MU-NLPC/Calc-aqua_rat huggingface dataset:
On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 10 percent. What was the total rent the motel actually charged for that night ?	Options: A) $600 B) $800 C) $1,000 D) $1,600 E) $2,000

Solution: Let total rent the motel charge for all rooms =x   If 10 rooms that were rented for 60 $ had instead been rented for 40 $,   then total difference in prices = 20 $ * 10 = 200 $   Total rent the motel charged would have been reduced by 10 %   .10x = 200   => x= 2000   Answer $2,000
Answer: E
A boat running downstream covers a distance of 40 km in 2 hours while for covering the same distance upstream,it takes 4 hours.What is the speed of the boat in still water ?  Choose one:
A) 4 km/hr	B) 6 km/hr	C) 8 km/hr	D) Data inadequate	E) 15 kmph

Solution: Solution   Rate downstream =(40/2)= 
(40/2) = 20
20 kmph, Rate upstream=(40/4)= 
(40/4) = 10
10 kmph.   ∴ Speed in still water=1/2(20+10) kmph = 15 kmph.   Answer 15 kmph
Answer: E
A student gets an aggregate of 60% marks in five subjects in the ratio 10 : 9 : 8 : 7 : 6. If the passing marks are 50% of the maximum marks and each subject has the same maximum marks, in how many subjects did he pass the examinaiton? Choose the correct option:
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: Explanation :   Let the full marks of each subject is 100. So, total marks in 5 subject is 500.   Student gets 60% aggregate marks i.e 60% of 500 = 300.   => 10x + 9x +8x +7x + 6x = 300   => 40x = 300.   => x = 300/40 = 7.5.   Hence,   The marks in first subject = 10x = 7.5 x 10 = 75.   The marks in 2ndsubject = 9x = 7.5 x 9 = 67.5.   The marks in 3rd subject = 8x = 7.5 x 8 = 60.   The marks in 4th subject = 7x = 7.5 x 7 = 52.5.   The marks in 5th subject = 6x = 7.5 x 6 = 45.   Thus , he passed in all 5 subjects.   Answer : 5
Answer: D
if f(f(X))=81. then. value of x=?
when f(X)=2X-1+f(X-1). is not equal to zero and f(X=0)=0	Choose the correct choice from the following answers
A) 2  B) 3  C) 4  D) 5  E) 6

Solution: f(X=0) = 0   f(X=1) = 2*1-1+f(1-1)   = 2-1+0= 
2-1+0 = 1
1   f(X=2) = 2*2-1+f(2-1)   = 4-1+1   2*2-1+ (2-1)= 
2*2-1+ (2-1) = 4
4-1+1= 
4-1+1 = 4
4   f(X=3) = 2*3-1+f(3-1)   = 6-1+4= 
6-1+4 = 9
9===>f(X=n) = n^2   f(f(X)) = 81   X = sqrt(sqrt(81)) = 3   ANSWER:3
Answer: B
The ratio of male to female in a class is 6:6. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one third of the males and two-third of the females in the class?	Options:
A) a)180 degree	B) b) 168 degree	C) c)191 degree	D) d)192 degree	E) e)204 degree

Solution: here is my approach => males => 6x and females =6x => total =12x   now 12x=> 360   therefore 6x => 180 degree .   P.S => 6x is nothing but total number of students with the given preference   a)180 degreenswer a)180 degree
Answer: A
A shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?  Choose the correct choice from the following answers:  A) 200%  B) 75%  C) 60%  D) 50%  E) 100 %

Solution: The total number of mangoes bought by the shopkeeper be 12.   If he buys 6 a rupee, his CP = 3   He selling at 3 a rupee, his SP = 6   Profit = SP - CP = 6 - 3= 
6 - 3 = 3
3   Profit Percent= 3/3 * 100= 
3/3 * 100 = 100
100 %   Answer:100 %
Answer: E
A firm is comprised of partners and associates in a ratio of 2:61. If 60 more associates were hired, the ratio of partners to associates would be 4:137. How many partners are currently in the firm?	Choose the correct choice from the following answers:  A) 12  B) 14  C) 16  D) 18  E) 20

Solution: The ratio 2:61 = 4:122 so the ratio changed from 4:122 to 4:137.   137-122= 
137-122 = 15
15 which is 1/4 of the increase in 60 associates.   The ratio changed from 16:488 to 16:548.   Thus the number of partners is 16.   The answer is 16.
Answer: C
x, y, a, and b are positive integers of E. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?
Pick one
A) 24 B) 21 C) 20 D) 17 E) 15

