MU-NLPC/Calc-aqua_rat huggingface dataset:
A certain store sells all maps at one price and all books at another price. On Monday the store sold 12 maps and 10 books for a total of $42.00, and on Tuesday the store sold 20 maps and 15 books for a total of $70.00. At this store, how much less does a map sell for than a book? Pick one: A) $0.25 B) $0.50 C) $3.5 D) $2.5 E) $l.25

Solution: 12x+10y=42   20x+15y=70   multiply eq 1 by 5 and eq 2 by 3   60x+50y=42*5   60x+45y=70*3   subtracting 1 from 2   5y=210-210= 
210-210 = 0
0   therefore   x=3.5   difference in price =3.5   $3.5
Answer: C
There are 12 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station? Choose the correct choice
A) 132	B) 145	C) 165`	D) 400	E) 300

Solution: The total number of stations= 12   From 12 Stations we have to choose any two stations and the direction of travel (Ernakulam to Chennai is different from Chennai to Ernakulam) in 12P2 ways.   12P2= 12*11= 870   132NSWER:132
Answer: A
courtyard 3.78 meters long 5.95 meters wide is to be paved exactly with square tiles, all of the same size. what is the largest size of the tile which could be used for the purpose?  Choose the correct choice from the following answers:
A) 22
B) 77
C) 877
D) 99
E) 88

Solution: 3.78 meters =378 cm = 2 × 3 × 3 × 3 × 7   5.25 meters=525 cm = 5 × 5 × 3 × 7   Hence common factors are 3 and 7   Hence LCM = 3 × 7 = 21   Hence largest size of square tiles that can be paved exactly with square tiles is 77 cm.   Answer:77
Answer: B
750 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ? Choose the correct choice:
A) a) 162
B) b) 15
C) c) 60
D) d) 38
E) e) 12

Solution: Passed in english = 65%   Passed in maths = 55%   Passed in both = 40% of 55% = 2/5 * (55%) = 22%   Passed in (English + Maths - b) 15oth + Neither) 2/5 * (55 )= 
2/5 * (55 ) = 22
22%   Passed in (English + Maths - b) 15oth + Neither)= 100%   65 + 55 - 22 + Neither = 100   Neither = 100 - 98= 
100 - 98 = 2
2%= 0.02 * 750= 
0.02 * 750 = 15
15   Answer: b) 15
Answer: B
A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?  Pick
A) m
B) m
C) m
D) m
E) m

Solution: A can give B (5 min - 4 1/2 min) = 30 sec start.   The distance covered by B in 5 min = 1000 m.   Distance covered in 30 sec = (1000 * 30)/300= 
(1000 * 30)/300 = 100
100 m.   A can give B 100m start.   ANSWER:m
Answer: D
The difference between the simple interest received from two different sources on Rs. 500 for 3 years is Rs. 13.50. The difference between their rates of interest is?  Select the correct option:
A) A)2.4% B) B)6.6% C) C)0.3% D) D)2.0% E) E)1.3%

Solution: (500 * R1 * 3)/100 - (500 * R2 * 3)/100 = 13.50 1500(R1 - R2) = 1350   R1 - R2 = 6.6%   Answer:6.6%
Answer: B
IF n >0 what is the remainder when 912^n+3 is divided by 10 Choose the correct option: A) 0 B) 1 C) 2 D) 7 E) 9

Solution: For every even power, units digit of 9 will be 1 and for every every odd power units digit of 9 will be 9.   Since expression 12n+3 is odd, the units digit will be 9, which will also be the reminder when the expression is divided by 10.   9 is the answer
Answer: E
The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers ?	Choose the correct choice from the following answers:
A) 5/7 B) 12/35 C) 2/47 D) 8/9 E) 7/5

Solution: Explanation:   Let the numbers be a and b. Then, a + b = 12 and ab = 35   a+b/ab=12/35   (1/b+1/a)=12/35   Sum of reciprocals of given numbers=12/35   ANSWER:12/35
Answer: B
If m/49 is an integer, then each of the following must be an integer EXCEPT
Choose the correct option:
A) 4
B) 3
C) 9/2
D) 4
E) 5

