MU-NLPC/Calc-aqua_rat huggingface dataset:
Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 15 minutes. If A, B & C are kept open successively for 2 minute each, how soon will the tank be filled? Choose the correct choice from the following options: A) 2 hours B) 4 hours C) 3 hours D) 5 hours E) 6 hours

Solution: in three minute 1/20+1/30-1/15=1/60 part is filled   6 min--------1/60 parts   x min--------- 1 part(full)   x=360 min =6 hours   ANSW6 hoursR:6 hours
Answer: E
If 0.4 of a number is equal to 0.06 of another number, the ratio of the numbers is :
Choose one.
A) 2 :3  B) 3 :4  C) 3:20  D) 20:3  E) 22:1

Solution: Expl : 0.4A = 0.06B -> A/B = 0.06/0.40 = 6/40 = 3/20   :. A : B = 3 : 20   Answer: 3:20
Answer: C
One pump drains one-half of a pond in 1 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone? Select the correct option
A) 1 hour	B) 1.2 hour	C) 3 hours	D) 5 hours	E) 6 hours

Solution: The tricky part here, I believed is one half hour = 1/2. Then everything would be easy.   We have the 1st pump working rate/hour = 1/2 : 1 = 1/2   Working rate of 2 pumps: 1/2 : 1/2 = 1.   Working rate of 2nd pump: 1 -1/2 = 1/2 --> Time taken for the 2nd pump to finish: 1 : 1/2 = 2/1= 
2/1 = 2
2 hours.   3 hours
Answer: C
A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?  Select the correct option:
A) 27%
B) 25%
C) 26%
D) 35%
E) 29%

Solution: 800 --- 200   100 --- ? => 25%   Answer: 25%
Answer: B
Efrida and Frazer who live 10 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is four miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home?	Choices.
A) 6 B) 7 C) 8 D) 10 E) 11

Solution: It's a simple geometry problem. Look at the diagram below:   6nswer: 6.
Answer: A
Two numbers are in the ratio of 1 : 2. If 7 be added to both, their ratio changes to 3 : 5. The greater number is	Pick one:
A) 20 B) 24 C) 28 D) 32 E) 36

Solution: Let the ratio be X : Y,   Given X/Y = 1/2 ,   (X + 7)/(Y + 7) = 3/5   => X = 14   And Y = 28   ANSWER:28
Answer: C
During a trip, Francine traveled x percent of the total distance at an average speed of 25 miles per hour and the rest of the distance at an average speed of 50 miles per hour. In terms of x, what was Francine's average speed for the entire trip?  Pick: A) (180-x)/2 B) (x+60)/4 C) (300-x)/5 D) 5000/x+100 E) 12,000/(x+200)

Solution: total distance =100 ;total time = T   t1 = x/25 t2 = 100-x /50   T =t1+t2 = x/25 + 100-x/50 = (50x + 2500- 25x)/1250   = (25x+2500)/1250   = x +100 / 50   av speed = 100*50/x+100 = 5000/x+100   5000/x+100
Answer: D
A train passes a station platform in 42 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?	Pick:
A) 180 m	B) 240 m	C) 330 m	D) 280 m	E) 380 m

Solution: Speed = 54 x 5/18 = 15 m/s   Length of the train = (15 x 20)m = 300 m.   Let the length of the platform be x metres.   Then, (x + 300)/42 = 15   --> x + 300 = 630   x = 330m.   Answer : 330 m.
Answer: C
A 300 meter long train crosses a platform in 36 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Select
A) 300  B) 266  C) 230  D) 288  E) 271

Solution: Speed = [300 / 18] m/sec = 50/3 m/sec.   Let the length of the platform be x meters.   Then, x + 300 / 36 = 50/3   3(x + 300) = 1800 è x = 300m.   300nswer: 300
Answer: A
In State X, all vehicle license plates have 2 letters from the 26 letters of the alphabet followed by 4 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?	Choose the correct choice from the following choices
A) 23,400  B) 60,840  C) 67,600  D) 45,697,600  E) 676,000