Solution: x, y, a, and b are positive integers of E. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Answer: 15.
Answer: E
Difference of 2 numbers is 1660. If 7.5% of one number is 12.5% of the other number, find the 2 numbers?  Select:	A) 125,150	B) 5124,4515	C) 4150,2490	D) 3250,4510	E) 1254,3210

Solution: Let the numbers be x and y   7.5% of x = 12.5% of y   x = 125y/75 = 5y/3   x-y = 1660   5y/3 - y = 1660   y = 2490   x = 5y/3 = 4150   Answer is 4150,2490
Answer: C
Rahul is younger than Karthi by 7 years. If the ratio of their ages is 7:9, find the age of Rahul Choose the correct choice from the following:
A) 20	B) 24	C) 24.5	D) 23	E) 23.5

Solution: karthi age is x and rahul x-7   => (x-7)/x = 7/9   => 9x-63 = 7x   => 2x = 63   => x = 31.5   then Rahul age is 31.5- 7= 
31.5- 7 = 24.5
24.5   ANSWER 24.5
Answer: C
A cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 8 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?	Choose the correct choice from the following answers:  A) 5.2 hrs  B) 13.3 hrs  C) 1.9 hrs  D) 7.2 hrs  E) 1.4 hrs

Solution: Net part filled in 1 hour = (1/5 - 1/8) = 3/40   The cistern will be filled in 40/3 hrs i.e., 13.3 hrs.   Answer:13.3 hrs
Answer: B
Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest? Choose the correct choice from the following answers.
A) 18% p.a.  B) 22% p.a.  C) 20% p.a.  D) 24% p.a.  E) None of these.

Solution: Rs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year.   Rate of interest = (100 * 240) / (100 * 1) = 20% p.a   ANSWER:20% p.a.
Answer: C
There are 13 cans in the refrigerator. 7 of them are red and 6 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator. Choose the correct choice from the following answers.
A) 460  B) 490  C) 493  D) 455  E) 445

Solution: 460nswer: 460.
Answer: A
The average (arithmetic mean) of eight numbers is 8. If 4 is added from each of five of the numbers, what is the new average?
Choose the correct choice from the following answers:  A) 4.5  B) 8.9  C) 10.5  D) 4.5  E) 5.6

Solution: Sum of 8 numbers = 8*8= 
8*8 = 64
64   If 4 is added from each of five of the numbers , we added  4*5= 
 4*5 = 20
20 from the total sum   Sum of 8 number after adding 4 from each of five of the numbers=64+20= 
64+20 = 84
84   New average= 84/8= 
84/8 = 21/2 = around 10.5
10.5   Answer 10.5
Answer: C
If a committee of 3 people is to be selected from among 6 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?	Choose the correct choice from the following choices:
A) 20  B) 40  C) 50  D) 80  E) 480

Solution: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 6C3=60.   But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.   Total # of ways: 6C3*2^3=480.   Answer: 480.
Answer: E
In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:
Select: A) 10 m B) 20 m C) 30 m D) 40 m E) 45 m

Solution: A - distance of  (500 - 140)= 
 (500 - 140) = 360
>360 m   A cover 3 m , 20 m covers 4 m=> 480 m   when A reaches the winning post 20 m covers 480 m and remains 20 m behind   = > A wins by 20 m   ANSWER 20 m
Answer: B
In a company of 10 employees, 5 employees earn $30,000, 3 employees earn $40,000, and the 2 highest-paid employees earn the same amount. If the average annual salary for the 10 employees is $65,000, what is the annual salary for each of the highest-paid employees? Choose the correct choice from the following answers.
A) $190,000 B) $170,000 C) $150,000 D) $130,000 E) $110,000

Solution: 5*30,000+3*40,000+2x=10*65,000   2x=650,000-150,000-120,000   2x=380,000   x=190,000   The answer is $190,000.
Answer: A
How many pieces of 75 cm can be cut from a rope 45 meters long? Choose the correct choice
A) 30
B) 40
C) 60
D) None
E) Cannot be determined

Solution: Explanation :   Total pieces of 75 cm that can be cut from a rope of 45 meters long is   = (45 meters)/(75 cm)   = (45 meters)/(0.75 meters)   = 60   Answer : 60
Answer: C
If grapes are 90% water and raisins are 15% water, then how many kilograms did a quantity of raisins, which currently weighs 12 kilograms, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.) Choose the correct choice: A) 96 B) 98 C) 100 D) 102 E) 104

