MU-NLPC/Calc-aqua_rat huggingface dataset:
When positive integer N is divided by positive integer J, the remainder is 28. If N/J = 154.04, what is value of J?	Choose the most appropriate option:  A) 400  B) 350  C) 700  D) 750  E) 800

Solution: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder   So, Dividend/Divisor = Quotient + Remainder/Divisor   Given that N/J = 154.04   Here 154 is the quotient.   Given that Remainder = 28   So, 154.04 = 154 + 28/J   So, J = 700   Answer: 700
Answer: C
A man recites the alphabet N times. What is the equation for the amount of every odd letter he said?  Options:
A) 25/2*N	B) 13N	C) 27/2*N	D) 26N	E) 11N

Solution: 13N is th 25/2*Nnswer 25/2*N
Answer: A
The ratio of a compound, by weight, consisting only of substances x, y, and z is 4:6:10,
respectively. Due to a dramatic increase in the surrounding temperature, the composition of the
compound is changed such that the ratio of x to y is halved and the ratio of x to z is tripled. In the
changed compound, if the total weight is 116 lbs, how much does substance x weigh? Pick:  A) 48  B) 36  C) 24  D) 12  E) 10

Solution: x:y=4:6   if the ratio is halevd then x:y=2:6   The old ratio of x to z was 4:10. If this ratio is tripled, then the new ratio of x to z is 12:10.   x:y=2:6=12:36 ( multiplied the ration with 6/6 to have a common co eff x in both the rations x:y and x:z)   so x:y:z= 12:36:10   and we know x + y + z = 116 lbs   from the ratio of x ,y and z we have x=12k y=36k z=10K   put it in the equation we have 12k+36k+10k=116   k=2   Hence x=12(2)=24   Ans 24
Answer: C
Albert buys 4 horses and 9 cows for Rs. 13,400. If he sells the horses at 10% profit and the cows at 20% profit, then he earns a total profit of Rs. 1880. The cost of a horse is?	Choose the correct choice from the following answers
A) 1299  B) 2788  C) 2000  D) 2981  E) 2881

Solution: Explanation:   Let C.P. of each horse be Rs. x and C.P. of each cow be Rs. y.   Then, 4x + 9y = 13400 -- (i)   And, 10% of 4x + 20% of 9y = 1880   2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii)   Solving (i) and (ii), we get : x = 2000 and y = 600.   Cost price of each horse = Rs. 2000.   Answer: 2000
Answer: C
A jar contains a mixture of two liquids Acid( nitric acid) and Base(ammonium chloride) in the ratio 4 : 1. When 10 litres of the mixture is taken out and 10 litres of liquid Base is poured into the jar, the ratio becomes 2 : 3. How many litres of liquid Acid was contained in the jar?	Choose one.
A) 14 lts
B) 18 lts
C) 20 lts
D) 16 lts
E) 26 lts

Solution: %age of liquid Base in the original mixture   =1/5 x 100 = 20%   In the final mixture % of the liquid Base   = 3/5 x 100 = 60%   Now using the rule of allegation   Hence reduced quantity of the first mixture and the quantity of mixture B which is to be added are the same.   Total mixture = 10 + 10= 
10 + 10 = 20
20 liters and quantity of liquid A= 20/5 x 4 = 16 lts   ANSWER:16 lts
Answer: D
On the Richter scale, which measures the total amount of energy released during an earthquake, a reading of x-1 indicates one-tenth the released energy as is indicated by a reading of x. On that scale, the frequency corresponding to a reading of 5 is how many times as great as the frequency corresponding to a reading of 3?  Choose the correct choice from the following answers
A) 100	B) 200	C) 10^4	D) 10^5	E) 10^6

Solution: If Richter scale reading goes from X-1 to X it will be 10   if Richter scale reading goes from 3 to 4 it will be 10   if Richter scale reading goes from 4 to 5 it will be 10   so it will from 3 to 5 i.e 4,5 = 10*10 = 10^2   100nswer is 100
Answer: A
A train can travel 50% faster than a car. Both start from point A at the same time and reach point B at 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is?
Choose the correct answer.
A) 2387 B) 267 C) 120 D) 277 E) 271