Solution: The choices give us the answer without any calculations--   4 one digits places can take 10*10*10*10 ways..   2 letters places can be filled up in 26*26 ways   ans= 26*26*10*10*10*10=45,697,600   ans 45,697,600
Answer: D
In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?  Choose the correct choice from the following choices:	A) 3!*8!*4!*4! Ways	B) 8!*4!*4! Ways	C) 8!*3!*4! Ways	D) 3!*4!*4! Ways	E) 4!*4! Ways

Solution: Taking all person of same nationality as one person, then we will have only three people.   These three person can be arranged themselves in 3! Ways.   8 Indians can be arranged themselves in 8! Way.   4 American can be arranged themselves in 4! Ways.   4 Englishman can be arranged themselves in 4! Ways.   Hence, required number of ways = 3!*8!*4!*4! Ways.   Option 3!*8!*4!*4! Ways
Answer: A
A tyre has two punctures. The first puncture alone would have made the tyre flat in 8 minutes and the second alone would have done it in 5 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?	Choose the most appropriate option
A) 3 1/5min	B) 3 2/5min	C) 3 3/5min	D) 3 4/5min	E) 3 1/13min

Solution: Explanation:   Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute.   Lets Solve it:   1 minute work done by both the punctures =   (1/8+1/5)=(13/40)   So both punctures will make the type flat in   (40/13)mins=3 1/13mins   Option 3 1/13min
Answer: E
A train 110 m long is running with a speed of 24 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?	Choose the correct choice from the following answers:
A) 7 sec  B) 6 sec  C) 8 sec  D) 14 sec  E) 13.2 sec

Solution: Speed of train relative to man = 24 + 6= 
24 + 6 = 30
30 km/hr.= 30 * 5/18 = 8.33 m/sec.   Time taken to pass the men = 110 /8.33   = 13.2 sec.   Answer:13.2 sec
Answer: E
Twenty percent of the skiers that tried out for the ski patrol were selected. Of those that were not selected, 29 skiers were CPR certified and 35 were not. How many skiers tried out for the ski patrol? Choose the correct choice from the following choices:
A) 40
B) 50
C) 60
D) 70
E) 80

Solution: Not Selected = 80%   If total is x.   Then 0.8x=29+35= 
29+35 = 64
64   x=80   Hence answer is 80.
Answer: E
If the product of two positive integers is 60, which of the following could be the LCM and HCF of the two numbers? a. LCM 10 : HCF 6 b. LCM 30 : HCF 2 c. LCM 15 : HCF 4  Select the correct option.
A) a only  B) b only  C) c only  D) a,b only  E) a,c only

Solution: b is the correct answer.   Answer : b only
Answer: B
Submarine X and Submarine Y are equipped with sonar devices that can operate within a 6,000 yard range. Submarine X remains in place while Submarine Y moves 5,400 yards south from Submarine X. Submarine Y then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine Y continue to move and still be within the sonar range of Submarine X?
I. North
II. South
III. West
Choose the correct choice from the following answers:
A) I only	B) II only	C) II, III only	D) III only	E) I and III only

Solution: It's evident if we make a diagram for the Movement of Y respect to X.   From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range.   Thus it can only move north or west or anything in that curve.   Answer : I and III only
Answer: E
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 70 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? Choose the correct choice from the following options:
A) 22	B) 36	C) 48	D) 99	E) 12

Solution: Relative speed =70 + 30= 
70 + 30 = 100
100 km/hr.   100 * 5/18= 250/9 m/sec.   Distance covered = 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 * 9/250= 
1000 * 9/250 = 36
36 sec.   Answer: 36
Answer: B
How many different words can be formed from the word DAUGHTER so that ending and beginning letters are consonants?	Options
A) 7200 B) 14400 C) 360 D) 1440 E) 2440

Solution: Here total letters are 8,3 vowels and 5 consonants. Here 2 consonants can be chosen in 5C2 ways   and these 2 consonants can be put it in 2! Ways. The remaining 6 letters can be arranged in 6! Ways.   The words beginning and ending letters with consonant = 5C2 *2! *6! = 14400   ANSWER:14400
Answer: B
The present population of a town is 1000. Population increase rate is 25% p.a. Find the population of town after 2 years? Options.
A) 1000  B) 2000  C) 1563  D) 2153  E) 1245