Solution: Let x be the original weight of the grapes.   The weight of the grape pulp was 0.1x.   Since the grape pulp is 85% of the raisins, 0.1x = 0.85(12 kg).   Then x = 8.5*12= 
8.5*12 = 102
102 kg.   The answer is 102.
Answer: D
The number 106 can be written as the sum of squares of 3 integers. Which of the following could be the difference between the largest and smallest integers of the 3?	Choose the correct choice from the following answers.
A) 6	B) 5	C) 7	D) 8	E) 9

Solution: Notice that the question asks which of the followingcouldbe the difference between the largest and smallest integers, not must be. The 3 integers could be: +/-4, +/-3 and +/-9, so the difference could be 6, or 12. Since only one of them is among the choices, then it must be the correct answer.   6nswer:6
Answer: A
On a certain transatlantic crossing, 25 percent of a ship's passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship's passengers held round-trip tickets? Choose the correct choice from the following choices.
A) 33.3% B) 40% C) 50% D) 60% E) 62.5%

Solution: 0.25P = RT + C   0.6(RT) = no C   => 0.40(RT) had C   0.25P = 0.40(RT)   RT/P = 62.5%   Answer - 62.5%
Answer: E
A is twice as good as workman as B and together they finish a piece of work in 18 days. In how many days will B alone finish the work. Choose the correct choice from the following:
A) 27 days
B) 54 days
C) 56 days
D) 68 days
E) 65 days

Solution: Explanation:   As per question, A do twice the work as done by B.   So A:54 days = 2:1   Also (A+54 days) one day work = 1/18   To get days in which 54 days will finish the work, lets calculate work done by 54 days in 1 day =1/18*1/3=1/54   [Please note we multiplied by 1/3 as per 54 days share and total of ratio is 1/3]   So 54 days will finish the work in 54 days   ANSWER IS 54 days
Answer: B
Juan and his five friends will sit on six fixed seats around a circular table. If Juan must sit on the seat closest to the window and Jamal must sit next to Juan, in how many can Juan and his five friends sit?	Pick one:  A) 20  B) 24  C) 48  D) 72  E) 120

Solution: J = Juan, F = Jamal   Since J is always fixed, set J, set F relative to J, then see how many options there are:   J F 4 3 2 1 = 24 or   F J 4 3 2 1 = 24   24+24= 
24+24 = 48
48 … 48   ANSWER:48
Answer: C
If I walk at 5 km/h, I miss the bus by 12 minutes. If I walk at 6 km/h, I reach 15 minutes before the arrival of the bus. How far I walk to reach the bus stand ?  Pick one
A) 11.0 km	B) 13.8 km	C) 11.5 km	D) 12.5 km	E) 13.5 km

Solution: d = product of speed difference of time /difference of speed   d = 5x6/60[12âˆ’(âˆ’15)/6-5]   [Here, â€“ve sign indicates before the schedule time]   â‡’ d = 13.5 km   Answer 13.5 km
Answer: E
When a positive integer A is divided by 11 and 3, the remainders obtained are 1 and 2, respectively. When the positive integer B is divided by 11 and 3, the remainders obtained are 1 and 2, respectively. Which of the following is a factor of (A - B)?
Choose one
A) 14	B) 28	C) 33	D) 42	E) 49

Solution: A = 11k+1 = 3j+2   B = 11m+1 = 3n+2   A-B = 11(k-m) = 3(j-n)   A-B is a multiple of both 11 and 3, so it is a multiple of 33.   The answer is 33.
Answer: C
In a group of ducks and cows, the total number of legs are 36 more than twice the number of heads. Find the total number of cows. Options:
A) 12  B) 14  C) 16  D) 18  E) 20

Solution: Let the number of ducks be d   and number of cows be c   Then, total number of legs = 2d + 4c = 2(d + 2c)   total number of heads = c + d   Given that total number of legs are 36 more than twice the number of heads   => 2(d + 2c) = 36 + 2(c + d)   => d + 2c = 18 + c + d   => 2c = 18 + c   => c = 18   i.e., total number of cows = 18   Answer is 18.
Answer: D
1100 boys and 700 girls are examined in a test; 31% of the boys and 23% of the girls pass. The percentage of the total who failed is ? Choose the correct choice.
A) A)63.3%	B) B)52.4%	C) C)81.2%	D) D)75.4%	E) E)72.11%

