MU-NLPC/Calc-aqua_rat huggingface dataset:
Dan can do a job alone in 12 hours. Annie, working alone, can do the same job in just 9 hours. If Dan works alone for 8 hours and then stops, how many hours will it take Annie, working alone, to complete the job? Choose the most appropriate option
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: Dan can complete 1/12 of the job per hour.   In 8 hours, Dan completes 8(1/12) = 2/3 of the job.   Annie can complete 1/9 of the job per hour.   To complete the job, Annie will take 1/3 / 1/9 = 3 hours.   The answer is 3.
Answer: B
The ratio of the radius of two circles is 1: 5, and then the ratio of their areas is?	Choose the correct choice from the following answers:
A) 1:7  B) 2:9  C) 1:25  D) 3:7  E) 3:4

Solution: r1: r2 = 1: 5   Î r1^2: Î r2^2   r1^2: r2^2 = 1:25   Answer: 1:25
Answer: C
10 camels cost as much as 24 horses, 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants. If the cost of 10 elephants is Rs.120000, find the cost of a camel?	Select:  A) s.9800  B) s.3800  C) s.9800  D) s.4800  E) s.6880

Solution: Cost of the camel = P   10 camels = 24 horses   16 horses = 4 oxen   6 oxen = 4 elephants   10 elephants = Rs.120000   P = Rs.[(24 * 4 * 4 * 120000)/(10 * 16 * 6 * 10)]   P = Rs.(46080000/9600) => P = Rs.4800   Answer:s.4800
Answer: D
A certain car uses 12 gallons of gasoline in traveling 360 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car’s gas mileage be increased?  Choose the correct answer:
A) 2
B) 4
C) 6
D) 8
E) 10

Solution: 360/10= 
360/10 = 36
36. The difference is  36 - 30= 
 36 - 30 = 6
6.   Answer 6
Answer: C
In a group of ducks and cows, the total number of legs are 26 more than twice the no. of heads. Find the total no.of buffaloes.
Choices.
A) 11  B) 12  C) 13  D) 16  E) 18

Solution: Let the number of buffaloes be x and the number of ducks be y   => 4x + 2y = 2 (x + y) + 26   => 2x = 26=> x = 13   13
Answer: C
(((13!)^16)-((13!)^8))/(((13!)^8)+((13!)^4))=a
then what is the units digit for a/((13!)^4)=	Pick: A) 7 B) 8 C) 9 D) 6 E) 5

Solution: (((13!)^16)-((13!)^8))/(((13!)^8)+((13!)^4))=a   solving it , we get   a/((13!)^4)= ((13!)^4-1)   last digit of (13!)^4 will be 0.   so last digit of ((13!)^4-1) will be 9.   ANSWER:9
Answer: C
Find the value for x from below equation: x/2=-2?
Select the correct option.
A) -6  B) 1  C) -2  D) -3  E) -4

Solution: 1. Multiply both sides by 2:   x*2/2= -2/2   Simplify both sides:   x = -4   -4
Answer: E
The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:
Select the correct option: A) 1520 m2 B) 2420 m2 C) 2480 m2 D) 2520 m2 E) None of these

Solution: Explanation:   We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103.   Solving the two equations, we get: l = 63 and b = 40.   Area = (l x b) = (63 x 40) m2 = 2520 m2.   Answer: 2520 m2
Answer: D
John and Ingrid pay 30% and 40% tax annually, respectively. If John makes $58000 and Ingrid makes $72000, what is their combined tax rate?  Pick.
A) 32%  B) 34.4%  C) 35%  D) 35.6%  E) 37.4%

Solution: (1) When 30 and 40 has equal weight or weight = 1/2, the answer would be 35.   (2) When 40 has larger weight than 30, the answer would be in between 35 and 40. Unfortunately, we have 2 answer choices D and E that fit that condition so we need to narrow down our range.   (3) Get 72000/130000 = 36/65. 36/65 is a little above 36/72 = 1/2. Thus, our answer is just a little above 35.   Answer: 35.6%
Answer: D
There are 9 executives, including the CEO and CFO, that are asked to form a small team of 4 members. However, the CEO and CFO may not both be assigned to the team. Given this constraint, how many ways are there to form the team?	Pick one:	A) 97	B) 99	C) 101	D) 103	E) 105

