MU-NLPC/Calc-aqua_rat huggingface dataset:
If the sides of a triangle are 30 cm, 40 cm and 50 cm, what is its area?	Pick one
A) 400	B) 500	C) 550	D) 600	E) 700

Solution: The triangle with sides 30 cm, 40 cm and 50 cm is right angled, where the hypotenuse is 50 cm.   Area of the triangle = 1/2 * 40 * 30= 
1/2 * 40 * 30 = 600
600 cm2   Answer: Option 600
Answer: D
From (1, 2, 3, 4, 5, 6), one number is picked out and replaced and one number is picked out again. If the sum of the 2 numbers is 10, what is the probability that the 2 numbers included the number 5?  Pick one
A) 1/5  B) 2/5  C) 3/10  D) 3/5  E) 1/3

Solution: We know that the sum of two numbers picked was 10. So, there could be the following cases:   (4, 6);   (6, 4);   (5, 5);   Total of 3 cases out of which 1 have 5, thus the probability is 1/3.   Ans 1/3
Answer: E
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 50 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options
A) 12 sec B) 24 sec C) 45 sec D) 60 sec E) 62 sec

Solution: Relative speed = 50 + 30= 
50 + 30 = 80
80 km/hr.   80 * 5/18= 200/9 m/sec.   Distance covered = 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 * 9/200= 
1000 * 9/200 = 45
45 sec.   ANSWER:45 sec
Answer: C
The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.9 the sixth number is?
Choose the correct choice from the following options.
A) 11.4 B) 14.5 C) 11.8 D) 11.5 E) 11.1

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 * 11.9= 
6 * 11.9 = 71.4
71.4   63 + 71.4= 
63 + 71.4 = 134.4
134.4 – 119.9= 14.5   6th number = 11.5   Answer: 14.5
Answer: B
F is a positive integer and 225 and 216 are both divisors of F. If F=(2^a)*(3^b)*(5^c), where a, b and c are positive integers, what is the least possible value of a+ b+ c?  Choices
A) 4 B) 5 C) 8 D) 7 E) 6

Solution: Lets make factorization of 225 and 216 ..   225 = 5 X 5 X 3 X 3 X 3   216 = 2 X 2 X 2 X 3 X 3 X 3   F would have to have 3 two's , 225 has 3 threes and and so does 216 but they can be the same three threes so we count them only once ... 225 has 2 fives ... So we had them together and we get 3 + 3 + 2= 
3 + 3 + 2 = 8
8(8) (answer) ...
Answer: C
Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day S on which the buses leave at the same time. Pick one:
A) S=Tuesday B) Wednesday C) Thursday D) Sunday E) S=The busses will never leave at the same time

Solution: The answer is E.   I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide.   Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.S=The busses will never leave at the same time
Answer: E
The average length of 6 snakes is 80 cm. If the average length of one third of the snakes is 70 cm, what is the average of the other snakes? Choose the correct option:
A) 75.
B) 85.
C) 90
D) 94
E) 100

Solution: Given ( X1 + X2 ... + X6 ) / 6 = 80   ( X1 + X2 ... + X6 ) = 480 --> Eq 1.   Now given avg length of one third snakes is 70. That means out  6 / 3= 
 6 / 3 = 2
2 snakes.   let the avg length of two snakes be ( X1 + X2 ) / 2= 70 .   ( X1 + X2 ) = 140. --> eq 2.   Now we are asked to find the average of the remaining i.e. ( X3 + X4 + X5 + X6 )   Substitute eq 2 in eq 1 then we get   140 + X3 + X4 + X5 + X6 = 480   => X3 + X4 + X5 + X6 = 340   Now divide 340 by 4 we get 85.   => ( X3 + X4 + X5 + X6) / 4 = 85 = avg length of remaining snakes.   Answer: correct option is 85..
Answer: B
Find the third proportional to 9 and 12?  Choose the most appropriate option:
A) 10  B) 12  C) 16  D) 19  E) 20