Solution: P = 1000   R = 25%   Required population of town = P(1 + R/100)^T   = 1000(1 + 25/100)^2   = 1000(5/4)^2   = 1563(approximately)   Answer is 1563
Answer: C
In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 12 days, working 16 hours a day, the number of men required is:  Options.
A) 4 B) 5 C) 6 D) 8 E) 9

Solution: Explanation :   Let the required number of men be x.   Less days, More men (Indirect Proportion)   More working hrs per day, Less men (Indirect Proportion)   Days 8 : 10   Working Hrs 16: 8 :: 12 : x   => 12 x 16 x x = 10 x 8 x 12   => x = 10 x 8 x 12 / (12 x 16)   => x = 5   Answer : 5
Answer: B
The number of people at Ovations Bar in the hour from 12 p.m. to 1 p.m. was 20% greater than the number of people there from 11 a.m. to 12 p.m. The number of the people at the bar from 11 a.m. to 12 p.m. was 10% more than the number there from 10 a.m. to 11 a.m. If 121 people were at the bar from 11 a.m. to 1 p.m., which of the following is the number of people in the bar from 10 a.m. to 11 a.m.?
Choose the correct choice from the following answers:
A) 10 B) 20 C) 30 D) 40 E) 50

Solution: No of people from 10 - 11 is x   No of people from 11 - 12 is 11x/10   No of people from 12 to 1 is (6/5)(11x/10)   Given that 11x/10 + (6/5)(11x/10) = 121x / 50 = 121   Then x = 50   50
Answer: E
An aeroplane covers a certain distance at a speed of 320 kmph in 4 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:	Choose the correct choice from the following answers:  A) 520  B) 620  C) 820  D) 768  E) 720

Solution: Distance = (240 x 5) = 1280 km.   Speed = Distance/Time   Speed = 1280/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]   Required speed = (1280 x	3/5) km/hr = 768 km/hr   Answer 768) 768 Km/hr
Answer: D
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand S nor Brand B soap, 60 used only Brand S soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?
Choose the correct choice from the following
A) 15  B) 20  C) 30  D) 40  E) 45

Solution: SOLUTION FOR SOAP S AN40 SOAP B= 40=40
Answer: D
If the radius of a circle that centers at the origin is 5, how many points Q on the circle have integer coordinates? Select:	A) 4	B) 8	C) 12	D) 15	E) 20

Solution: I understand this might not be required but I used the equation of a circle.   Since the origin is at 0, x^2+y^2=5^2.   X,Y could be +/- (0,5 or 5,0) - 4 possibilities.   X,Y could be +/- (3,4 or 4,3) - 8 possibilities.   Ans: Q=12
Answer: C
A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives?	Answers:
A) 14200 B) 14700 C) 14800 D) 14500 E) None of these

Solution: Explanation :   Total amount invested = 50000   Assume that investment of C = x.   Then investment of 14700 = 5000 + x ,   Investment of A = 4000 + 5000 + x = 9000 + x   x + 5000+x + 9000 + x = 50000   => 3x + 14000 = 50000   => 3x = 50000 – 14000 = 36000   => x = 36000/3= 
36000/3 = 12_000
12000=> Investment of C = x = 12000 ,   Investment of 14700 = 5000 + x = 17000,   Investment of A = 9000 + x = 21000   Ratio of the investment of A : 14700 : C = 21000 : 17000 : 12000 = 21 : 17 : 12   Share of A = Total Profit * 21/50 = 35000 * 21/50 = 700*21= 
700*21 = 14_700
14700, Answer : Option 14700
Answer: B
A car is traveling 72 kilometers per hour. How many meters does the car travel in one minute?
Answers: A) 1200m/min B) 1360m/min C) 2560m/min D) 1670m/min E) 1890m/min