Solution: The total number of ways to form a team of 4 is 9C4=126.   We need to subtract the number of teams that have both the CEO and the CFO.   The number of teams with both the CEO and CFO is 7C2=21.   The number of ways to form an acceptable team is  126-21= 
 126-21 = 105
105.   The answer is 105.
Answer: E
If x is divisible by 6 and 5, which of the following must divide evenly into x? I. 64 II. 32 III. 15	Pick one:	A) I only	B) II only	C) III only	D) II,III only	E) none of these

Solution: If x is divisible by 6,5 means it will be = or > 30, 60,90 etc...   That are not divisible by 32, 64.   So, the answer is III only
Answer: C
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is? Choose the correct choice from the following.
A) 65 km/hr
B) 50 km/hr
C) 21 km/hr
D) 25 km/hr
E) 76 km/hr

Solution: Speed of the train relative to man   = (125/10) m/sec   = (25/2) m/sec. [(25/2) * (18/5)] km/hr   = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed   = (x - 5) km/hr. x - 5 = 45 ==> x   = 50 km/hr.   Answer: 50 km/hr
Answer: B
How many numbers between 400 and 1000 can be made with the digits 2,3,4,5,6 and 0?
Choose one
A) 30	B) 60	C) 90	D) 120	E) 150

Solution: Required number = 3 * 5P2 = 3*20= 
3*20 = 60
60   Answer is 60
Answer: B
If there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 40% of the total. What fraction of the total is women who own cars?	Choose the correct choice from the following options
A) 3⁄20
B) 11⁄60
C) 9⁄40
D) 1⁄5
E) 2⁄15

Solution: Consider a group of 200 men and 100 women, a total of 300 people. 40% of them, which is 120, form a group of people who don't own a car.   Half of them are men, and the other half are women, more precisely 60.   It means that there are 100-60= 
100-60 = 40
40 women who own a car, and this represents 40/300= 2/15 of the total.   Answer 2⁄15
Answer: E
The length of a train and that of a platform are equal. If with a speed of 144 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?  Choose the correct choice from the following options: A) 757 B) 758 C) 718 D) 1200 E) 738

Solution: Speed = [144 * 5/18] m/sec = 40 m/sec; Time = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 40 è x = 40 * 60 / 2= 
40 * 60 / 2 = 1_200
1200   Answer:1200
Answer: D
If a boat goes 6km upstream in 36 minutes and the speed of the stream is 4 kmph, then the speed of the boat in still water is ?  Choose one.
A) 10 B) 11 C) 12 D) 13 E) 14

Solution: Rate upsteram =(6/36*60)= 
(6/36*60) = 10
10kmph.   speed of the stream=4kmph let speed in still water be xkm/hr. then speed upstream=(x-4)km/hr. x-4=10==>x=14km/hr Answer(14)
Answer: E
A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train? Choose the correct choice.
A) 118	B) 150	C) 277	D) 250	E) 191

Solution: Speed = 60 * 5/18 = 50/3 m/sec   Length of the train = speed * time = 50/3 * 15= 
50/3 * 15 = 250
250 m   Answer: 250
Answer: D
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.6270.What was his original salary?
Choose the correct option.
A) 6000  B) 2999  C) 1000  D) 2651  E) 1971

Solution: X * (110/100) * (95/100) = 6270   X * (11/10) * (1/100) = 66   X = 6000   6000nswer: 6000
Answer: A
The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:	Choose the correct choice from the following answers:	A) 1%	B) 2%	C) 3%	D) 5%	E) 4%

Solution: D   5%   Increase in 10 years = (262500 - 175000)= 
(262500 - 175000) = 87_500
87500.   Increase%= (87500/175000 x 100)% = 50%.   Required average = (50/10)= 
(50/10) = 5
5%.
Answer: D
Find the cost of fencing around a circular field of diameter 42 m at the rate of Rs.3 a meter?  Choose the correct choice from the following answers:	A) 138	B) 390	C) 393	D) 279	E) 222