Solution: Now plug m =49 into the answer choices:   A. (49- 28)/7 =3This is an integer   B. (49+ 21)/7 = 10. This is an integer   C. 14(49)/98 = 7. This is an integer   D. (49^2 - 49)/49 =48. This is an integer   E. (49+ 14)/14 = 9/2. This is NOT an integer   Answer: 9/2
Answer: C
If x and y are positive integers, and x^3*y^4 = 432, which of the following is the value of xy?  Select
A) 6	B) 10	C) 14	D) 15	E) 21

Solution: 432 = 2*216 = 2^2*108 = 2^3*54 = 2^4*27 = 2^4*3^3   xy = 2*3= 
2*3 = 6
6   The answer is 6.
Answer: A
20 women can do a work in 9 days. After they have worked for 6 days. 6 more men join them. How many days will they take to complete the remaining work?	Choose the most appropriate option.
A) 4:7	B) 4:3	C) 4:2	D) 4:0	E) 4:1

Solution: (20 * 16) women can complete the work in 1 day.   1 woman's 1 day work = 1/320   (16 * 15) men can complete the work in 1 day   1 man's 1 day work = 1/240   So, required ratio = 1/240 : 1/320 = 4:3.   Answer: 4:3
Answer: B
What is the area S of the square with the following coordinates: (x, y), (20, 20), (20, 5), (x, 5)?	Answers
A) 60.
B) 85.
C) 125.
D) 225.
E) It cannot be determined from the information given

Solution: Length of one side= 15 (20-5)   Since, its a square, the area will be S= 15^2= 225   225. is the answer
Answer: D
The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.  Pick:
A) 24 cm
B) 17 cm
C) 14 cm
D) 10 cm
E) 12 cm

Solution: Side of first square = (40/4)= 
(40/4) = 10
10 cm;   Side of second square= (32/4)= 
(32/4) = 8
8 cm.   Area of third square= [(10) 2 - (8) 2] cm2 = (100 - 64) cm2 = 36 cm2.   Side of third square = (36)(1/2) cm = 6 cm.   Required perimeter = (6 x 4) cm = 24 cm.   24 cmNSWER 24 cm 24cm
Answer: A
The payment per hour for a daily-wages employee is increased by 33.33 and the working time is reduced by 33.33%. What is the percentage change in the employee's income?
Choose the correct choice from the following:  A) Rs. 0.7889  B) Rs. 0.8889  C) Rs. 0.9889  D) Rs. 1.8889  E) Rs. 2.8889

Solution: If payment per hr is increased by 33.33 % , then   11.11 % decrease in income   If earlier he is getting Rs 1 hr per hr and working for 1 hr, income = Rs 1   Now he is getting Rs 1.3333 per hr and working for 0.66667 hrs, income = Rs. 0.8889   ANSWER:Rs. 0.8889
Answer: B
The sides of a cube are in the ratio 1:2 the ratio of their volume is? Answers:
A) 1:9
B) 1:7
C) 1:8
D) 1:6
E) 1:4

Solution: 1:8   Answer: 1:8
Answer: C
Nine pens are in the table.To create three pens in each group like as three group. How many ways are there to create these 3 teams? Choices
A) 27  B) 45  C) 90  D) 175  E) 280

Solution: Arrange the 6 pen in a straight line in 6! ways.   The first three form team 1, next three form team 2 and last three form team 3. But in each team, the boys are arranged in first, second third positions so you need to un-arrange them by dividing by 3! three times (once for each team). You get 6!/(2! * 2! * 2!)   Also, there are no distinct teams - team1, team2 and team3. You just have three teams. So you also need to un-arrange the three teams by dividing by another 3!.   You get 6!/(2! * 2! * 2!) * 2! = 45   Answer (45)   You get 6!/(2! * 2! * 2!) * 2!   Answer : 45
Answer: B
With a slope of 4, with a straight line in the xy- plane which has a point with x-coordinate of the point 14 and y-coordinate 19, find the y-intercept.
Select the correct option.
A) -19  B) 18  C) -37  D) 50  E) 37