Solution: Let speed of the car be x km/hr.   Then, speed of the train = 150/100 x = 3/2 x km/hr.   75/x - 75/(3/2 x) = 125/(10 * 60)   75/x - 50/x = 5/24 = 120 km/hr.   Answer: 120
Answer: C
The difference between a two-digit number and the number obtained by interchanging the digit is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1:2?	Select the correct option
A) 8  B) 15  C) 14  D) 12  E) 10

Solution: Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.   Let the ten's and unit's digits be 2x and x respectively.   Then, (10 * 2x + x) - (10x + 2x) = 36   9x = 36   x = 4   Required difference = (2x + x) - (2x - x) = 2x = 8.   8NSWER 8
Answer: A
Among 260 viewers interviewed who watch at least one of the three TV channels namely A, BC. 116 watch A, 127 watch C, while 107 watch B. If 50 watch exactly two channels. How many watch exactly one channel?	Choose the correct choice from the following choices:
A) 185
B) 180
C) 175
D) 190
E) 195

Solution: 260 = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels)   260 = n(Exactly 1 channel) + 50 + n(Exactly 3 channels)   Let's find the value of n(Exactly 3 channels) = x   260 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)   Note that each of n(A and B) is the sum of 'number of people watching exactly two channels A and B' and 'number of people watching all three channels'.   260 = 116 + 127 + 107 - n(Exactly 2 channels) - 3x + x   260 = 116 + 127 + 107 - 50 - 2x   x = 20   260 = n(Exactly 1 channel) + 50 + 20   n(Exactly 1 channel) = 190   Answer (190)
Answer: D
The probability that a computer company will get a computer hardware contract is 4/5 and the probability that it will not get a software contract is 3/5. If the probability of getting at least one contract is 9/10, what is the probability that it will get both the contracts?
Select:  A) 1/8  B) 2/9  C) 3/10  D) 4/11  E) 5/12

Solution: Let, A ≡ event of getting hardware contract   B ≡ event of getting software contract   AB ≡ event of getting both hardware and software contract.   P(A) = 4/5, P(~B) =5/9   => P(B) = 1- (3/5) = 2/5.   A and B are not mutually exclusive events but independent events. So,   P(at least one of A and B ) = P(A) + P(B) - P(AB).   => 9/10 = (4/5) + (2/5) - P(AB).   => P(AB) = 3/10.   Hence, the required probability is 3/10.   The answer is 3/10.
Answer: C
Out of 5 consonants and 3 vowels, how many words of 4 consonants and 2 vowels can be formed?  Options.
A) 21000
B) 10500
C) 25200
D) 10800
E) None of these

Solution: Solution   Number of ways of selecting (4 consonants out of 5) and (2 vowels out of 3)   5c4 x 3c2= (5/1)x(3/1) =15   Number of group,each having 4 consonants and 2 vowels = 15   Each group contains 6 letter.   Number of ways of arranging 5 letters among themselves   = 5 ! = (6 x 5 × 4 × 3 × 2 × 1) = 720 .   So, Required number of words = (720 × 15) = 10800 .Answer 10800
Answer: D
A machine puts c caps on bottles in m seconds. How many hours will it take to put caps on b bottles?	Choose the correct choice from the following:
A) 60bm/c	B) bm/3600c	C) bc/60m	D) 60b/cm	E) b/60cm

Solution: A machine puts c caps on bottles in m seconds.   So, the machine puts 1 cap in m/c minutes   To put caps on b bottles, the machine will take bm/c minutes   In order to calculate the no. of hours taken , divide the product by 3600.   So, our answer is bm/3600c   Answer : bm/3600c
Answer: B
A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 4 volts, what was the smallest possible recording in volts? Choose the correct choice from the following answers:
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: if average of 3 is 4 so sum of 3 should be 12   3 recording can be from 0-10 inclusive   to find one smallest other two should be highest   so, lets assume three var are a,b,c   say a is smallest and give b and c greatest readings say 5 and 5   so a has to be 2   2
Answer: A
On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 2 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on September 1 than were in stock on January 1?	Choose the most appropriate option: A) 18 B) 12 C) 20 D) 32 E) 36