Solution: 2 * 22/7 * 21 = 131   131 * 3   = Rs.393   Answer: 393
Answer: C
The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? Pick:
A) 4 years	B) 6 years	C) 8 years	D) 10 years	E) 12 years

Solution: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.   Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50   5x = 20   x = 4.   Age of the youngest child = x = 4 years.   4 yearsnswer: Option 4 years
Answer: A
A, B and C rents a pasture for Rs.841. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?  Choose the correct choice from the following answers.
A) 270  B) 279  C) 276  D) 261  E) 262

Solution: 12*8 :16*9 = 18*6   8: 12: 9   9/29 * 841= 
9/29 * 841 = 261
261   Answer: 261
Answer: D
Find the numbers which are in the ratio 3 : 2 : 4 such that the sum of the first and the second added to the difference of the third and the second is 21 ?
Answers:
A) 9, 6, 11
B) 9, 6, 17
C) 9, 6, 19
D) 9, 6, 12
E) 9, 6, 10

Solution: Let the numbers be a, b and c.   Given that a, b and c are in the ratio 3 : 2 : 4.   let, a = 3x, b = 2x and c = 4x   Given, (a+b) + (c - b) = 21   = > a + b + c - b = 21 = > a + c = 21   = > 3x + 4x = 21 = >7x = 21 = > x = 3   a , b , c are 3x, 2x, 4x.   a, b, c are 9 , 6 , 12.   Answer: 9, 6, 12
Answer: D
The owner of a furniture shop charges his customer 100% more than the cost price. If a customer paid Rs. 1000 for a computer table, then what was the cost price of the computer table? Choose the correct choice from the following choices:
A) 800
B) 650
C) 500
D) 600
E) 250

Solution: CP = SP * (100/(100 + profit%))   = 1000(100/200) = Rs. 500.   Answer: 500
Answer: C
Find the unit's digit in 264^102+264^103
Select the correct option.
A) 0  B) 2  C) 3  D) 5  E) 6

Solution: Required unit's digit = unit's digit in 4102+4103.4102+4103.   Now, 4242 gives unit digit 6.   ⇒ 41024102 gives unit digit 6.   ⇒ 41034103 gives unit digit of the product 6×46×4 i.e., 4.   Hence, unit's digit in 264102+264103264102+264103   = unit's digit in (6+4)=0   0
Answer: A
A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 5:3 and B:C = 5:2. If the total runs scored by all of them are 60, the runs scored by B are?  Choices:
A) 20.23
B) 20.13
C) 30.93
D) 19.56
E) 10.93

Solution: A:B = 5:3   B:C = 5:2   A:B:C = 25:15:6   15/46 * 60 = 19.56   ANSWER:19.56
Answer: D
A boy incurs 5% loss by selling a book for Rs. 1000. At what price should the book be sold to earn 5 % profit?  Choose one:	A) Rs. 1105.26	B) Rs. 1251.50	C) Rs. 1085.13	D) Rs. 1885.13	E) None of these

Solution: Explanation:   Let the new selling price be Rs. x   (100 – loss %) /1000 = (100 + gain %) / x   (100 – 5) / 1000 = (100 + 5) / x   x = (105 × 1000) / 95 = 105000 / 95   x = 1105.26.   Rs. 1105.26NSWER Rs. 1105.26
Answer: A
In a store, the profit is 320% of the cost. If the cost increases by 25% but the SP remains constant, approximately what % of the sellingprice is the profit?	Choose the correct option:  A) 50%  B) 70%  C) 90%  D) 100%  E) 120%

Solution: Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420   New C.P. = 125% of Rs. 100 = Rs. 125.   New S.P. = Rs. 420   Profit = 420 - 125 = Rs. 295   Required percentage = 295/420 * 100 = 1475/21 = 70%   70%
Answer: B
The average of ten numbers is 0. In those 10, at the least, how many may be greater than or equal to zero?	Choose the correct answer.
A) 0  B) 1  C) 2  D) 3  E) 5

Solution: Explanation :   Average of 10 numbers = 0   Sum of 10 numbers =(0 x 10) =0.   It is quite possible that 9 of these numbers may be negative and if there sum is -a, then 10th number is (a).   Answer : 1
Answer: B
The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 57 kmph, find the speed of the stream?  Choose the correct choice from the following answers:
A) 16 kmph
B) 19 kmph
C) 14 kmph
D) 11 kmph
E) 13 kmph