Solution: Eq of line = Y = MX +-37   M = 4   X= 14   Y= 19   -37= Y - MX   Substitute given:   -37= 19 - (4)(14)   -37 = -37   correct option is -37
Answer: C
A honey bee flies for 10 seconds, from a daisy to a rose. It immediately continues to a poppy, flying for 6 additional seconds. The distance the bee passed, flying from the daisy to the rose is 14 meters longer than the distance it passed flying from the rose to the poppy. The bee flies to the poppy at 3 meters per second faster than her speed flying to the rose. The bee flies how many meters per second from the daisy to the rose?  Choose the correct choice from the following answers
A) 2 B) 5 C) 6 D) 8 E) 10

Solution: Let the speed be 's' and let the distance between rose and poppy be 'x'   The problem boils down to:   Rose to Poppy: s+3=x/6 ------- 1   Daisy to Rose: s=(x+14)/10------ 2   so from 1 we can re write x as x=6s+18   substitute the value of x in 2 gives us s=2 m/s   2
Answer: A
If x+y=270, x-y=200, for integers of x and y, y=?  Choose the correct choice from the following options:	A) 200	B) 235	C) 50	D) 115	E) 150

Solution: x+y = 270   x-y = 200   2x = 70   x = 35   y = 235   Answer is 235
Answer: B
Subtracting 10% from X is the same as multiplying X by what number?
Choose the correct option
A) 98% B) 90% C) 230% D) 97% E) 921%

Solution: X - (10/100) X = X * ?   ? = 90%   Answer:90%
Answer: B
In a simultaneous throw of two coins the probability of getting at least one head is ?
Choose the correct choice from the following answers
A) 3/4
B) 1/2
C) 1/4
D) 2/3
E) 1/5

Solution: S={HH,HT,TH,TT}   E be the event of getting at least one head is {HT,TH,HH}   P(E)=n(E)/n(S)=3/4   3/4nswer(3/4)
Answer: A
1,257
1,275
1,527
........
........
+7,521
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,5 and 7 exactly once in each integer. What is the sum R of the 24 integers ? Choices:	A) 26,996	B) 44,406	C) 60,444	D) 66,660	E) 99,990

Solution: This is the way i solved it :   Total no. of different combos = 24, total digits 4 therefore each digit must repeat  24/4= 
 24/4 = 6
6 times in each row .. So the right most row would add up to 1x6 + 2x6 + 5x6 + 7x6= 6+12+30+42= 
6+12+30+42 = 90
90 .. Each row would add up to 90, so 90 in the first means we have 9 that carries over and we get 0 , the second time its 90+9 and 9 stays and one 9 goes to the row to the left, so the last two digits of the SUM R should be 90 (E) .. We could go on and solve the exact number but since only one answer choice has the last digits as 90 we needn't go any further..
Answer: E
In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.60 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?  Choose the correct choice from the following options: A) 165 B) 175 C) 190 D) 200 E) 210

Solution: Suppose the man works overtime for x hours.   Now, working hours in 4 weeks = (5 x 8 x 4) = 160.   160 x 2.60 + X x 3.20 = 432   X = 5.   Hence, total hours of work = (160 + 5)= 
(160 + 5) = 165
165.   answer :165
Answer: A
What least number must be added to 3000 to obtain a number exactly divisible by 19 ?  Choose the correct choice from the following options:	A) 3	B) 2	C) 5	D) 6	E) 9

Solution: EXPLANATION:   On dividing 3000 by 19, we get 17 as remainder.   Number to be added = (19 - 17)= 
(19 - 17) = 2
2   Answer 2
Answer: B
Jill is dividing her 12-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?	Options
A) 10 B) 25 C) 462 D) 252 E) 630

Solution: With 12 players, the process of figuring out how many groups of 6 can be formed is pretty straight-forward....   12C6 = 12!/(6!6!) = 924 possible groups of 6   Once forming that first group of 6, the remaining 6 players would all be placed on the second team by default.   The 'twist' is that the two teams of 6 canshow upin either order:   462
Answer: C
The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 35% profit?	Select:
A) 2000
B) 2160
C) 2299
D) 2778
E) 2771

