevery 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 30%, only answer choice D fits.   Answer: 133%
Answer: D
Machine–A produces 50% of the total output and Machine-B produces 75% of the total output. An average of nine units out of a thousand goods manufactured by Machine-A and one unit of 250 units produced by Machine-B prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective?	Choose the correct option:	A) 0.06	B) 0.006	C) 0.07	D) 0.08	E) 0.09

Solution: Suppose machine A produce 1000 units   total defective = 9   Machine 0.006 then produces=1500 units   total defective=6   probability=15/2500= 
15/2500 = 3/500 = around 0.006
0.006   Answer : 0.006
Answer: B
A bag contains equal number of 25 paise, 50 paise and one rupee coins respectively. If the total value is Rs 105, how many types of each type are present? Pick.
A) 75 coins
B) 60 coins
C) 30 coins
D) 25 coins
E) 15 coins

Solution: EXPLANATION:   Bag consists of 25 paise, 50 paise and 1 rupee (100 paise) so the ratio becomes 25 : 50 : 100 or 1 : 2 : 4   Total value of 25 paise coins =(1 / 7 ) x 105 = 15   Total value of 50 paise coins = (2 / 7) x 105 = 30   Total value of 100 paise coins = (4 / 7) x 105 = 60   No. of 25 paise coins = 15 x 4 = 60 coins   No. of 50 paise coins = 30 x 2 = 60 coins   No. of 1 rupee coins = 60 x 1 = 60 coins   Therefore, there are 60 number of coins of each type.   ANSWER IS 60 coins
Answer: B
At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 40% on the cost price?  Choose the correct answer
A) 62.5 B) 69.5 C) 67.5 D) 62.5 E) 70

Solution: CP = 47.50   SP = 47.50*(140/100)= 
47.50*(140/100) = 66.5
66.5   MP*(95/100)= 66.5   MP = 70   Answer:70
Answer: E
A room is 15m long, 4m broad and 3m height. Find the cost of white washing its four walls at 50p per m2 ?	Pick one.
A) Rs.60
B) Rs.57
C) Rs.55
D) Rs.52
E) Rs.53

Solution: 2 *3(15 + 4) = 114   114 * 1/2 = Rs.57   ANSWER:Rs.57
Answer: B
A plane flies 420 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 23 mph, what is the speed of the plain in still air?  Select.
A) 253 mph. B) 275 mph. C) 296 mph. D) 278 mph. E) 235 mph.

Solution: The speed of the plane in still air = x miles/hour   The speed of the wind is 23 mph   Speed with the wind = (x + 23) mph   Speed against the wind = (x – 23) mph   Time = Distance/ Speed   According to the problem,   420/(x + 23) = 350/(x – 23)   420(x – 23) = 350(x + 23)   420x – 9660 = 350x + 805   420x – 350x = 8050 + 9660   70x = 17710   x = 17710/70= 
17710/70 = 253
253   Therefore, the speed of the plane in still air= 253 mph.   correct answer 253 mph.
Answer: A
A man can row upstream at 10kmph and downstream at 12kmph. Find man's rate in still water ?  Pick:	A) 11km/hr	B) 15km/hr	C) 10km/hr	D) 20km/hr	E) 7.5km/hr

Solution: Rate in still water = 1/2 (10+12) = 11km/hr   11km/hrnswer is 11km/hr
Answer: A
A lump of two metals weighing 18 g is worth Rs. 87 but if their weight is interchanged, it would be worth Rs. 78.60. If the price of one metal be Rs. 6.70 per gram, find the weight of the other metal in the mixture.  Select:	A) 8g	B) 12g	C) 15g	D) 18g	E) None

Solution: Solution: Cost of (18 g of 1st metal + 18 g of 2nd metal) = Rs. 165.60   Cost of (1 g of 1st metal + 1 g metal of 2nd metal) = Rs. 9.20   Hence cost of 1 g of 2nd metal,   = 9.20 - 6.70   = Rs. 2.5   Mean price = Rs. 87/18   quantity of 1st metal /quantity of 2nd metal = 14/6:56/30 = 5:4   Quantity of 2nd metal = (18*4)/9= 
(18*4)/9 = 8
8 g.   8gnswer: Option 8g
Answer: A
A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is? Options:
A) 33
B) 77
C) 20
D) 99
E) 71