Solution: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify   72 kilometers per hour = 72 km/hr   = (72 × 1000 meters) / (60 minutes) = 1,200 meters / minute   correct answer is 1200m/min)1200m/min
Answer: A
Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour ? Choose one: A) 30 min B) 20 min C) 50 min D) 40 min E) 10 min

Solution: Explanation:   In 1hr, the bus covers 60 km without stoppages and 40 km with stoppages.   Stoppage time = time take to travel (60 - 40) km i.e 20 km at 60 km/hr.   stoppage time = 20/60 hrs = 20 min.   Answer: 20 min
Answer: B
ACME’s manufacturing costs for sets of horseshoes include a $11,450 initial outlay, and $19.75 per set. They can sell the sets $50.50. If profit is revenue from sales minus manufacturing costs, and the company producessells 987 sets of horseshoes, what was their profit?  Choose the correct choice from the following choices: A) $18,900.25 B) $30,943.25 C) $41,308.50 D) $51,817.50 E) $53,624.25

Solution: its $18,900.25   since options are not so close we can solve this by uniting calculation and guessing   total sales will be bit lower than 50500   from that initial outlay will get deducted 11500 so we left with 31500   variable cost say 20 X 1000 = 20000 will be deducted so finally we left with 19000   since we have considered the price greater than it actually is, the correct answer will certainly not cross the threshold of 19000.
Answer: A
Light glows for every 13 seconds . How many times did it between 1:57:58 and 3:20:47 am  Answers:
A) 382
B) 368
C) 388
D) 390
E) None

Solution: Explanation :   For every 13 seconds means in an hour light will glow 276 times and 12 seconds extra. Means in   second hour immediately after 1 second light will glow.   Means at 1:57:58 seconds 267 times and 7 seconds are more in it. Means first time light will glow at 1:58:05.   The difference in seconds between 1:58:05 and 3:20:47 is 4962 seconds. Light will glow 381 times and 9 seconds left   So total 382 times light will glow.   382nswer : 382
Answer: A
Anthony and Michael sit on the six-member board of directors for company R. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?
Choices.
A) 20%	B) 30%	C) 40%	D) 50%	E) 60%

Solution: Soln: Let the commitees be I and II   Assuming that Anthony and Michael R go into commitee I, there is just one more place left to be filled in that commitee and it can be taken by any of the 4 remaining people. Thus 4 ways.   Since the Anthony and Michael can also go into commitee II, we get 4 ways for that commitee also.   So in total = 8 ways   Now total number of ways of choosing 3 from 6 people is   = 640%3   = 6 * 5 * 4/3!   = 20 ways   Therefore Probability is = (8 /20) * 100= 
(8 /20) * 100 = 40
40%
Answer: C
There are 3 workers in the factory A, B, C. The age of A is 4 more than the age of B and the age of B is 4 more than the age of C. If the sum of the square of the ages is 1202. What is the sum of their ages?  Choose the correct choice from the following answers:
A) 50
B) 55
C) 60
D) 65
E) 70

Solution: let age of b=x;   age of a=x+4;   age of c=x-4;   sum of squares of ages =>3x^2+32   =>x=19.7=>20   sum of ages=60   ANSWER:60
Answer: C
A painting at an art gallery is framed such that the area of the square frame is 1/3 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 12, what is the area of the painting inside the frame?  Choose the correct option
A) 10 B) 20 C) 30 D) 40 E) 54

Solution: Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b   Area of painting = a^2 and we know that the area of the frame is (1/3) of that of the painting so   Area of frame = (1/3) * a^2   Area of Frame + Painting = a^2 + (1/3)*a^2 = (4/3)*a^2 which is equal to b^2   Line connecting the corners of the frame is the diagonal of the outer square which is equal to b*sqrt2   so, b * sqrt2 = 12   so, b = 6 * sqrt2   b^2 = 72   we know that b^2 = (4/3)*a^2   so, a^2 = (3/4)*b^2 = (3/4)*72= 
(3/4)*72 = 54
54   And area of painting= a^2 = 54   So, answer will be 54.
Answer: E
In the next Cricket World Cup T-20, Team Y has decided to score 200 runs only through 4s and 6s. In how many ways can the Team Y score these 200 runs?	Select.
A) 13  B) 15  C) 16  D) 17  E) 18