Solution: Formula = Third proportional = (b × b)/a   A = 9 and B = 12   (12 × 12)/ 9 = 144/9= 
144/9 = 16
16   16
Answer: C
What is the place value of 2 in the numeral 52468? Select:
A) 200
B) 2
C) 200
D) 20
E) 2000

Solution: place value of 2 = 2 * 2000 = 2000   Answer is 2000
Answer: E
A man sitting in a train which is travelling at 64 kmph observes that a goods train travelling in a opposite direction, takes 18seconds to pass him. If the goods train is 420 m long, find its speed. Choose the correct choice from the following options.
A) 32  B) 15  C) 18  D) 20  E) 25

Solution: Relative speed = (420/18)m/s = (420/18)*(18/5)= 
(420/18)*(18/5) = 84
84 kmph   speed of goods train= 84-64= 
84-64 = 20
20 kmph   Answer is 20
Answer: D
A train 1500 m long can cross an electric pole in 50 sec and then find the speed of the train? Choose the correct choice from the following answers.
A) 106
B) 107
C) 108
D) 109
E) 110

Solution: Length = Speed * time   Speed = L/T   S = 1500/50= 
1500/50 = 30
30 M/Sec   Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 108 Kmph   Answer:108
Answer: C
A triangle has a perimeter 13. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?
Choose the correct answer.
A) 3
B) 6
C) 7
D) 9
E) 8

Solution: Explanation:   The measure of the third side of a triangle must lie between the sum and the difference of the other two sides. Using this fact along with the answer choices, we can eliminate the wrong answers.   cannot be correct because 4 would not be the longest side.(sides 4, 5, and 4)   could be correct because the other two sides would be 3 and 4.   cannot be correct because this third side would be greater than the sum of the other two sides.   Answer: 6) 6
Answer: B
Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 300 milliliters of solution X to create a solution that is 25 percent alcohol by volume?	Select the correct option
A) 250/3  B) 500/3  C) 900  D) 480  E) 600

Solution: we know that X is 10% , Y is 30% and W.Avg = 25% . what does this mean with respect to W.Avg technique ?   W.Avg is 1 portion away from Y and 3 portion away from X so for every 1 portion of X we will have to add 3 portions of Y.   If X = 300 then Y = 900   ANSWER:900
Answer: C
A mixture of 85 kg contains milk and water in the ratio 27 : 7. How much more water is to be added to
get a new mixture containing milk and water in the ratio 3:1?  Choose the correct choice from the following answers
A) 5 kg  B) 6.5 kg  C) 7.5 kg  D) 8 kg  E) 9 kg

Solution: Explanation :   Expl : Milk in 85 kg of mix = 85* (27/34) = 135/2 kg.   Water in it = 85-135/2 = 35/2 kg.   Let x kg of water be added to it.   Then, (135/2)/(35/2 + x) = 3/1; 135/(35 +2x) = 3/1;   105 + 6x = 135 ; 6x = 30; x = 5   The quantity of water to be added = 5 kg   5 kgnswer :5 kg
Answer: A
I chose a number and divide it by 5. Then I subtracted 154 from the result and got 6. What was the number I chose? Answers:	A) 200	B) 800	C) 400	D) 500	E) 100

Solution: Let x be the number I chose, then   x/5−154=6   x/5=160   x=800   Answer is 800.
Answer: B
A certain company reported that the revenue on sales increased 40 % from 2000 to 2003, and increased 70 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005?
Choose the correct option:
A) 50 %  B) 40 %  C) 35 %  D) 32 %  E) 21 %

Solution: Assume the revenue in 2000 to be 100. Then in 2003 it would be 140 and and in 2005 170, so from 2003 to 2005 it increased by (170-140)/140=30/140=~21%.   Answer: 21 %.
Answer: E
If (n+2)!/n!=72, n=? Answers:
A) 7	B) 9	C) 10	D) 11	E) 12