Solution: M = 15   S = 5   DS = 15 + 5= 
15 + 5 = 20
20   Answer: 20
Answer: C
In a deck of 52 cards, how many ways are there to select 13 Spade and 13 heart cards without repetition?	Choose the correct choice:
A) 169 B) 170 C) 171 D) 172 E) 173

Solution: 13*13= 
13*13 = 169
169 ways   169NSWER:169
Answer: A
A completes a work in 10 days and B complete the same work in 15 days. If both of them work together, then the number of days required to complete the work will be
Choose the correct choice from the following options
A) 8 days  B) 9 days  C) 10 days  D) 6 days  E) 13 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days   Therefore, here, the required number of days = 12 × 15/ 25 = 6 days.   6 days
Answer: D
By selling 20 pencils for a rupee a man loses 60%. How many for a rupee should he sell in order to gain 60%?
Choices:
A) 8 B) 9 C) 7 D) 6 E) 5

Solution: 40% --- 20   160% --- ?     40/160 * 20= 
  40/160 * 20 = 5
5   Answer: 5
Answer: E
In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr?	Choose the correct choice from the following options: A) 2.5 sec B) 1.9 sec C) 3.8 sec D) 6.9 sec E) 2.9 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 150/40   = 3.8 sec.   Answer: 3.8 sec
Answer: C
If x is a whole number, then x2(x2-1) is always divisible by: Choose the correct choice from the following options
A) 12	B) 24	C) 36	D) 48	E) 26

Solution: Putting x=2, we get 22(22-1)= 12.   So, x2(x2-1) is always divisible by 12.   12NSWER:12
Answer: A
If each and every term in the sum a1+a2+a3+.....+an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?	Choose the correct option: A) 38 B) 39 C) 40 D) 41 E) 42

Solution: For example: as units digit of 350 is zero then # of terms must be multiple of 10. Only answer choice which is multiple of 10 is C (40).   To illustrate consider adding:   *7   *7   ...   77   77   ----   =350   So, several 7's and several 77's, note that the # of rows equals to the # of terms. Now, to get 0 for the units digit of the sum the # of rows (# of terms) must be multiple of 10. Only answer choice which is multiple of 10 is C (40).   Answer: 40.
Answer: C
6) A marketing firm determined that , of 260 households surveyed, 80 used neither Brand A nor Brand B soap.60 used only Brand A soap and for every household that used both brands of soap, 3 used only brand B soap.how many of the 200 household surveyed used both brands of soap? Select the correct option
A) a) 15
B) b) 20
C) c) 30
D) d) 40
E) e) 45

Solution: 180 = At least one of Soap A or B   Both brands = x   Brand B = 3x   => 60 + x + 3x = 180   => 4x = 120   => x = 30   Answer - c) 30
Answer: C
A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleable and there are 12 unsaleable mangoes in the crate then how many mango are there in the crate? Options:
A) 480  B) 520  C) 360  D) 280  E) 420

Solution: Let the total no of mangoes in the crate be X.   Then the no of bruised mango = 1/30 X   Let the no of unsaleable mangoes =3/4 (1/30 X) ==> 3/120 X = 12   1/40 X =12   X=480   so the answer is Option 480) 480.
Answer: A
Solve the quickfire maths brain teaser âˆš4% = ?  Pick:
A) 30%	B) 40%	C) 85%	D) 19%	E) 20%

Solution: âˆš4%   => âˆš4/âˆš100   => 2/10   => 20/100   => 20%   20%
Answer: E
A sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $2,250 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week?
Choose the most appropriate option:
A) 25%	B) 30%	C) 35%	D) 40%	E) 45%

Solution: C for me.   Let managers comminsion rate be M.   m*5000+ 2*0.05*5000=2250   5000*m=1750   m=35/100=35%
Answer: C
X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
Select the correct option
A) 2:1  B) 1:2  C) 1:3  D) 3:1  E) 1:4