Solution: The ratio of the times taken is 2:1.   The ratio of the speed of the boat in still water to the speed of the stream   = (2+1)/(2-1)= 
(2+1)/(2-1) = 3
3/1= 
3/1 = 3
3:1   Speed of the stream= 57/3= 
57/3 = 19
19 kmph.   Answer: 19 kmph
Answer: B
In the county of Veenapaniville, there are a total of 50 high schools, of three kinds: 25 public schools, 16 parochial schools, and 9 private independent schools. These 50 schools are divided between three districts: A, B, and C. District A has 18 high schools total. District B has 17 high schools total, and only one of those are private independent schools. If District C has an equal number of each of the three kinds of schools, how many private independent schools are there in District A? Choose one.
A) 2  B) 3  C) 4  D) 5  E) 6

Solution: Total Private Schools = 9   Dist A: High Schools = 18 ==> Private Schools = ?   Dist 3: High Schools = 17 ==> Private Schools = 1   Dist C: High Schools = 15 ==> Private Schools = 5   Therefore, 9 - 1 - 5 ==> 3   Answer 3)
Answer: B
An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.
Select the correct option: A) 8 : 6 B) 8 : 7 C) 8 : 8 D) 8 : 9 E) 8 : 3

Solution: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.   Let the dimensions of the carpet in the second case be 7y, 3y units respectively.   From the data,.   2(3x + 2x) = 2(7y + 3y)   => 5x = 10y   => x = 2y   Required ratio of the areas of the carpet in both the cases   = 3x * 2x : 7y : 3y   = 6x2 : 21y2   = 6 * (2y)2 : 21y2   = 6 * 4y2 : 21y2   = 8 : 7   Answer: Option 8 : 7
Answer: B
A man walks at a rate of 10 mph. After every ten miles, he rests for 6 minutes. How much time does he take to walk 60 miles? Select the correct option:
A) 300
B) 318
C) 322
D) 324
E) 390

Solution: To cover 60 miles the man needs (time) = (distance)/(rate) = 60/10= 
60/10 = 6
6 hours= 360 minutes. He will also rest 5 times (after 10, 20, 30,40 and 50 miles), so total resting time = 5*6= 
5*6 = 30
30 minutes.   Total time= 360 + 30= 
360 + 30 = 390
390 minutes.   Answer: 390.
Answer: E
In one hour a boat goes 18 km long the stream and 6 km against the stream.The speed of the boat in still water is?  Choose the correct answer:
A) 12
B) 14
C) 16
D) 17
E) 18

Solution: Speed in still water 12 = ½ ( 18+6) km/hr 12= 12 kmph   12nswer: 12
Answer: A
A bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 3:4:5. If the total value of all the coins in the bag is Rs.400, find the number of 50 paise coins ? Choose the correct choice from the following choices:
A) 498	B) 488	C) 428	D) 528	E) 418

Solution: 50*3k + 20*4k + 10*5k = 40000   280k = 40000 => k = 142.85   50p coins = 3k = 3*142.85 = 428   20p coins = 4k = 4*142.85 = 571   10p coins = 5k = 5*142.85 = 714   ANSWER:428
Answer: C
A shop produces sarongs. The daily average production is given by 5n + 20, where n is the number of workers aside from the owner. In the first k days, 500 units are produced, and then 5 workers are added to the team. After another k days, the cumulative total is 1200. How many workers were part of the latter production run?	Pick one:
A) A)6
B) B)14
C) C)11
D) D)15
E) E)23.5

Solution: The daily average production is given by 5n + 20- given   In the first k days, 500 units are produced   = (5n+20)K =500   k = 500/5n+20...................................1   5 workers were added = 5(n+5)+20 = 5n +45   cumulative is 1200 .. thus for the current period = 1200 -500= 
1200 -500 = 700
700   (5n+45)K= 700   k = 700/5n+45........................................2   equate 1 and 2   500/5n+20 = 700 /5n+45   500(5n+45) = 700(5n+20)   25n + 225 = 35n + 140   -10n = -85   n = 8.5   thus n+5 = 14   hence 14
Answer: B
a series of natural number 1+2+3+4+5+6+7+8+9+10 is divisibel by 11 so we has to find how many such series is possible upto n where n is less than 1000.  Choose one: A) 90 B) 99 C) 180 D) 96 E) 92