Solution: Let C.P. be Rs. x.   Then, (1920 - x)/x * 100 = (x - 1280)/x * 100   1920 - x = x - 1280   2x = 3200 => x = 1600   Required S.P. = 135 % of Rs. 1600 = 135/100 * 1600 = Rs. 2160.   Answer:2160
Answer: B
A bonus of Rs.2800 is to be divided among 3 people such that Alex gets twice as much as David, who receives one-fourth as much as Peter. What amount did Peter get?
Choose the correct choice:
A) 1200
B) 2000
C) 1600
D) 1500
E) 1700

Solution: Explanation:   Let Peter’s share be x.   Hence, David gets x/4 and Alex gets x/2.   x + x/4 + x/2 = 2800   7x/4 = 2800   x = Rs.1600   ANSWER 1600
Answer: C
In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip
was reduced by 200 km/hr and the time of flight increased by 30 minutes. What is the duration of the
flight ?  Answers
A) 3 hours B) 2.4 hours C) 1.4 hours D) 1 hour E) None of these

Solution: Explanation:   Let the duration of the flight be x hours.   Then   600x−600x+12=200600x−12002x+1=200x(2x+1)=32x2+x−3=0=>(2x+3)(x−1)=0   Neglecting the negative value for x we get x = 1   Answer: 1 hour
Answer: D
A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 72.Find the number of notes of Rs.50 denomination.  Choose the correct answer.
A) 15 B) 21 C) 17 D) 37 E) 57

Solution: Total Money = Rs. 10350.   Let 50 rupees note was X.   Then 500 rupees note = 72 - X   Now,   50*X + 500 * (72 - X) = 10350   50X + 36000 - 500X = 10350   - 450X = - 25650   X = 57.   No. of 50 rupees note = 57.   Answer: Option 57
Answer: E
A vendor bought bananas at 6 for $10 and sold them at 4 for $6. Find his gain or loss percent?
Choose the correct choice from the following options
A) 5%	B) 10%	C) 15%	D) 20%	E) 25%

Solution: Number of bananas bought = L.C.M of 6 and 4 = 12   C.P. = 10/6 * 12= 
10/6 * 12 = 20
$20   S.P.= 6/4 * 12= 
6/4 * 12 = 18
$18   Loss%= 2/20 * 100= 
2/20 * 100 = 10
10%   Answer is 10%
Answer: B
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.  Select the correct option.
A) 20/60	B) 20/63	C) 20/69	D) 20/61	E) 20/611

Solution: Required probability = (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126 = 20/63   Answer: 20/63
Answer: B
A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 9:30 am in the same direction at the rate of 84 km/h. At what time will the second train catch the first train?
Choose the correct option:
A) 11:00  B) 11:30  C) 12:00  D) 12:30  E) 1:00

Solution: In thirty minutes the first train travels 35 km.   The second train catches the first train at a rate of 84 km/h - 70 km/h = 14 km/h.   The second train will catch the first train in   35/14= 
  35/14 = 5/2 = around 2.5
2.5 hours, so at 12:00 noon.   The answer is 12:00.
Answer: C
A ladder 14 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 5 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip?
Choices.
A) 4  B) 5  C) 8  D) 10.72  E) 15

Solution: 14^2-5^2=171   it means that the height is equal to 13.07~=13.   since the top of the ladder slips down 4 feet, then the height of the wall =13-4= 
13-4 = 9
9   the bottom=sqrt(14^2-9^2)=sqrt(196-81)=10.72   ans is 10.72
Answer: D
An athlete runs 200 meters race in 10sec. His speed is? Select
A) 20km/hr  B) 15km/hr  C) 30km/hr  D) 72km/hr  E) 40km/hr

Solution: speed = 200/10= 
200/10 = 20
20 m/sec= 20 * 18/5 km/hr = 72km/hr   Answer is 72km/hr
Answer: D
What is the compound interest paid on a sum of Rs.3000 for the period of 3 years at 10% per annum. Choose the correct choice from the following answers
A) 900 B) 930 C) 990 D) 993 E) None of these