Solution: (n+2)!/n!= 72   Rewrite as:[(n+2)(n+1)(n)(n-1)(n-2)....(3)(2)(1)]/[(n)(n-1)(n-2)....(3)(2)(1)]= 132   Cancel out terms: (n+2)(n+1) = 72   From here, we might just TEST the answer choices.   Since (9)(8) = 72, we can see that n = 7   7
Answer: A
How many integers are between 4 and 88/9, inclusive? Options:
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: 88/9 = 9.xx   We are not concerned about the exact value of 88/9 as we just need the integers.   The different integers between 4 and 88/9 would be 4, 5, 6, 7, 8, 9   Total number of integers = 6   Option 6
Answer: D
The sum of the two numbers is 14 and their product is 35. What is the sum of the reciprocals of these numbers?  Choose the correct choice from the following answers
A) 12/35
B) 14/35
C) 35/8
D) 7/32
E) None of these

Solution: Let the numbers be a and b. Then, a+b=14 and ab =35.   a+b/ab=14/35; (1/b+1/a)=14/35   Sum of reciprocals of given numbers=14/35.   Correct Option: 14/35
Answer: B
What is the probability of rolling the same number exactly three times with five six-sided dice? Options
A) 1/5
B) 5/18
C) 35/216
D) 125/648
E) 225/1296

Solution: Explanations:   1. Rolling any number on a dice three times in a row is equal to the number of throws {{1/6}^3}*6 = 1/36, where 3 represents the number of throws and 6 is the number of different ways to get three of the same number (e.g. 1, 1, 1 2, 2, 2 3, 3, 3…).   Next we have to use the combinations formula to determine how many ways three out of five can be the same. {5!}/{3!*2!}=10. We want to multiply this number to {1/36}*10=10/36   We are not finished yet – there is one little twist to the problem. The question says “exactly three times.” Meaning we have to discount all the instances in which we roll the same number four times and those instance in which we roll the same number five times.   One way to do so is by multiplying by the probability that the fourth and fifth dice will NOT land on the same number as the three dice. Because there are five other possibilities on dice that will not compromise “exactly three numbers” we can multiply by {5/6{*{5/6}=25/36   Finally this gives us {10/36}*{25/36}={125/648}   Answer 125/648
Answer: D
David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 11 family members in a row for the picture?	Answers.
A) 12!
B) 10×9!
C) 9×10!
D) 11!/2!
E) 11!

Solution: The number of ways to arrange 11 people is 11!   We need to subtract the arrangements when these two people are together.   Let's think of these two people as a single unit so there are 10 units.   The number of ways to arrange 10 units is 10!   We need to multiply this by 2 since these two people could switch places.   The total number of valid arrangements is 11! - 2*10! = 10!*(11-2) = 9x10!   The answer is 9×10!.
Answer: C
If a light flashes every 10 seconds, how many times will it flash in 2/3 of an hour?	Options.
A) 152	B) 241	C) 345	D) 451	E) 542

Solution: There are 60 minutes in an hour.   In 2/3 of an hour there are  (60 * 2/3)= 
 (60 * 2/3) = 40
40minutes.   In 2/3 of an hour there are  (60 * 40)= 
 (60 * 40) = 2_400
2400 seconds.   Light flashed for every 10 seconds.   In 2400 seconds 2400/10= 
2400/10 = 240
240 times.   The count start after the first flash, the light will flashes 241 times in 2/3 of an hour.   Answer:241
Answer: B
You have 7 sticks of lengths 10, 20, 30, 40, 50, 60 and 70 centimeters. The number of non-congruent triangles that can be formed by choosing three of the sticks to make the sides is Choose the correct choice
A) 3
B) 6
C) 7
D) 10
E) 13

Solution: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.   Based on this there can be only 13 triangles formed: (20, 30, 40), (20, 40, 50), (20, 50, 60), (30, 40, 50), (30, 40, 60), (30, 50, 60), (40, 50, 60), (50, 60, 70), (40,60, 70), (30,60, 70), (20,60, 70). (30, 50, 70), (40, 50,70)   Answer; 13.
Answer: E
Let the number which when multiplied by 11 is increased by 300. Choose the correct choice from the following answers:
A) 14  B) 20  C) 26  D) 28  E) 30

