MU-NLPC/Calc-aqua_rat huggingface dataset:
Ben
ips a fair coin repeatedly. Given that Ben's first coin
ip is heads, compute the probability
Ben
ips two heads in a row before Ben
ips two tails in a row.	Choose the correct answer:
A) 2/3	B) 3/3	C) 1/3	D) 1/1	E) 2/2

Solution: If Ben successfully   ips two heads in a row, then Ben must have   ipped the coin an   even number of times. If Ben successfully   ips two tails in a row, then he must have   ipped   the coin an odd number of times. However, the coin must have been   ipped at least twice. The   desired probability is therefore   (1/3)/(1/2)=2/3   correct answer 2/3
Answer: A
Suppose 5 monkeys take 5 minutes to eat 5 bananas. How many monkeys would it take to eat 15 bananas in 15 minutes? Select.
A) 9
B) 10
C) 11
D) 5
E) 13

Solution: One monkey takes 5 min to eat 1 banana , so in 15 mins 1 monkey will eat 3 bananas , so for 15 bananas in 15 min we need  15/3= 
 15/3 = 5
5 monkeys   ANSWER:5
Answer: D
The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.6 the sixth number is?  Choose the correct answer:
A) 11.4	B) 11.3	C) 11.8	D) 11.5	E) 12.7

Solution: 1 to 11 = 11 * 10.9= 
11 * 10.9 = 119.9
119.9   1 to 6= 6 * 10.5= 
6 * 10.5 = 63
63   6 to 11= 6 * 11.6= 
6 * 11.6 = 69.6
69.6   63 + 69.6= 
63 + 69.6 = 132.6
132.6 – 119.9= 12.7   6th number = 12.7   Answer: 12.7
Answer: E
A cask is filled with alcohol and water in the ratio 5”3 Sixteen gallons of this are drawn off and the cask is filled with water and then the proportion of alcohol to water becomes 3:5 How many gallons does the cask hold ?
Pick:
A) 32
B) 36
C) 38
D) 40
E) 42

Solution: ratio of alcohal and water is 25:15   Initially when Sixteen gallons of this are drawn off   ratio of alcohal and water is 15:9   and the cask is filled with water 15:25 which is 3:5   ANSWER:40
Answer: D
The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.7 kg. the weight of the new student is ?  Choose the correct choice from the following choices
A) 10.6 kg  B) 10.8 kg  C) 11 kg  D) 14.9 kg  E) None

Solution: Answer   Weight of new student = Total weight of all 20 students - Total weight of initial 19 students   = (20 x 14.7 - 19 x 15) kg   = 9 kg.   Correct Option: None
Answer: E
There are 5 men and 11 women. In how many ways one can select a group of 6 with at-least 3 men?	Choices:
A) 1932
B) 1933
C) 1934
D) 1935
E) 1936

Solution: (5c3*11c3)+(5c4*11c2)+(5c5*11c1)   1936   ANSW1936R:1936
Answer: E
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 22 years. The present age of the husband is	Choose the correct option:
A) 40  B) 36  C) 45  D) 55  E) 65

Solution: Explanation:   Sum of the present ages of husband, wife and child = (27 * 3 + 3 * 3)= 
(27 * 3 + 3 * 3) = 90
90 years.   Sum of the present ages of wife and child= (22 * 2 + 5 * 2)= 
(22 * 2 + 5 * 2) = 54
54 years.   Husband's present age= (90 - 54)= 
(90 - 54) = 36
36 years   Option 36
Answer: B
Sand is poured into a box so that the box is being filled at the rate of 3 cubic feet per hour. If the empty rectangular box is 5 feet long, 4 feet wide, and 3 feet deep, approximately how many hours does it take to fill the box?
Answers
A) 14  B) 16  C) 18  D) 20  E) 22

Solution: The volume the box is: length*width*depth = 5*4*3= 
5*4*3 = 60
60 cubic feet.   60 cubic feet / 3 cubic feet per hour= 20 hours.   It will take 20 hours to fill the box.   The answer is 20.
Answer: D
The present worth of a certain sum due sometime hence is Rs. 3400 and the true discount is Rs. 340. The banker's gain is:  Choices
A) Rs. 21  B) Rs. 17  C) Rs. 18  D) Rs. 34  E) None of these

Solution: Explanation :   BG = (TD)2/PW=(340)2/3400=340 × 340/3400 = 340/10 = Rs. 34 Answer : Option Rs. 34
Answer: D
A woman complete a journey in 5 hours. She travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
Choose the most appropriate option:
A) 334 km. B) 216 km. C) 112 km. D) 224 km. E) 544 km.