Solution: Jan 1 = C   Feb 1 = C - 2   March 1 = C - 4   18pril 1 = C - 8   May 1 = C - 10   June 1 = C - 12   July 1 = C - 14   18ug 1 = C - 16   Sept 1 = C - 18   Difference between stock on September 1 than were in stock on January 1 will be -   C - ( C - 18 )= 18   Hence answer will be (18)
Answer: A
By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?	Choose the correct option
A) 95%
B) 25%
C) 29%
D) 27%
E) 21%

Solution: SP = CP + g   150 SP = 150 CP + 30 SP   120 SP = 150 CP   120 --- 30 CP   100 --- ? => 25%   Answer: 25%
Answer: B
Find out the two signs to be interchanged for making following equation correct
5 + 3 x 8 - 12 / 4 =3
Choose the correct choice from the following answers:
A) 7
B) 3
C) 4
D) 5
E) 6

Solution: Explanation:   On interchanging - and /, we get the equation as   5 + 3 x 8 / 12 - 4 = 3   or 5 + 3 x (2/3) - 4 = 3   or 3 = 3, which is true.   Answer: 3
Answer: B
Wife man got salary Rs.1000 and Husband got 30% extra compare with A's salary.If boths salary are joined, when will the salary become 10,350?  Select.
A) 120
B) 130
C) 135
D) 142
E) 150

Solution: since husband got 30% more,thus the salary is 1300Rs for 30 days(1 month)   in 60 days(2 months) total salary will be :     1000+1300= 
  1000+1300 = 2_300
2300   in 90 days(3 months):    2300+2300= 
 2300+2300 = 4_600
4600   in 120 days(4 months):    4600+4600= 
 4600+4600 = 9_200
9200   now only 800 more amount are required to finish , which will take Half of the month(15 days)   (2300/2=1150-------------->9200+1150=10350)   thus in all 135 days.   Ans:135
Answer: C
In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:	Choices
A) 18
B) 24
C) 13
D) 29
E) 17

Solution: Let there were x teams participating in the games, then total number of matches,   nC2 = 153.   On solving we get,   => n =−17 and n =18.   It cannot be negative so,   n = 18 is the answer   18ns: 18
Answer: A
A train 300 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?	Choose the most appropriate option:
A) 32	B) 48	C) 29	D) 27	E) 21

Solution: S = (300 + 300)/45 = 600/45 * 18/5= 
600/45 * 18/5 = 48
48   Answer: 48
Answer: B
A grocery shop has a sale of Rs. 6335, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500? Choose the correct choice
A) 4857	B) 4184	C) 4012	D) 5091	E) 5291

Solution: Let the sale in the sixth month =x   Then   (6335+6927+6855+7230+6562+x)/6 =6500   =>6335+6927+6855+7230+6562+x =6×6500   => 33909+x=39000   => x=39000−33909   =5091   ANSWER:5091
Answer: D
Set S has a mean of 10 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?  Choose the correct choice from the following choices:
A) {2, 10} B) {9, 11} C) {10, 18} D) {7, 13} E) {16, 16}

Solution: answer B,C, and E mean is not 10 therefore not accepted . D mean is 10 but S.D is more. therefore accepted   answer is B mean is 10 and S.D decreases minimum.   {9, 11}
Answer: B
Find the odd man out
253, 136, 352, 324, 631, 244 Choose the correct choice:
A) 324
B) 136
C) 352
D) 631
E) 531

Solution: The sum all three digits comes to 10 except 324   324NSWER:324
Answer: A
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Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 12 days. In how many days Peter complete the work separately. Select the correct option
A) 26 days
B) 27 days
C) 30 days
D) 25 days
E) 24 days