Solution: Solution= Interest % for 1st year= 10   Interest % for 2nd year= 10+ 10% of 10= 10+ 10 *10/100= 
10+ 10 *10/100 = 11
11   Interest % for 3rd year= 10+ 10%(10+11)=10+ 2.1= 
10+ 2.1 = 12.1
12.1   Total % of interest= 10 + 11+12.1= 
10 + 11+12.1 = 33.1
33.1   Total interest= 33.1 % 3000= 3000 * (33.1/100)= 
3000 * (33.1/100) = 993
993   Answer 993
Answer: D
A ball is bought for Rs.400 and sold at a gain of 20% find its selling price  Choose the correct choice.
A) Rs.400/- B) Rs.480/- C) Rs.500/- D) Rs.520/- E) Rs.540/-

Solution: 100 % ------> 400 (100 * 4 = 400)   120 % ------> 480 (120 * 4 = 480)   Selling price = Rs.480/-   Rs.480/-
Answer: B
In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $2,800 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $8,400 higher that M, then what percentage of apartments in the building are two-bedroom apartments?	Choose the correct choice from the following
A) 30%
B) 35%
C) 25%
D) 40%
E) 50%

Solution: Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 2800 : 8400 -----> 1 : 3   Let total number of Apartments be X   No. of 2 Bedroom Apartment = (1 / 4) * X   percentage of apartments in the building are two-bedroom apartments ---->   (1/4) * 100 ---> 25%   Answer : 25%
Answer: C
A rectangular-shaped carpet that measures x feet by y feet is priced at $18. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
Select the correct option
A) 180xy
B) 162/(xy)
C) 20xy
D) 20xy/9
E) xy/180

Solution: The area of the carpet in feet is xy.   The area in square yards is xy / 9.   The price per square yard is 18 / (xy/9) = 162/(xy).   The answer is 162/(xy).
Answer: B
What is the difference between the place value of 2 in the numeral 7449?
Choose the correct choice from the following.
A) 360
B) 165
C) 180
D) 190
E) 200

Solution: 360nswer: Option '360'    400 - 40= 
 400 - 40 = 360
360
Answer: A
Of the four numbers, whose average is 60, the first is one-fourth of the sum of the last three. The first number is :
Choose the correct choice from the following answers.
A) 17	B) 29	C) 36	D) 48	E) 58

Solution: Explanation:   Let the first number be x,   Then, sum of the four numbers = x + 4x = 5x.   so, 5x/4 = 60 or x = (60 * 4) / 5= 
(60 * 4) / 5 = 48
48. Answer: 48
Answer: D
During a certain week, a seal ate 40% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?  Choose the correct choice from the following.
A) 32	B) 40	C) 55	D) 64	E) 80

Solution: Total smelt = x.   Then, 0.4*80+0.3(x-80)=0.4*x --> x=80 --> 0.4*x=32   32nswer: 32.
Answer: A
If 14m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
Choose the correct option:
A) 2m −1
B) 4m
C) 5m
D) m/5
E) 6m/5

Solution: 14m - n = p   Add n to both sides:   14m = n + p   Add m to both sides:   15m = n + p + m   Now, divide both sides by 3   5m = (n + p + m)/3 = the average of n, p, and m   5m
Answer: C
It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:	Answers.
A) 2 : 3 B) 3 : 2 C) 3 : 4 D) 4 : 3 E) 2 : 1

Solution: Explanation:   Let the speed of the train be x km/hr and that of the car be y km/hr.   Then,	120/x+480/y=8 =>1/x+4/y=1/15....(i)   And, 200/x+400/y=25/3	=>1/x+2/y=1/24....(ii)   Solving (i) and (ii), we get: x = 60 and y = 80.   Ratio of speeds = 60 : 80 = 3 : 4.   ANSWER IS 3 : 4
Answer: C
The average age of a husband and a wife is 23 years when they were married FOUR years ago but now the average age of the husband, wife and child is 19 years(the child was born during the interval). What is the present age of the child?	Answers:
A) 6	B) 5	C) 8	D) 4	E) 2