Solution: Solution   Let the number be x .   Then, 11x - x = 300   ‹=›10x = 300   x ‹=› 30.   Answer 30
Answer: E
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is: Select.
A) 1 : 3  B) 3 : 2  C) 3 : 4  D) 2 : 1  E) None of these

Solution: Let the speeds of the two trains be S1 m/sec and S2 m/sec respectively. Then, length of the first train = 27S1 metres, and length of the second train = 17S2 metres.   ∴ 27S1+17S2/S1+S2=23 ⇒ 27S1 + 17S2 = 23S1 + 23S2   ⇒ 4S1 = 6S2 ⇒ S1⁄S2 = 3⁄2   Answer 3 : 2
Answer: B
Solve:-
444 x 444 x 444 + 555 x 555 x 555 = ?(444 x 444 - 444 x 555 + 555 x 555)  Options
A) 888 B) 333 C) 999 D) 988 E) 889

Solution: Given Exp. = (a3 + b3) = (a + b) = (444 + 555)= 
(444 + 555) = 999
999(a2 - ab + b2)   Answer 999
Answer: C
If n is a 45-digit positive integer, all of whose digits are the same, which of the following must be true?
I. n is divisible by 3
II. n is divisible by 9
III. n is divisible by 5
IV n is divisible by 45
Choose the correct option:  A) I only  B) I and II only  C) I and III only  D) I .II, III and IV only  E) I, II and III

Solution: Rule for divisibility by 3: The sum of the digits of the number should be multiple of 3   Rule for divisibility by 9: The sum of the nos digits of the number should be divisible by 9 or the number should be divisible by 3 two times.   Rule for divisibility by 5: The sum of the digits of the number should be multiple of 5   Rules for divisibility by 45: The sum of the digits should a multiple of 45   Consider no 11111111...45 times = The sum 45*1= 
45*1 = 45
45----> divisbible by 3,9,5 and 45   consider number to be 222....45 times, then sum of the no. 45*2=90 divisibly by 3,9,5 and 45   So why so because when you sum the numbers either you can add the digits 45 times or multiply the digit *45..   Note that since 45 is divisble by 27,9 ,5 and 3 and thus the sum of the nos will be divisible by all the nos.   Ans is I .II, III and IV only
Answer: D
How many different words beginning with O and ending with E can be formed with the letters of the word ORDINATE, so that the words are beginning with O and ending with E?  Select the correct option:  A) 8!  B) 6!  C) 7!  D) 7!/2!  E) None of these

Solution: Solution   6! ways, O fixed 1st and E fixed in last. Answer 6!
Answer: B
What is the average (arithmetic mean) of the numbers 16, 17, 17, 18, 19, 19 and 20?	Choose the correct option
A) 18 B) 17 C) 16 D) 15 E) 19

Solution: {16, 17, 17, 18, 19, 19, 20}={18-2,18-1,18-1, 18, 18+1, 18+1,18+2} --> the average = 18.   18nswer: 18.
Answer: A
Using all the letters of the word "NIA", how many words can be formed, which begin with N and end with A?  Choices.
A) 8  B) 6  C) 9  D) 3  E) 1

Solution: There are five letters in the given word.   Consider 3 blanks ....   The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 1! ways.   The number of words = 1! = 1.   Answer:1
Answer: E
Joe is painting a rectangular room whose dimensions are given by a, b and c meters. Joe takes 4 hours to paint a wall with dimensions a and c. He takes 2 hours to paint a wall with dimensions b and c and 6 hours to paint the ceiling with dimensions a and b. If Joe works at a constant rate and a = 6, then what is the volume of the room?  Choices:
A) 18 cubic meters B) 24 cubic meters C) 36 cubic meters D) 30 cubic meters E) It can’t be determined.