Solution: Together they complete the job in 20 days means they complete 12/20 of the job after 12 days.   Peter completes the remaining (8/20) of the job in 12 days which means that the whole job(1) can be completed in X days.   <=> 8/20->12 <=> X=12/(8/20)= 
12/(8/20) = 30
30   Thus the answer is 30 days.
Answer: C
The number of new words that can be formed by rearranging the letters of the word 'LETTERRS' is? Choose the correct option.
A) 40320 B) 40318 C) 40319 D) 40124 E) 40154

Solution: Number of words which can be formed   = 8! - 1 = 40320- 1= 
40320- 1 = 40_319
40319.   Answer:40319
Answer: C
What is the difference between the largest number and the least number written with the digits 9, 3, 1, 2?
Select.
A) 6084
B) 3788
C) 2077
D) 8082
E) 1812

Solution: Explanation:   1239   9321   ------------   8082   Answer:8082
Answer: D
What value will come in place of question mark in the following equation? ? + 0.025 = 80	Choose the correct choice from the following choices.
A) 1
B) 5
C) 6
D) 3
E) 2

Solution: Let x / 0.025 = 80, Then, x = 80 * 0.025= 
80 * 0.025 = 2
2   Answer is 2.
Answer: E
Two trains 140 m and 190 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? Choose the correct answer
A) 11.88 sec	B) 13.8 sec	C) 53.8 sec	D) 10.8 sec	E) 10.4 sec

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 140 + 190= 
140 + 190 = 330
330 m.   Required time= 330 * 9/250= 
330 * 9/250 = 297/25 = around 11.88
11.88 sec.   11.88 secnswer: 11.88 sec:
Answer: A
Joe invested a certain sum of money in a simple interest bond whose value grew to $560 at the end of 3 years and to $660 at the end of another 5 years. What was the rate of interest in which he invested his sum?	Choose the correct answer:
A) 3%  B) 4%  C) 5%  D) 6%  E) 7%

Solution: In 5 years, the value grew $100, so the simple interest was $20 per year.   In 3 years, the total interest was 3*$20 = $60   The principal is $560 - $60 3* 20= 
3* 20 = 60
$60   The principal is $560 - $60 = 500.   The interest rate is $20/$500 560 -  60= 
560 -  60 = 500
500.   The interest rate is $20/$500= 4%   The answer is 4%.
Answer: B
Which of the following fractions can be written as the difference of reciprocals of two consecutive integers Answers:
A) 1/28 B) 7/30 C) 1/45 D) 13/56 E) 1/72

Solution: Difference of reciprocals means 1 has to be in the numerator;   So option BD can be ignored   For option A, BE, we require to search two consecutive numbers whose product is the denominator   28 = 4 * 7 ......... Ignore   45 = 5 * 9 ........ Ignore   72 = 8 * 9 ................ Answer   Answer = 1/72
Answer: E
In an election a candidate who gets 60% of the votes is elected by a majority of 1504 votes. What is the total number of votes polled?  Choose the most appropriate option.
A) A)4500	B) B)5200	C) C)6900	D) D)7520	E) E)6000

Solution: Let the total number of votes polled be x   Then, votes polled by other candidate = (100-60)= 
(100-60) = 40
40% of x   60% of x - 40% of x= 1504   20x/100 = 1504   x = 1504*100/20= 
1504*100/20 = 7_520
7520   Answer is 7520
Answer: D
Aravind had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he
take along with him?  Choose the correct choice from the following choices
A) 2000  B) 2300  C) 3000  D) 3200  E) 3400

Solution: Let the money he took for shopping be m.   Money he spent = 30 % of m   = 30/100 × m   = 3/10 m   Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10   But money left with him = $ 2100   Therefore 7m/10 = $ 2100   m = $ 2100× 10/7   m = $ 21000/7= 
21000/7 = 3_000
$ 3000   Therefore, the money he took for shopping is $ 3000.   3000
Answer: C
Of 60 applicants for a job, 28 had at least 4 years' experience, 36 had degrees, and 6 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?  Choose the most appropriate option
A) 10 B) 13 C) 9 D) 7 E) 5