Solution: Team Y can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6's.   So the number of fours scored forms an AP 2, 5, 8, ... 50 with a common difference of 3.   Number of ways of scoring 200 only through 4's and 6's = (50 - 2)/3 + 1= 
(50 - 2)/3 + 1 = 17
17   Answer: D   Alternate solution: 4x + 6y= 200 --> 2x + 3y = 100   x = (100 - 3y)/2 --> 100 - 3y should be even. This is possible when 3y is even.   There are 17 even multiples of 3 between 0 and 100.   Answer: 17
Answer: D
A river 2m deep and 45 m wide is flowing at the rate of 7 kmph the amount of water that runs into the sea per minute is?  Options
A) 4500 M3 B) 4580 M3 C) 10500 M3 D) 4900 M3 E) 4700 M3

Solution: Explanation:   (7000 * 2 * 45)/60= 
(7000 * 2 * 45)/60 = 10_500
10500 M3   Answer: Option 10500 M3
Answer: C
After giving a discount of rs.80 the shopkeeper still gets a profit of 10%,if the cost price is rs.200.find the markup %?  Choices:
A) 31%  B) 33%  C) 28%  D) 30%  E) 32%

Solution: cost price=180   s.p=200*110/100= 
200*110/100 = 220
220   disc=80   so...mark price=216+80=296......   mark up%=261-200/200=61/200= 
61/200 = 61/200 = around 0.305
0.305 or 31%   31%NSWER:31%
Answer: A
Rashmi and Rakhi were partners in a business. Rashmi contributed 2/3rd of the capital for 20 months and Rakhi received 3/5th of the total profit. What was the time duration of Rakhi’s investment in the business?  Select:	A) 60 months	B) 63 months	C) 62 months	D) 30 months	E) 67 months

Solution: Explanation:   Ratio of the capital = 2 : 1   Ratio of the profit = 2 : 3   Let the duration of Rakhi’s investment be x months.   (2*20) : (1*x) = 2 : 3   x = 60 months   60 monthsNSWER:60 months
Answer: A
The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is:	Answers:
A) 1769
B) 1764
C) 1768
D) 1762
E) 1761

Solution: Let P.W. be Rs. x.   Then, S.I. on Rs. x at 16% for 9 months = Rs. 189.   x x 16 x	9	x	1	= 189 or x = 1575.   12	100   P.W. = Rs. 1575.   Sum due = P.W. + T.D. = Rs. (1575 + 189) = Rs. 1764.   Answer: 1764
Answer: B
When two coins are tossed,Find the probability of getting all tails?  Choose the correct choice from the following choices
A) 1/3
B) 3/4
C) 1/8
D) 3/8
E) P(E) =1/4

Solution: When two coins are tossed,   S = {HH, HT, TH, TT} where H = Head and T = Tail   Let P( =1/4 = event of getting all tails   Then P( =1/4 = {TT}   so, P(P( =1/4) = n(P( =1/4)/n(S) =1/4
Answer: E
A can do a work in 6 days , B can do a work in 8 days and C can do it in 12 days. B left work after 1 day. For how many number of days should A and C should work together to complete the remaining work ?	Choose one
A) 1/7  B) 2/7  C) 3/7  D) 4/7  E) 5/7

Solution: b work 1/8 * 1=1/8   remaining work =1-1/8=7/8   a and c work together =1/6+1/12=3/12=1/4   take reciprocal 7/8 * remaining work =8/7 *1/4=2/7   ANSWER:2/7
Answer: B
The sum of ages of 6 children born at the intervals of 3 years each is 75 years. What is the age of the youngest child?
Answers: A) 10 B) 15 C) 6 D) 5 E) 8