Solution: 0.5x/21 + 0.5x/24 = 5   --> x/21 + x/24 = 10   --> x = 112 km.   112 km.
Answer: C
P and Q are the only two applicants qualified for a short-term research project that pays 480 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage?	Choose the most appropriate option:	A) $5	B) $8	C) $11	D) $14	E) $17

Solution: Let Q's hourly wage be x, then P's hourly wage is 1.5x   Let T be the number of hours that Q needs, then P needs T-10 hours to do the job.   Since they both are paid an equal total amount of $480:   x*T=1.5x*(T-10)   T = 30 hours and Q's hourly wage is 480/30= 
480/30 = 16
$16   P's hourly wage is 480/(T-10)= $24 which is $8 per hour more.   The answer is $8.
Answer: B
A semicircular shaped window has diameter of 63cm. Its perimeter equals	Pick.
A) 162  B) 766  C) 298  D) 277  E) 198

Solution: Explanation:   perimeter of window = {\color{Blue} \Pi }r+2r   = [{(22/7) * (63/2)} +63]   = 99+63= 
99+63 = 162
162 cm   162nswer: 162) 162
Answer: A
Among 700people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam? Choose the most appropriate option: A) 20 B) 60 C) 80 D) 186 E) 210

Solution: 56%+44%-30%=70% who like either Strawberry, Apple, or both.   That means 100%-70% 56 +44 -30= 
56 +44 -30 = 70
70% who like either Strawberry, Apple, or both.   That means 100%-70% = 30% do not like either Apple of Strawberry jam.   30% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any)   210  100 -70= 
  100 -70 = 30
30% do not like either Apple of Strawberry jam.   30% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any)   210
Answer: E
Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 0.5. What value is exactly 2 standard deviations less than the mean?  Choose the correct answer
A) 10.5  B) 11  C) 11.5  D) 12  E) 12.5

Solution: The value which is exactly two SD below the mean is: mean-2*SD=13.5-2*0.5=12.5.   Answer: 12.5.
Answer: E
The average age of the mother and her six children is 10 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?  Choose the correct choice from the following answers:
A) 40
B) 41
C) 42
D) 43
E) 44

Solution: Total age of mother and 6 children = avg x n = 10 x (6+1)= 70   If mother is excluded new average is  (10 - 5)= 
 (10 - 5) = 5
5   so for 6 children= 6 x 5 =30   so mother's age is  70 - 30= 
 70 - 30 = 40
40   40nswer: Option 40
Answer: A
Today Jim is four times as old as Fred, and Sam is 2 years younger than Fred. Four years ago Jim was 9 times as old as Sam. How old is Jim now? Choose the correct choice
A) 8
B) 12
C) 16
D) 20
E) 40

Solution: We're asked how old Jim is NOW. We're given three facts to work with:   1) Today, Jim is 4 times as old as Fred   2) Today, Sam is 2 years younger than Fred   3) Four years ago, Jim was 9 times as old as Sam.   let's TEST Answer E: 40   IF....Jim is currently 40 years old....   Fred is 10 years old   Sam is 8 years old   4 years ago, Jim was 36 and Sam was 4, so Jim WAS 9 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer.   40
Answer: E
The positive two-digit integers m and n have the same digits, but in reverse order. Which of the following must be a factor of m + n?  Choose the correct choice from the following.
A) 33  B) 9  C) 10  D) 12  E) 14