Solution: Time to paint each wall as given in problem:   A36 cubic meters = 4 hours   B36 cubic meters = 2 hours   AB = 6 hours   Since he works at constant rate and it takes him twice as long to paint A36 cubic meters compared to B36 cubic meters   A36 cubic meters=2B36 cubic meters   Plug in 6 for A and you find that B=3   Since painting AB takes 3 times as long compared to B36 cubic meters,   AB=3B36 cubic meters   Plug in 6 for A and 3 for B and you find that 36 cubic meters=2   A*B*36 cubic meters=6*3*2= 
6*3*2 = 36
36 cubic meters   Answer: 36 cubic meters
Answer: C
In how many years will the benefit Janet receives from her work double given that she receives a simple interest of 10% per annum on the initial agreed paid benefit.
Choose the correct answer
A) 15
B) 10
C) 5
D) 12
E) 20

Solution: P = (P*10*R)/100   100P = P*10*R   100 = 10R   Therefore R = 10 Years   10 = 10
Answer: B
If C is the temperature in degrees Celsins and F is the temperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C=5(F-32). In two sets of experiment, the temperature recorded for a chemical reaction to complete differed by 40 degrees on the Fahrenheit scale, by how many degrees did the temperature extremes differ on the Celsius scale? Pick one:
A) a) 65/9	B) b) 13	C) c) 22	D) d) 45	E) e) 81

Solution: The relationship is 9/5 - 32, so approximately half of difference in Celsius (the -32 part won't be used in this case).   Just looking at the answer choices you can pick C which is the only number near half of 40. The other answer choices are too far apart so no need to calculate.
Answer: C
Reena took a loan of 1400 with simple interest for as many years as the rate of interest. If she paid 224 as interest at the end of the loan period, what was the rate of interest?	Choose the correct choice:
A) 3.6	B) 4	C) 14	D) Cannot be determined	E) None

Solution: Explanation: Let rate = R% and time = R years.   Then, (1400 x R x R)/100 = 224   14RÂ² = 224   RÂ² = 16   R = 4.   Answer: Option 4
Answer: B
How many times do the hands of a clock coincide in a day? Choose the correct answer:
A) 33	B) 77	C) 22	D) 23	E) 21

Solution: The hands of a clock coincide 11 times in every 12 hours   (Since between 11 and 1, they coincide only once,   i.e. at 12 o'clock).   ==> The hands coincide 22 times in a day.   Answer: Option '22'
Answer: C
How many bricks, each measuring 40 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
Choices.
A) 1400  B) 2400  C) 4000  D) 7000  E) 3400

Solution: Number of bricks = Volume Of the wall / Volume of 1 brick = (800 x 600 x 22.5) / (40 x 11.25 x 6) = 4000   ANSWER:4000
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 option:
A) 4.5 hrs B) 5 hrs C) 6.5 hrs D) 7.2 hrs E) None

Solution: Solution   Net part filled in 1 hour	= (1/4 - 1/9)   = 5/36.   Therefore,the cistern will be filled in 36/5 hrs i.e, 7.2 hrs.   Answer 7.2 hrs
Answer: D
Nine men went to a hotel. Eight of them spent Rs.3 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?
A. Rs.29.25 Choose the correct choice from the following answers.
A) 29.25 B) 29.28 C) 29.27 D) 29.22 E) 29.21

Solution: 29.25verage of 9 = x   9x = 8 * 3 + x * 2 x = 3.25   Total = 9 * 3.25 = 29.25.29.25nswer: 29.25
Answer: A
On a magical-intellectual land of gpuzzles , all the animal are rational(real smart).
There are six leopards and one sheep.
Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s).
If we leave them for some time then how many sheep and leopard will be there , when we come back ?	Choose the correct choice from the following choices:
A) 8 leopard and 1 sheep B) 3 leopard and 3 sheep C) 6 leopard and 2 sheep D) 5 leopard and 1 sheep E) 3 leopard and 3 sheep

Solution: 5 leopard and 1 sheep   5 leopard and one sheep   since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.
Answer: D
There are 6 people in the elevator. Their average weight is 160 lbs. Another person enters the elevator, and increases the average weight to 151 lbs. What is the weight of the 7th person.	Options:
A) 97
B) 168
C) 189
D) 190
E) 200