Solution: Ratio in which they should share the profit   = Ratio of the investments multiplied by the time period   =45000×12:30000×9   =45×12:30×9   =3×12:2×9   =2:1   Correct 2:1nswer is 2:1
Answer: A
In a public show 62 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant? Options.
A) 100 B) 110 C) 120 D) 140 E) 228

Solution: 75 % of 600   = 62/100 × 600   = 372   Therefore, the number of vacant seats = 600 - 372= 
600 - 372 = 228
228.   Answer:228
Answer: E
Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions:
The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow.
The paint will be namedBrun Xif the paint contains 3 jars of brown paint.
The paint will be namedJaune Xif the paint contains at least 2 jars of yellow.
The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow.
What is the probability Q that the new color will be one of theJaunecolors?  Choose the correct answer:	A) 5/42	B) 37/42	C) 1/21	D) 4/9	E) 5/9

Solution: I get B.   Jaune Y = (4 choose 1)*(5 choose 2) = 4*10= 
4*10 = 40
40   Jaune X= (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4= 
6*5 + 4 = 34
34   Total combinations= 9 choose 3 = 84   Probability of Jaune Q= (40 + 34)/84 = 37/42
Answer: B
Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 9km apart, if they walk in the same direction?  Choose the correct choice.
A) 15 hours  B) 16 hours  C) 17 hours  D) 18 hours  E) 19 hours

Solution: The relative speed of the boys = 5.5kmph â€“ 5kmph   = 0.5 kmph   18 hoursistance between them is 9 km   Time = 18 hoursistance/Speed   Time= 9km / 0.5 kmph = 18 hrs   answer :18 hours
Answer: D
X can finish a work in 15 days. Y can finish the same work in 20 days. Y worked for 12 days and left the job. how many days does X alone need to finish the remaining work?  Choose the most appropriate option:	A) 5	B) 3	C) 4	D) 7	E) 8

Solution: Work done by X in 1 day = 1/15   Work done by Y in 1 day = 1/20   Work done by Y in 12 days = 12/20 = 3/5   Remaining work = 1 – 3/5 = 2/5   Number of days in which X can finish the remaining work = (1/3) / (1/15)= 
(1/3) / (1/15) = 5
5   5
Answer: A
solve the given equation 9^y = 3^12, what is y?
Choose the correct option: A) 1 B) 3 C) 4 D) 5 E) 6

Solution: 3^2y = 3^12   2y=12, therefore y=6   6
Answer: E
100 identical coins each with probability "p" showing up heads & tossed. If 0 then show the number of heads? Pick:
A) 33/100
B) 41/101
C) 51/101
D) 87/101
E) 98/101

Solution: Let aa be the number of coins showing heads   Then, P(A=50)=P(A=51)P(A=50)=P(A=51)   ⇒10051/10150×P50×(1−P)50⇒10051/10151×P51×(1−P)49⇒10051/10150×P51×(1−P)50=10051/10151×P⇒51(1âˆ′P)=50P⇒P=51/101   51/101
Answer: C
Abby, Brandon, Cedric, and Deirdre are planning to attend a concert. If their friend Kim also goes with them, they will get a group discount on their tickets. If the total price of the tickets with the group discount is the same as the total price of the tickets without the group discount, how much is the discount? Answers: A) 5% B) 10% C) 20% D) 25% E) 33%

Solution: Let A,B,C and D individual tickets be X and total tickets is 4X..   Now with Kelly they get a discount , total tickets here is 5x.   We are told that group discount is same as total price without discount..   When we need to solve 5X till we get 4X..   Take options..5X - 5%(5X) = 5x - (0.05)(5X) = 5x - 0.25X = 4.75X...not same as 4X..   (B) 5X - 10% of 5x 5  - 0.25= 
5  - 0.25 = 4.75
4.75X...not same as 4X..   (B) 5X - 10% of 5x=> 5x - (0.1)(5x) = 4.5X, which is again not equal to 4x. So, this is not the correct option.   (C) 5X - 20% of 5x => 5x - (0.2)(5x) = 4X, this is same as 4X...no need to do other options..   Answer: option 20% is correct answer.
Answer: C
Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 5600. What was Simran share in the profit?	Choose the correct choice from the following choices.
A) s 9500 B) s 2400 C) s 10500 D) s 11000 E) s 1400