Solution: 27 * 2= 
27 * 2 = 54
54   20 * 3= 
20 * 3 = 60
60   -----------   6 years.6nswer: 6
Answer: A
John and David work at a hospital with 10 other workers. For an internal review, 2 of the 10 workers will be randomly chosen to be interviewed. What is the probability that John and David will both be chosen?	Pick one:
A) 1/45
B) 1/35
C) 1/25
D) 1/15
E) 1/10

Solution: Probability that John and David will both be chosen out of 8 workers   = (2/10)*(1/9)   = 1/45   1/45nswer 1/45
Answer: A
If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x + 2, and 3x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?	Choose the correct choice.
A) 3  B) 4  C) 5  D) 6  E) 8

Solution: Soln:   Given that x is positive and single digit and based on 4/3*x being one of them,   Assume x as 3   this gives the list as 4, 6, 3, 5, 7   when ordered, 3,4,5,6,7   hence median is 5   Answer is 5
Answer: C
In May, the groundskeeper at Spring Lake Golf Club built a circular green with an area of 95π square feet. In August, the groundskeeper doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green? Choices:
A) 190π  B) 210π  C) 240π  D) 320π  E) 380π

Solution: Area = πR^2, so doubling the radius results in an area that is 4 times the original area.   4(95π) = 380π   The answer is 380π.
Answer: E
If a < b < c , which of the following must be true?
(I) a^2 < b^2
(II) b − a < c
(III) a^2 < b^2 < c^2 Answers
A) None
B) I only
C) II only
D) III only
E) II and III

Solution: (I) a^2 < b^2. Not necessarily true fractions: try a=0.1 and b=0.2.   (II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1.   (III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1.   None of the options must be true.   Nonenswer: None.
Answer: A
A bag contains 23 purple jellybeans, 12 green jellybeans, and 15 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be green? Options
A) 15%	B) 20%	C) 24%	D) 30%	E) 35%

Solution: p = 23 , g=12 , y=15   total = 50   p(green)=(12/50)*100= 
(12/50)*100 = 24
24% . Ans= 24%
Answer: C
A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled ? Choose the correct choice:
A) 4.5 hrs	B) 5 hrs	C) 6.5 hrs	D) 7.2 hrs	E) 9.2 hrs

Solution: Net part filled in 1 hour= 1/4 -1/9= 5/36   Therefore the cistern will be filled in 36/5 hours or 7.2 hours.   ANSWER:7.2 hrs
Answer: D
A lady grows Cauliflower in her garden that is in the shape of a square. Each Cauliflower takes 1 square foot of area in her garden. This year, she has increased her output by 223 Cauliflower when compared to last year. The shape of the area used for growing the Cauliflower has remained a square in both these years. How many Cauliflowers did she produce this year?
Choose the correct choice from the following.
A) 12541 B) 12542 C) 12544 D) 12545 E) Cannot be determined

Solution: Explanatory Answer   The shape of the area used for growing Cauliflower has remained a square in both the years.   Let the side of the square area used for growing Cauliflower this year be X ft.   Therefore, the area of the ground used for cultivation this year = X2 sq.ft.   Let the side of the square area used for growing Cauliflower last year be Y ft.   Therefore, the area of the ground used for cultivation last year = Y2 sq.ft.   As the number of Cauliflower grown has increased by 223, the area would have increased by 223 sq ft because each Cauliflower takes 1 sq ft space.   Hence, X2 - Y2 = 223   (X + Y)(X - Y) = 223.   223 is a prime number and hence it will have only two factors. i.e., 223 and 1.   Therefore, 223 can be expressed as product of 2 numbers in only way = 223* 1   i.e., (X + Y)(X - Y) = 223 * 1   So, (X + Y) should be 223 and (X - Y) should be 1.   Solving the two equations we get X = 112 and Y = 111.   Therefore, number of Cauliflower produced this year = X2 = 1122 = 12544.   Alternative Approach : Use answer choices   The area in both the years are squares of two numbers.   That rules out choice A,B and D. as 12541,12542 and 12545 are not the square of any number.   Check Choice C: If this year's produce is 12544, last year's produce would have been  12544 - 223= 
 12544 - 223 = 12_321
12321   12321 is the square of 111.   So, 12544 is the answer.   12544hoice 12544.
Answer: C