Solution: Remember: When you take the difference between the two, it will always be 9. e.g 23-32=9, 89-98=9   and when you add both integers, the sum will always be a multiple of 11 e.g 23+32=55, 89+98= 187   33 is multiple of 11.   33nswer : 33
Answer: A
If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is?	Choose the correct choice from the following options:	A) 281	B) 125	C) 288	D) 266	E) 121

Solution: D = 90 * 5/18 * 5= 
90 * 5/18 * 5 = 125
125 m   Answer: 125
Answer: B
Aish started a business investing Rs. 25,000 in 2010, In 2011, he invested an additional amount of Rs. 10,000 and Roshan joined him with an amount of Rs. 35,000. In 2012, Aish invested another additional amount of Rs. 10,000 and Atul joined them with an amount of Rs. 35,000. What will be Roshan’s share in the profit of Rs. 1,50,000 earned at the end of 3 years from the start of the business in 2010? Options:
A) Rs.45000 B) Rs.50000 C) Rs.60000 D) Rs.70000 E) None of these

Solution: Explanation :   Aish : Roshan : Atul   = (25000 x 12 + 35000 x 12 + 45000 x 12) : (35000 x 24) : (35000 x 12)   = 1260000 : 840000 : 420000 = 3 : 2 : 1   Roshan's share = Rs. 150000 x 2/6   = Rs. 50000.   Answer : Rs.50000
Answer: B
Find the sum of all odd numbers upto 100.  Choices:  A) 200  B) 1000  C) 2500  D) 3140  E) 3200

Solution: Sol. The given numbers are 1, 3, 5, 7, ..., 99.   This is an A.P. with a = 1 and d = 2.   Let it contain n terms. Then,   1 + (n - 1) x 2 = 99 or n = 50.   Required sum = (n/2) (first term + last term)   = 50(1 + 99)/2 = 2500.   ANSWER 2500 2500
Answer: C
How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?
Choose the correct choice from the following answers: A) 16.6 B) 16.0 C) 16.3 D) 16.8 E) 16.1

Solution: 16.8 = 110 + 170= 
110 + 170 = 280
280 m   S= 60 * 5/18 = 50/3   T = 280 * 3/50= 
280 * 3/50 = 84/5 = around 16.8
16.8 sec   Answer: 16.8
Answer: D
The area of sector of a circle whose radius is 12 metro and whose angle at the center is 40° is?  Select the correct option
A) 53m2
B) 51m2
C) 50.2m2
D) 45m2
E) 40m2

Solution: 40/360 * 22/7 * 12 * 12   = 50.2 m2   Answer:50.2m2
Answer: C
If the average (arithmetic mean) of the four numbers K, 2K + 3, 4K – 4 and 5K + 1 is 63, what is the value of K?  Choose the correct choice from the following answers:
A) 11
B) 15 3/4
C) 21
D) 23
E) 25 3/10

Solution: K + 2K +3 + 4K - 4 + 5K +1 = 12K   (12K)/4 = 63   12K = 63 * 4= 
63 * 4 = 252
252   K= 252 / 12= 
252 / 12 = 21
21   Answer 21.
Answer: C
The average amount with a group of seven numbers is Rs. 30. If the newly joined member has Rs. 75 with him, what was the average amount with the group before his joining the group?  Choose the correct answer.
A) s. 25.6 B) s. 45/2 C) s. 16.6 D) s. 26 E) s. 25/2

Solution: Total members in the group = 7   Average amount = Rs. 30   Total amount with them = 7 * 30 = Rs. 210   One number has Rs. 50. So, the amount with remaining 6 people = 210 - 75 = Rs. 135   The average amount with them = 135/6 = Rs. 45/2   ANSWER:s. 45/2
Answer: B
With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 3 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?
Choose one
A) 360 km B) 480 km C) 278 km D) 297 km E) 671 km

Solution: Let the distance be x km. Then,   x/(7 1/2) - x/8 = 3   2x/15 - x/8 = 3 => x = 360 km.   360 kmnswer:360 km
Answer: A
The sum of the first 50 positive even integers is 2,550. What is the sum of the odd integers from 101 to 200, inclusive?	Choose the most appropriate option:
A) 5,050
B) 7,500
C) 10,500
D) 15,000
E) 19,600