Solution: the total multiple of 11 less then 1000 are 90 .   and for every multiple there are two such series which are divisible by 11.   . .   . sum of series = n(n+1)/2   for multiple 11 we can take n=10 and 11   for 22 '' '' ''' n=21 and 22   and so on and for 990 multiple of 11 we can take n=989 and 990   so total series formed are 90*2= 
90*2 = 180
180   ANSWER:180
Answer: C
A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x – 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number G of people surveyed by the company?
Choose the most appropriate option:
A) 46
B) G=80
C) G=90
D) G=100
E) 200

Solution: 100 = x + x - 20 + 23 - 23   x = 60,   So, Product A = 60%, Product B = 40%, Both = 23%, Neither = 23%   23% of the total no. of people should be an integer. So, A,BC are out.   60% of D and 40% of D are both integers. So, D satisfies all conditions.   So, answer is G=100.
Answer: D
A firm is divided into four departments, each of which contains four people. If a project is to be assigned to a team of three people, none of which can be from the same department,what is the greatest number of distinct teams to which the project could be assigned?
Choose the correct choice from the following answers: A) 4^3 B) 4^4 C) 4^5 D) 6(4^4) E) 4(3^6)

Solution: First member: 4*4= 
4*4 = 16
16 choices;   Second member: 4*3= 
4*3 = 12
12 choices (as one department already provided with a member);   Third member: 4*2= 
4*2 = 8
8 choices (as two departments already provided with members);   So, we have: 16*12*8.   Since the order of the members in a team does not matter (we don't actually have 1st, 2nd and 3rd members) then we should divide above by 3! to get rid of duplication: 16*12*8/3!=4^4.   ANSWER:4^4
Answer: B
Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction M of the work will be done by Adam?
Select the correct option.
A) 1/4
B) 12/47
C) 1/3
D) 5/12
E) 20/47

Solution: Let the total work be 60 units. Pual does   60/3= 
  60/3 = 20
20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12)= 
(20 + 15 + 12) = 47
47 units per hr. So the time taken to finish the work= 60/47 hrs.   adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work   M>( 60/47 *12)/60 =12/47   Answer 12/47
Answer: B
A car during its journey travels 30 minutes at a speed of 60 kmph, another 45 minutes at a speed of 60 kmph, and 2 hours at a speed of 80 kmph.The average speed of the car is Choose the correct choice from the following answers:
A) 63.07 kmph
B) 64 kmph
C) 72.30 kmph
D) 64.02 kmph
E) None of these

Solution: First car travels 30 min at speed of 60 kmph   distance = 60 x 1/2 = 30 m   Then car travels 45 min at a speed of 60 kmph   distance = 45 min at speed of 60 kmph   distance = 60 x 3/4 = 45 m   at last it travels 2 hours at speed of 70 kmph   distance = 80 x 2 = 160 m   Total distance = 30 + 45 + 160= 
30 + 45 + 160 = 235
235   Total time= 1/2 + 3/4 + 2= 
1/2 + 3/4 + 2 = 13/4 = around 3.25
3.25   Average speed of the car= 235/3.25 = 72.30   ANSWER:72.30 kmph
Answer: C
What is the greatest of 3 consecutive integers whose sum is 21 ? Choose the correct choice from the following options.
A) 6 B) 7 C) 8 D) 9 E) 5

Solution: The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3   If the sum is 24, we need to solve the equation 3n + 3 + (  + 1) + (  + 2)= 
+ (  + 1) + (  + 2) = 3
3n + 3   If the sum is 24, we need to solve the equation 3n + 3= 21;   => 3n = 18;   => n = 6   The greatest of the three numbers is therefore   6 + 2= 
  6 + 2 = 8
8 Answer: 8
Answer: C
Equal weights of two alloys containing tin, copper and lead in the ratio 6:8:7 and 1:2:4 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy? Select the correct option:	A) 11:8:3	B) 3:1:8	C) 17:28:27	D) 9:4: 11	E) 9:14: 11