Solution: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.   Simran's share = Rs. 5600 x	3/7	= Rs. 2,400   ANSWER :s 2400
Answer: B
What is the area of a square field whose diagonal of length 28 m?  Choices:
A) 288
B) 289
C) 200
D) 112
E) 392

Solution: d2/2 = (28 * 28)/2= 
(28 * 28)/2 = 392
392   Answer: 392
Answer: E
The second of two numbers is two less than three times the first. Find the numbers if there sum is
26. Choose the most appropriate option:	A) 7-19	B) 8-20	C) 10-16	D) 15-9	E) 20-6

Solution: We are looking for two numbers.   #1 - x   #2 - 3x – 2   The sum is 26. #1 + #2 = 26   Substituting x + 3x – 2 = 26   4x – 2 = 26   4x = 28   x = 7   The first number is 7, the second number is two less than three times 7 or 19.   correct answer 7-19
Answer: A
A money lender lent a total of $1600 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1600, how much did he lend to each of the two customers? Choose the most appropriate option:  A) 700; 1100  B) 1072; 528  C) 1000; 800  D) 1200; 800  E) None of the above

Solution: The method given above is the one given in the book.   However the method I used was   (1*x*5)/100 + (1600-x)*6/100 = 1600*5.67/100   Simplifying we get x= 528   1072; 528
Answer: B
In a certain neighborhood, there are half as many beige houses as white houses, and six times as many white houses as brown houses. What is the ratio of the number of brown houses to the number of beige houses? Choose the correct option:
A) 1:3
B) 1:9
C) 2:5
D) 5:3
E) 6:1

Solution: The ratio of beige:white:brown = 3:6:1   The answer is 1:3.
Answer: A
A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 260 m long?	Choose the correct choice from the following answers:
A) 34 Seconds
B) 22 Seconds
C) 41 Seconds
D) 24 Seconds
E) 29 Seconds

Solution: 24 Seconds   24 Seconds   24 Secondsistance travelled = 140 + 260= 
140 + 260 = 400
400m   Speed= 60 * 5/8 = 50/3m   Time = 400 * 3/50= 
400 * 3/50 = 24
24 Seconds
Answer: D
Machine P and Machine Q are each used to manufacture 440 sprockets. It takes Machine P 10 hours longer to produce 440 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?
Pick one.
A) 2  B) 4  C) 6  D) 8  E) 10

Solution: P makes x sprockets per hour.   Then Q makes 1.1x sprockets per hour.   440/x = 440/1.1x + 10   1.1(440) = 440 + 11x   11x = 44   x = 4   The answer is 4.
Answer: B
A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss?  Pick
A) 17 B) 15 C) 11 D) 16 E) 12

Solution: CP of 20 dozen of bananas = 15 * 20 = Rs. 300   Number of bananas which are rotten = 1/4 * 20= 
1/4 * 20 = 5
5 dozen.   SP of two-third of remaining bananas= (2/3 * 15) * 22.5 = Rs. 225   SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75.   SP of 1 dozen bananas = 75/5 = Rs. 15.   Answer: 15
Answer: B
Lake A has a duck population of 30 females and 36 males. Lake B’s duck population consists of the same ratio of females to males. If 4 new female ducks are added to Lake B and no other ducks are added or removed, the new total duck population of Lake B could be which of the following? Choose the most appropriate option.
A) 144
B) 105
C) 78
D) 75
E) 36

Solution: Lake A has a duck population of 30 females and 36 males --> the ratio is F:M = 30:36 = 5:6.   Lake B’s duck population consists of the same ratio of females to males --> F:M = 5:6.   75
Answer: D
In how many ways Chief Minister and Minister be elected froma team of 12 members?	Choose the correct choice from the following
A) 120 B) 124 C) 132 D) 135 E) 139

Solution: To do this, if captain is elected first, then we have 12 ways of doing this.   For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)   So, the ans is 12*11= 
12*11 = 132
132 ways.   132
Answer: C