Solution: 101+103+.......199   If we remove 100 from each of these it will be sum of 1st 100 odd numbers.   so 101+103+.......199 = 50 * 100 + (1+3+5+7+......)   sum of 1st 100 natural numbers = (100 * 101) / 2= 
(100 * 101) / 2 = 5_050
5050   Sum of 1st 50 positive even integers= 2550   sum of 1st 100 odd numbers = 5050 - 2550= 
5050 - 2550 = 2_500
2500   so 101+103+.......199= 50 * 100 + (1+3+5+7+......) = 5000 + 2500= 
5000 + 2500 = 7_500
7500   7,500 is the answer.
Answer: B
The measures of angles A, B and C of a triangle are in the ratio 3:4:5. What is the measure, in degrees, of the largest angle?	Choose the most appropriate option:  A) 35°  B) 65°  C) 85°  D) 75°  E) 55°

Solution: Let the sizes of angles A, B and C be written as follows   A = 3 x, B = 4 x and C = 5 x , where x is a common factor.   The sum of all three angles is equal to 180°. hence   3 x + 4 x + 5 x = 180°   Solve the above equation for x   x = 15   The size of the largest angle is equal to   5 x = 5 * 15= 
5 * 15 = 75
75°   correct answer 75°
Answer: D
X does a work in 30 days. Y does the same work in 45 days. In how many days they together will do the same work?	Choose the correct choice from the following choices.
A) 18 B) 12 C) 20 D) 30 E) 15

Solution: X's 1day's work= 1/30   Y's 1 day's work=1/45   (X+Y)'s 1day's work= (1/30+1/45)=1/18   both together will finish the work in 18 days.   correct option is 18
Answer: A
The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers
Pick
A) 7 B) 8 C) 6 D) 4 E) 2

Solution: Explanation:   Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.   Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61.   or 5x + 20 = 305 or x = 57.   So, required difference = (57 + 8) - 57= 
(57 + 8) - 57 = 8
8   Answer: 8
Answer: B
The amount of time that three people worked on a special project was in the ratio of 1 to 2 to 3. If the project took 120 hours, how many more hours did the hardest working person work than the person who worked the least?
Choose the correct choice from the following answers:
A) 35 hours  B) 40 hours  C) 36 hours  D) 38 hours  E) 42 hours

Solution: Let the persons be A, B, C.   Hours worked:   A = 1*120/6= 
1*120/6 = 20
20 hours   B= 2*120/6= 
2*120/6 = 40
40 hours   C= 3*120/6= 
3*120/6 = 60
60 hours   C is the hardest worker and A worked for the least number of hours. So the difference is  60-20= 
 60-20 = 40
40 hours.   Answer : 40 hours
Answer: B
The simple interest in 14 months on a certain sum at the rate of 6 per cent per annum is 250 more than the interest on the same sum at the rate of 8 per cent in 8 months. How much amount was borrowed?
Select:
A) 15000	B) 25000	C) 7500	D) 14500	E) None of these

Solution: Let the amount be x.   From the question, x×14×6/1200−x×8×8/1200=250   ∴ x = 15000   15000nswer 15000
Answer: A
The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area W of that hemisphere? Choose one:
A) 6/π
B) 9/π
C) 6
D) 9
E) 12

Solution: Given Area of the base of a hemisphere is 3 = PI * R^2   Thus R = Sqrt ( 3 / PI ) .   Surface area of whole sphere = 4*PI*R^2 .   = 4 * PI * 3 / PI   = 12 .   Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2= 
12 / 2 = 6
6 ( curved part , not including the flat rounded base ) .   But the total surface area= 6 + Area of the base of a hemisphere .   = 6 + 3= 
6 + 3 = 9
9.   Answer is 9 !!
Answer: D
If P is a prime number greater than 3, find the remainder when P^2 + 12 is divided by 12.  Choose the correct choice from the following options:
A) 6 B) 1 C) 0 D) 8 E) 7