Solution: Total number of students = 1100+700= 
1100+700 = 1_800
1800   Number of students passed= (31% of 1100+23% of 700) = 341+161= 
341+161 = 502
502   number of failures= 1298*100/1800= 72.11%   Answer is 72.11%
Answer: E
The banker's gain on a sum due 3 years hence at 12% per year is Rs. 270. The banker's discount is:	Pick one.
A) 960  B) 840  C) 1020  D) 760  E) 920

Solution: T.D. =(B.G. x 100/R x T)   = Rs.(270 x 100/12 x 3)= Rs. 750.   Therefore, B.D. = Rs.(750 + 270) = Rs. 1020.   Answer is 1020
Answer: C
There are 4 books on fairy tales,5 novels and 3 plays.In how many ways can you arrange these so that books on fairy tales are together,novels are together and plays are together and in the order,books on fairy tales,novels and plays.	Choose the correct choice from the following answers.
A) 22000 B) 19261 C) 17280 D) 18168 E) 21671

Solution: There are 4 books arranged in 4!ways   Similarly,5 novels arranged in 5!ways.   And 3 plays arranged in 3!ways.   17280ounting principle all of them together can be arranged=4!*5!*3!   =[(4*3*2*1)*(5*4*3*2*1)*(3*2*1)= 
(4*3*2*1)*(5*4*3*2*1)*(3*2*1) = 17_280
17280 ways   Option 17280
Answer: C
M is the set of all consecutive odd integers between A and B. If B>A>1, and both A and B are even integers, what is the average (arithmetic mean) of M?	Choose the correct choice:
A) (A−B)/2
B) (A−B)/2 + 1
C) (A+B−1)/2
D) (A+B)/2
E) (A+B+1)/2

Solution: Let A be 2 and B be 6...as per condition..A and B have to be even...   2,3,4,5 and 6...then M is avg of odd integers...in our case 3+5/2 = 4..   We need to check which option is going to yield 4 and only option D does..   6+2/2 = 4...   Answer option (A+B)/2.
Answer: D
If x represents the sum of the interior angles of a square and y represents the sum of the interior angles of a regular pentagon, then the difference between x and y is equal to the sum of the interior angles of what geometric shape?
Choose the correct choice from the following answers:
A) Triangle  B) Square  C) Rhombus  D) Trapezoid  E) Pentagon

Solution: Sum of angles of square = 180*(4-2)= 
180*(4-2) = 360
360=> using formula sum of angles of polygon = 180*(n-2) where n is the number of sides in a polygon   Sum of angles in Pentagon = 180*(5-2)= 
180*(5-2) = 540
540   Difference= 540 - 360= 
540 - 360 = 180
180=> Triangle   hence (Triangle).
Answer: A
Bradley owns b video game cartridges. If Bradley’s total is one-third the total owned by Andrew and five times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?  Options.
A) (16/3)b  B) (17/4)b  C) (13/4)b  D) (21/5)b  E) (7/12)b

Solution: Step 1: Categorize the problem   This problem is testing basic algebra and equations, with an extra layer of complexity by having variables in the answer choices.   Step 2: Think like the test maker   What is the key detail or key details in the problem? The key detail to immediately recognize is that the problem gives you Andrew and Charlie’s totals in relation to Bradley’s total rather than giving you Bradley’s total in relation to the other two; and then the problem asks you to solve the problem in terms of b. This means that you have to relate Andrew and Charlie’s values in relation to Bradley’s total. The test maker is attempting to force you to structure the problem in the opposite way that most people are used to structuring information. By gaining this insight, it makes it easier to solve the problem.   Step 3: Solve the problem   b = Bradley’s total   3b = Andrew’s total   (1/5)b = Charlie’s total   Add each total   b + 3b+ (1/5)b = 4b + (1/5)b = (16/4)b + (1/5)b = (21/5)b   Therefore,choose (21/5)b.
Answer: D
If the volume of two cubes are in the ratio 27:1, the ratio of their edges is:
Choose the correct choice from the following.
A) 3:1
B) 3:5
C) 3:8
D) 3:29
E) 3:11

Solution: Let the edges be a and b of two cubes, then   a3b3=271=>(ab)3=(31)3ab=31=>a:b=3:1   3:1nswer: 3:1
Answer: A
Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 252 runs?	Options.
A) 6	B) 6.25	C) 7.25	D) 5.5	E) 8