Solution: Let the weight of the two alloys be w each   Required ratio =   (6w/21+1w/7): (8w/21+2w/7 ): (7w/21+4w/7)   = 9w/21 : 14w/21 : 11w/21   = 9:14: 11   ANSW9:14: 11R:9:14: 11
Answer: E
Which of the following fraction is the smallest?	Choose the correct choice from the following answers:
A) 12/14	B) 13/19	C) 17/21	D) 7/8	E) None of these

Solution: Explanation:   12/14 = 0.857, 13/19 = 0.684, 17/21 = 0.8095 and   7/8= 
  7/8 = 7/8 = around 0.875
0.875   Since 0.684 is the smallest, so 13/19 is the smallest fraction.   ANSWER: 13/19
Answer: B
At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000? Choose the correct choice from the following.
A) 6620	B) 3277	C) 2688	D) 2998	E) 2789

Solution: 6620 = 20000(11/10)3   = 26620   = 20000   ----------   6620   6620nswer:6620
Answer: A
A man covers a certain distance by car driving at 30 km/hr and he returns back to the starting point riding on a scooter at 10 km/hr. Find his average speed for the whole journey. Choose the correct option:
A) 8 Km/hr B) 17 Km/hr C) 15 Km/hr D) 12 km/hr E) None of these

Solution: Explanation:   = (2 x a x b)/(a + b)   = (2 x 30 x 10)/(30 + 10)   = (2 x 30 x 10)/40   = 15 km/hr   Answer: Option 15 Km/hr
Answer: C
Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?  Choose the correct option:
A) 2388
B) 2778
C) 1279
D) 6150
E) 2771

Solution: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15   = 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60   Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.   The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k   It is given that A paid Rs. 1125   45k 45  + 60  + 81  + 60= 
45  + 60  + 81  + 60 = 246
246k   It is given that A paid Rs. 1125   45k= 1125 => k = 25   246k = 246(25) = Rs. 6150   Thus the total rent paid by all the four agencies is Rs. 6150.   Answer: 6150
Answer: D
A sum of money at simple interest amounts to Rs. 830 in 3 years and to Rs. 854 in 4 years. The sum is: Pick one.
A) 647  B) 698  C) 758  D) 847  E) 976

Solution: S.I. for 1 year = Rs. (854 - 830) = Rs. 24.   S.I. for 3 years = Rs.(24 x 3) = Rs. 72.   Principal = Rs. (830 - 72) = Rs. 758.   Answer:758
Answer: C
A company pays project contractors a rate of a dollars for the first hour and b dollars for each additional hour after the first, where a > b.
In a given month, a contractor worked on two different projects that lasted 6 and 8 hours, respectively. The company has the option to pay for each project individually or for all the projects at the end of the month. Which arrangement would be cheaper for the company and how much would the company save? Select the correct option:
A) Per month, with savings of $(5a + 5b)  B) Per month, with savings of $(5a - 5b)  C) The two options would cost an equal amount.  D) Per project, with savings of $(5a + 5b)  E) Per project, with savings of $(5a - 5b)

Solution: Per Project, company will pay as follows:   For 6 hours work = a+5b   For 8 hours work = a+7b   Total = 2a+12b   Per Month, company will pay for 14 hours work = a+13b   Total per contract - total per month   6a+8b - (a+13b)   5a-5b   Since a>b Amount 6a+8b(per contract amount) > a+13b (per project amount) by 5a-5b.   Hence per month payment will be cheaper by 5a-5b .   OA Per month, with savings of $(5a - 5b)
Answer: B
A rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered. If the area of the field is 720 sq. feet, how many feet of fencing will be required? Select the correct option.
A) 78  B) 40  C) 68  D) 88  E) None

Solution: EXPLANATION   We have: l = 30 ft and lb = 720 sq. ft.   So, b = 24 ft.   Length of fencing = (l + 2b) = (30 + 48)= 
(30 + 48) = 78
78 ft.   78nswer 78
Answer: A