Solution: Every prime number greater than 3 can be written 6N+1 or 6N-1.   If P = 6N+1, then P^2 + 13 = 36N^2 + 12N + 1 + 12 = 36N^2 + 12N + 12 + 1   If P = 6N-1, then P^2 + 13 = 36N^2 - 12N + 1 + 12 = 36N^2 - 12N + 12 + 1   When divided by 12, it must leave a remainder of 1.   The answer is 1.
Answer: B
A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, his speed (in km/hr) must be :
Select:
A) 7 km/hr
B) 8 km/hr
C) 11 km/hr
D) 12 km/hr
E) None of these

Solution: Sol.   Remaing distance = 3 km and   Remaining time = [1/3 * 45= 
1/3 * 45 = 15
15 min= 1/4 hour.   ∴ Required speed = (3*4) km/hr = 12 km/hr.   Answer 12 km/hr
Answer: D
Two members of a certain club are selected to speak at the next club meeting. If there are 78 different possible selections of the 2 club members, how many members does the club have?	Choose the correct choice from the following options
A) 5	B) 6	C) 7	D) 8	E) 13

Solution: Method-1   Total No. of Selection of r out of n objects are defined by nCr = n! / [(r!)(n-r)!]   i.e. If total member = n   then nC2 = n! / [(2!)(n-2)!] = 78   i.e. n*(n-1)*n-2!/ [(2!)n-2!] = 78   i.e. n*(n-1) = 156   (for Positive Values of n)   therefore, n*(n-1) = 156   i.e. n= 13   Answer: Option 13
Answer: E
A present value of a machine is $128000. Its value depletiation rate is 25% per annum then find the machine value after 3 years  Choose the correct answer:
A) A)$48000 B) B)$54000 C) C)$36520 D) D)$32450 E) E)$42500

Solution: P= $128000   R = 25%   T = 3 years   Machine value after 3years = P/(1-R/100)^T   =128000*3/4 * 3/4 * 3/4= 
128000*3/4 * 3/4 * 3/4 = 54_000
$54000   Answer is $54000
Answer: B
There are 18 balls in a box: 10 balls are green, 6 are blue and 2 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a blue ball is selected at random from the box?
Options:
A) 5/16
B) 4/13
C) 3/13
D) 5/13
E) 6/13

Solution: If 1 green and 1 blue ball are taken from the box, then there are 9 green, 5 blue and 2 white balls, a total of 16 balls. If one ball is selected at random, the probability that it is blue is given by 5 / 16   5/16nswer : 5/16
Answer: A
A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?	Options
A) 3:4:8	B) 3:4:7	C) 3:4:5	D) 3:4:1	E) 3:4:0

Solution: A:3:4:7:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)   = 144:192:336 = 3:4:7   Answer: 3:4:7
Answer: B
In how many ways can three boys can be seated on five chairs? Select the correct option:
A) 72 B) 28 C) 60 D) 58 E) 39

Solution: There are three boys.   The first boy can sit in any of the five chairs (5 ways).   5   Now there are 4 chairs remaining. The second boy can sit in any of the four chairs (4 ways).   5	4   Now there are 3 chairs remaining. The third boy can sit in any of the three chairs (3 ways).   5	4	3   Hence, total number of ways in which 3 boys can be seated on 5 chairs   =5×4×3=60   Ans: 60
Answer: C
How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?
Select:	A) 99	B) 88	C) 77	D) 665	E) 41

Solution: 30 * 33/2 = 5/2 * 2 * x => x = 99   99nswer:99
Answer: A
Tough and Tricky questions: Number Properties.
What is the smallest positive integer x such that 320x is the cube of a positive integer? Choose the correct choice from the following
A) 2	B) 3	C) 5	D) 15	E) 25