Solution: 60 - 6= 
60 - 6 = 54
54   54 - 28 - 36= -10   Then 10 are in the intersection between 4 years experience and degree.   10nswer : 10
Answer: A
In what time will a railway train 40 m long moving at the rate of 36 kmph pass a telegraph post on its way?  Choose the correct choice from the following:
A) 3 sec
B) 4 sec
C) 5 sec
D) 6 sec
E) 7 sec

Solution: T = 40/36 * 18/5= 
40/36 * 18/5 = 4
4 sec   ANSWER:4 sec
Answer: B
When the integer j is divided by 12, the remainder is 3. Which of the following, when divided by 12, will have a remainder of 6 ?
I. 2j
II. 6j
III. 4j + 6	Choices
A) I only	B) II only	C) III only	D) I and II only	E) I, II, and III

Solution: is it E.   j= 12*a + 3   2j = 12*2*a + 6   6j = 12*6*a + 18 ( 18 = 12+6)   4j + 6 = 12*4*a + 18 (18 = 12 + 6)
Answer: E
If the price of a computer were reduced by 15 percent, which of the following could not be the final price of the computer? (Assume initial price to be integer in cents)	Choose the correct choice:
A) $844.10
B) $895.90
C) $1,055.70
D) $1,135.60
E) $1,263.10

Solution: Let X be the initial price of computer without discount   then price (final) after discount should be=X(1-15/100)------->X(17/20)=A(say)   means X=A*(20/17).....   so initial price to be integer(As per stem) final price must be multiple of 17   if we check options all were divisible by 17 except option (A)..which is Ans.   $844.10ns $844.10
Answer: A
The distance from City A to City B is 120 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 120 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara?
Select: A) 42 B) 44 C) 60 D) 48 E) 50

Solution: The time it takes Cara to drive to City B is 120 / 30= 
120 / 30 = 4
4 hours.   Dan needs to take less than 2 hours for the trip.   Dan needs to exceed a constant speed of  120 / 2= 
 120 / 2 = 60
60 miles per hour.   The answer is 60.
Answer: C
A milkman purchases the milk at Rs. x per litre and sells it at Rs. 2x per litre still he mixes 2 litres water with every 6 litres of pure milk. What is the profit percentage?
Choose the most appropriate option
A) 116%
B) 166.66%
C) 60%
D) 100%
E) 150%

Solution: Explanation:   Let the cost price of 1 litre pure milk be Re.1, then   {6 litres(milk)->cp=Rs.6, 2 litres(water)->cp=Rs.0}->cp=Rs.6 only   and 8 litre mixture ->SP -> 8 x 2 = Rs.16   Profit %= [16/6 -6]x100=100/6=166.66%   ANSWER IS 166.66%
Answer: B
Two cyclist start from the same places in opposite directions. One is going towards north at 10kmph and the other is going towards south 10kmph. What time will they take to be 50km apart? Choose one
A) 1.2hr B) 2.5hrs C) 3hrs D) 5.2hrs E) 6hrs

Solution: To be (10+10) km apart, they take 1 hour   To be 50 km apart, they take   1/20*50= 
  1/20*50 = 5/2 = around 2.5
2.5 hrs   Answer is 2.5hrs
Answer: B
A train travels 240 km in 3 hours and 450 km in 5 hours.find the average speed of train.	Choose one
A) 80 kmph
B) 60 kmph
C) 86 kmph
D) 90 kmph
E) None of these

Solution: As we know that Speed = Distance / Time   for average speed = Total Distance / Total Time Taken   Thus, Total Distance = 240 + 450= 
240 + 450 = 690
690 km   Thus, Total Speed= 8 hrs   or,Average Speed = 690/8   or, 86kmph.   ANSWER:86 kmph
Answer: C
A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Select the correct option
A) 220 meter  B) 225 meter  C) 230 meter  D) 235 meter  E) None of these

Solution: Explanation:   As trains are running in opposite directions so their relative speed will get added   So, Relative speed = 120 +80= 
120 +80 = 200
200 kmph= 200*(5/18) = 500/9 m/sec   Let the length of other train is x meter then   x+270 /9=500 /9   =>x+270=500   =>x=230   So the length of the train is 230 meters   Option 230 meter
Answer: C
If d=1/(2^3*5^8) is expressed as a terminating decimal, how many nonzero digits will d have?	Choose the correct choice.
A) One
B) Two
C) Three
D) Seven
E) Ten