Solution: Let the ages of children be x, (x + 3), (x + 6), (x + 9), (x + 12), (x+15)years.   Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) +(x+15) = 75   6x =30   x = 5.   Age of the youngest child = x = 4 years.   Answer:5
Answer: D
The price of copper has steadily declined by 25% for the past 8 months, but analysts predict an increase of 14% in its price in the next 2 months. This will bring its price to $54.What was the price of copper 8 months ago. Choose one.
A) 65.2  B) 76.2  C) 63.4  D) 66.6  E) 78.1

Solution: -25+14-(25*14)/100=-14.5% net decrease   let initial price be Y   Y(1-14.5/100)=54   Y=54/0.855 = ~63.4   Ans is 63.4)
Answer: C
Rs. 6000 is lent out in two parts. One part is lent at 5% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest? Choose the correct choice from the following options:
A) 5:1	B) 5:5	C) 5:8	D) 5:4	E) 5:2

Solution: Let the amount lent at 5% be Rs. x   Amount lent at 10% is Rs. (6000 - x)   Total interest for one year on the two sums lent   = 5/100 x + 10/100 (6000 - x) = 600 - 1x/20   => 600 - 1/20 x = 450 => x = 3000   Amount lent at 10% = 3000   Required ratio = 3000 : 3000 = 5:5   Answer:5:5
Answer: B
A dishonest dealer professes to sell goods at the cost price but uses a weight of 700 grams per kg, what is his percent?
Choose one:
A) 42.8%	B) 25%	C) 55%	D) 28%	E) 55%

Solution: 700 --- 300   100 --- ? => 42.8%   42.8%nswer: 42.8%
Answer: A
A van takes 5 hours to cover a distance of 450 km. What speed in kph should the van maintain to cover the same distance in 3/2 of the previous time?	Select.
A) 56  B) 60  C) 64  D) 68  E) 72

Solution: (3/2)*5= 
(3/2)*5 = 15/2 = around 7.5
7.5 hours   450 / 7.5= 
450 / 7.5 = 60
60 kph   The answer is 60.
Answer: B
Find the Compound interest on 16000 at 20% per annum for 9 months.Find Compounded Quarterly?
Select:
A) 2500
B) 2510
C) 2520
D) 2530
E) 2522

Solution: Principle=16000   Interest=20   9 months=3 quarters   Amount=Rs[16000*(1+(20/5)/100))^3)]   =[16000*(1+(4/100)^3)]   =[16000*(104/100)^3]   =[(16000*21*21*21*21)/(20*20*20*20)]   =Rs.18522   Compound interest=Rs.(18522-16000)=Rs.2522   Option 2522
Answer: E
Find the fourth proportional to 1.9,2.3 and 4.8?
Options.
A) 5.01  B) 6.52  C) 5.81  D) 4  E) 6.81

Solution: Formula= Fourth proportional =(b x c)/a   a=1.9, b=2.3 and c=4.8   (2.3 x 4.8)/1.9 = 5.81   5.81
Answer: C
USC invited each South Carolina high school to send up to 39 students
to watch a football game. A section which has 199 seats in each row is
reserved for those students. What is the least number of rows needed to
guarantee that if 2006 students show up, then all students from the same
high school can be seated in the same row? Pick one:	A) 11	B) 12	C) 13	D) 14	E) 15

Solution: The answer is 12 rows. If 59 schools send 34 students each, then we can sit at   most 5 groups of students in the same row, so we will need 12 rows. Next, 12 rows are   sufficient. Assume that this is not the case. Suppose the groups of students are seated   like this: first the largest group, then the second largest group, then the third largest   group, etc. Suppose we run out of space - there are not enough seats in any row to   seat together the next group. Suppose the first group that can not be seated together   is the kth group and it consists of N students. Then k 61 since any row fits at least   5 groups. Also, N 2006/k 2006/61 < 33 (all groups already seated are no smaller   than the kth group). So, N 32. Since there is not enough space in any of the 12 rows   to seat the kth group, then there must be at least 168 students seated in each of the 12   rows. Now, 12 × 168 = 2016 > 2006 a contradiction. So, 12 rows are sufficient.   correct answer 12
Answer: B