Solution: We want to know the smallest x that will make 320x a CUBE of some number. Let's call that number y.   Let's first figure out what we're working with. The prime factorization of 320 can be visualized:   ...........320   ......../.......\   ......32.......10   ...../..\....../...\   ...8.....4...2.....5   .../.\ ../.\   ..4..2 2..2   ./.\   2..2   So, we have 2 * 2 * 2 * 2 * 2 * 2* 5 that can be multiplied together to get 320. Now we need to figure out what we need to make 320 * x into a cube of y (y^3=320*x).   We have six 2s, and one 5. To arrange these numbers in identical triples (2,2,5), we need at least two more 5s. Each of these triples will give us the value of y (2*2*5=20), which, multiplied by itself three times, gives us 320 * x.   Looking at the factors we need to complete the triples, we get   5 * 5= 
  5 * 5 = 25
25. We know this is the smallest number possible because prime factors by definition cannot be broken down any further.   Therefore, we can go with answer choice E.   If time permits, we can do a sanity check. We calculated that y should be 2 * 2 * 5, or 20. 20 * 20 * 20= 8000. Also, 320 * 25 = 8000.   Answer: 25
Answer: E
What is the sum of the integers from -150 to 155, inclusive?	Choose the correct choice:	A) 865	B) 955	C) 1050	D) 765	E) 750

Solution: In an arithmetic progression,   the nth term is given by tn=a+(n-1)d   here tn=155, a=-150, d=1   hence, 155=-150+(n-1)   or n=306   Sum of n terms can be calculated by sn=n/2(a+l)   a=first term, l=last term, n=no. of terms   sn=306*(-150+155)/2   sn=306*5/2= 
306*5/2 = 765
765   Answer : 765
Answer: D
The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum? Choose the correct choice from the following choices:
A) 13518
B) 13519
C) 13527
D) 13500
E) 13521

Solution: P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)]   P = 13500   Answer: 13500
Answer: D
. A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
Answers.
A) 338 B) 2767 C) 1023 D) 1877 E) 1722

Solution: Explanation:   Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.   Hence, the required number of ways = 45 - 1.   = 210 - 1 = 1024 - 1= 
1024 - 1 = 1_023
1023   Answer:1023
Answer: C
Tough and Tricky questions: Word Problems.
It takes Sarah 44 minutes to do one oil change, and it takes Alice 20 minutes. If Sarah and Alice both begin doing oil changes at exactly 9:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously?
Choose the correct choice from the following answers:
A) 10:00 a.m. B) 10:42 a.m. C) 12:00 a.m. D) 12:40 p.m. E) 2:00 p.m.

Solution: LCM of 2044   20 = 2 * 2 * 5   44 = 2 * 2 * 11   LCM = 2 * 2 * 5 * 11= 
2 * 2 * 5 * 11 = 220
220= 3 hour 40 minutes   1240PM   12:40 p.m.
Answer: D
A lady grows Broccoli in her garden that is in the shape of a square. Each Broccoli takes 1 square foot of area in her garden. This year, she has increased her output by 79 Broccoli when compared to last year. The shape of the area used for growing the Broccoli has remained a square in both these years. How many Broccoli did she produce this year?  Choose the correct choice:  A) 1600  B) 1500  C) 1650  D) 1700  E) Cannot be determined

Solution: Explanatory Answer   The shape of the area used for growing Broccoli has remained a square in both the years.   Let the side of the square area used for growing Broccoli 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 Broccoli last year be Y ft.   Therefore, the area of the ground used for cultivation last year = Y2 sq.ft.   As the number of Broccoli grown has increased by 79, the area would have increased by 79 sq ft because each Broccoli takes 1 sq ft space.   Hence, X2 - Y2 = 79   (X + Y)(X - Y) = 79.   79 is a prime number and hence it will have only two factors. i.e., 79 and 1.   Therefore, 79 can be expressed as product of 2 numbers in only way = 79 * 1   i.e., (X + Y)(X - Y) = 79 * 1   So, (X + Y) should be 79 and (X - Y) should be 1.   Solving the two equations we get X = 40 and Y = 39.   Therefore, number of Broccoli produced this year = X2 = 402 = 1600.   Alternative Approach : Use answer choices   The area in both the years are squares of two numbers.   That rules out choice B,C and D. as 1500,1650 and 1700 are not the square of any number.   Check Choice A: If this year's produce is 1600, last year's produce would have been  1600 - 79= 
 1600 - 79 = 1_521
1521   1521 is the square of 39.   So, 1600 is the answer.   Choice 1600
Answer: A