Solution: Another way to do it is :   We know x^a*y^a=(X*Y)^a   given = 1/(2^3*5^8)   = Multiply and divide by 2^5   =2^5/(2^3*2^5*5^8)   =2^5/10^8   => non zero digits are 32=> Ans Two
Answer: B
If W is the set of all the integers between 39 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?  Choose one
A) 26 B) 32 C) 33 D) 34 E) 40

Solution: Multiples of 2 from 39 to 99=Multiples of 2 from 1 to 99-Multiples of 2 from 1 to 38=[99/2]-[38/2]=49-19= 
49-19 = 30
30   Multiples of 3 from 39 to 99=Multiples of 3 from 1 to 99-Multiples of 3 from 1 to 38=[99/3]-[38/3]=33-13= 
33-13 = 20
20   Multiples of2 and 3 bothi.e.6 from 39 to 99=Multiples of 6 from 1 to 99-Multiples of 6 from 1 to 38=[99/6]-[38/6]=16-6= 
16-6 = 10
10   These 8 Numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3   i.e. Total Numbers in W= 30 + 20 - 10= 
30 + 20 - 10 = 40
40   Answer Option 40
Answer: E
Heinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many litres of tomato puree will be obtained from 20 litres of tomato juice?  Select the correct option.
A) 2 litres	B) 2.4 litres	C) 2.5 litres	D) 6 litres	E) 4 litres

Solution: Tomato Juice has 90% water and 10% tomato   Tomato puree has 20% water and 80% tomato   So 20 liter of tomato juice has 20*90/100= 
20*90/100 = 18
18 liters of water and 2 liters of tomato.   As tomato puree has 80% content of tomato, so 2 liters of tomato from 20 liter juice corresponds to 80% so tomato purees that can be obtained=100*2/80= 
100*2/80 = 5/2 = around 2.5
2.5   ANSWER:2.5 litres
Answer: C
A can do a job in 15days and B in 30days. If they work on it together for 4 days, then the fraction of the work that is left is?  Choose the correct choice from the following answers:  A) 2/15  B) 3/5  C) 3/11  D) 1/12  E) 6/13

Solution: A's 1 day work = 1/15   3/5's 1day work = 1/30   A+3/5 1day work = 1/15 + 1/30 = 3/30=1/10   A+3/5 4days work = 1/10*4 = 2/5   Remaining work = 1 - 2/5 = 3/5   Answer is 3/5
Answer: B
A professional janitor can clean a certain high school in 480 minutes, working at a constant rate. A student sentenced to detention can clean that same high school in 20 hours, also working at a constant rate. If the student is paid $7 total per hour and the janitor is paid $21 per hour, how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together? Choose the correct option:	A) -$56	B) -$6	C) $0	D) $6	E) $8

Solution: A professional janitor can clean a certain high school in 480mins or (480/60) or 8 hours   So (applying rule #1), the janitor can clean 1/8 of the school in ONE HOUR   A student sentenced to detention can clean that same high school in 20 hours   So (applying rule #1), the student can clean 1/20 of the school in ONE HOUR   So, COMBINED, the student and janitor can clean (1/8 + 1/20) of the school in ONE HOUR   1/8 + 1/20 = 5/40 + 2/40 = 7/40   So, in ONE HOUR they can clean 7/40 of the school.   Applying rule #2, it will takethem40/7 hoursto clean the ENTIRE school.   The janitor earns $21/hour and the student earns $7/hour, so their combined rate is$28/hour.   Theircombined wages= (pay rate)(time) = ($28/hour)(40/7 hours) =$160   Working ALON$8, the janitor takes 8 hours and earns $21/hour   So, working alone, the janitor's earnings = (pay rate)(time) = ($21/hour)(8 hours) =$168   $168-$160= $8, so the answer is $8 168- 160= 
 168- 160 = 8
$8, so the answer is $8
Answer: E