Solution: Solution   Average of 7 people after the last one enters = 151 .   âˆ´ Required weight = (7x151)-(6x160)   = 1057- 960= 
1057- 960 = 97
97.   97nswer 97
Answer: A
The guidelines at a certain college specify that for the introductory English class, the professor may choose one of four specified novels, and choose two plays from a list of 5 specified plays. Thus, the reading list for this introductory class has one novel and two plays. How many different reading lists could a professor create within these parameters?	Choices:  A) 15  B) 40  C) 90  D) 150  E) 360

Solution: 4C1*5C2 = 4*10= 
4*10 = 40
40   The answer is 40.
Answer: B
Consider a right triangle AQC with length of sides being x,y and z where y represents the hypotenuse , Which of these represent the radius of the circle which is inscribed in triangle AQC Choose the correct option:
A) [A] x+y+z/3
B) [B] x-y+z/3
C) [C] x-y+z/2
D) [D] (x^2 + y^2 + z^2)/3
E) [E] cannot be determined

Solution: Radius of a circle inscribed in the right triangle AQC r = (x + z - y)/2 where y is the hypotenuse and x and y are other two sides.   Answer: [C] x-y+z/2
Answer: C
If a man buys 20 lollipops for $90 and sold them for $2 dollars determine his loss.
Choose the correct choice from the following answers: A) $20 B) $25 C) $30 D) $45 E) $50

Solution: Cost of 20 lollipops = $90   Sold each lollipop for $2   So he sold 20 lollipops for $(20 × 2) = $40   Loss = $(90 – 40) = $50   Therefore, loss = $ 50   correct answer $50)$50
Answer: E
A charitable association sold an average of 66 raffle tickets per member. Among the female members, the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What was the average number E of tickets sold by the male members of the association	Choose the correct choice from the following choices:
A) 50	B) 56	C) 58	D) 62	E) 66

Solution: Given that, Total average E sold is 66, Male/Female = 1/2 and Female average is 70. Average of Male members isX.   (70*F+X*M)/(M+F) = 66 -> Solving this equation after substituting 2M=F, X = 58. ANS 58.
Answer: C
36 identical chairs must be arranged in rows with the same number of chairs in each row. Each row must contain at least three chairs and there must be at least three rows. A row is parallel to the front of the room. How many different arrangements are possible?	Choose the correct choice from the following answers:
A) 4 B) 2 C) 8 D) 9 E) 5

Solution: Three conditions have to be satisfied.   1. The number of students per row has to be at least 3.   2. Number of row has to be at least 3.   3. Equal number of students has to be seated in a row.   The following arrangements satisfy all 3 conditions.   Arrangement 1: 3 students to a row; 12 rows.   Arrangement 2: 4 students to a row; 9 rows.   Arrangement 3: 6 students to a row; 6 rows.   Arrangement 4: 9 students to a row; 4 rows.   Arrangement 5: 12 students to a row; 3 rows.   You will observe that the number of students in a row is a factor of 36.   So, an alternative and faster approach is to list down factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36.   And then start from 3 and quickly find out if the number of rows is at least 2.   Both the conditions are satisfied for the following factors : 3, 4, 6, 9, and 12. i.e., 5 arrangements.   Ans:5
Answer: E
A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined
by B after 10 days. The number of days taken in completing the wotk were ?	Choose the correct choice from the following answers
A) 1423kmph	B) 1523kmph	C) 1623kmph	D) 1723kmph	E) None of these

Solution: Explanation:   Work done by A in l0 days = (1/25) *10 = 2/5   Remaining work = 1 - (2/5) = 3/5   (A+B)s 1 days work = (1/25) + (1/20) = 9/100   9/100 work is done by them in 1 day   hence 3/5 work will be done by them in (3/5)*(100/9)   = 20/3days.   Total time taken = (10 + 20/3) = 16*(2/3) days   Answer: 1623kmph
Answer: C