Solution: Required run rate = 252 - (3.2 x 10) =	220 = 5.5   40	40   5.5
Answer: D
Raj is working on a set of Data Sufficiency problems for his December GMAT: a geometry problem, an algebra problem, and a data interpretation problem. He has determined that statement 1 of the geometry problem is insufficient on its own, that both statement 1 and 2 of the algebra problem are insufficient on their own, and that statement 2 of the data interpretation problem is insufficient on its own. If the probabilities are expressed as percents W, approximately how much greater is the probability that all three answers are “C” after Raj figures out that statement 1 of the data interpretation problem is also insufficient on its own? Select:
A) W=2.3%  B) W=2.8%  C) W=3.3%  D) 5.6%  E) 8.3%

Solution: Step 1: Figure out what we need to know.We have two probabilities that we need to figure out: the one before Raj figures out that statement 1 of the data interpretation problem is also insufficient, and the one after. The answer is the difference between them, in the form of a percent.   Step 2: The first probability.   If statement 1 of the geometry problem is insufficient, then the only valid answer choices are B, C, and E; the probability that it is C is 1/3.   If both statements of the algebra problem are insufficient on their own, then the only remaining valid answers are C and E; the probability that it is C is 1/2   If statement 2 of the data interpretation problem is insufficient, then the remaining answers are A, C, and E, and the probability that C is correct is 1/3.   The probability of all three occurring is the product of the probability fractions: (1/3)*(1/2)*(1/3) = 1/18.   Step 3: The second probability.   Only the third problem has changed; if Raj now knows that statement 1 is also insufficient, the valid answer choices are only C and E, leaving a 1/2 probability that the answer is C.   The probability of all three occurring is still the product of those fractions, but this time they are (1/3)*(1/2)*(1/2) = 1/12.   Step 4: The answer.Note that here, as will sometimes happen on the GMAT, values that you compute “along the way” appear as wrong answer choices. This problem calls for the difference between our two numbers,W (1/12)-(1/18) = 1/36, which is a 2.77777% chance, rounded to 2.8% —the correct answer is Choice W=2.8%.
Answer: B
At Company X, senior sales representatives visit the home office once every 15 days, and junior sales representatives visit the home office once every 10 days. The number of visits that a junior sales representative makes in a 2-year period is approximately what percent greater than the number of visits that a senior representative makes in the same period? Choices
A) 10%
B) 25%
C) 33%
D) 50%
E) 67%

Solution: Each 30-day period, senior representatives visit the home office 2 times while junior representatives visit 3 times, thus 50% more.   The answer is 50%.
Answer: D
A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 130 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?
Options: A) 50 B) 100 C) 150 D) 260 E) 250

Solution: It is simply a weighted average question. Since the given average of 50% and 60% is 55% (right in the middle), it means the number of people surveyed in Eros (n) is same as the number of people surveyed in Angie.   So n = 130   Total = 130 + 130= 
130 + 130 = 260
260   Answer (260)
Answer: D
A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280more at the second station it drops one half the new total and takes twelve more .on arriving at the third station it is found to have 248 passengers. Find the no of passengers in the beginning?
Choose the correct answer
A) 288  B) 321  C) 651  D) 246  E) 248

Solution: Let no of passengers in the beginning be x   288fter first station no passengers=(x-x/3)+280=2x/3 +280   288fter second station no passengers =1/2(2x/3+280)+12   ½(2x/3+280)+12=248   2x/3+280=2*236   2x/3=192   x=288   Option 288 is answer
Answer: A
The ratio of the number of boys and girls in a college is 7:8. If the percentage increase in the number of boys and girls be 20% and 10% respectively. What will be the new ratio?	Choose the correct choice from the following options:  A) 21:24  B) 21:24  C) 21:22  D) 21:45  E) 21:97

Solution: Originally, let the number of boys and girls in the college be 7x and 8x respectively.   Their increased number is (120% of 7x) and (110% of 8x).   i.e., (120/100 * 7x) and (110/100 * 8x)   i.e., 42x/5 and 44x/5   Required ratio = 42x/5 : 44x/5 = 21:22   Answer: 21:22
Answer: C
The ratio between the sale price and the cost price of an article is 6:2. What is the ratio between the profit and the cost price of that article?	Select the correct option
A) 23
B) 1:2
C) 2:5
D) 3:5
E) 2:1

Solution: C.P. = Rs. 2x and S.P. = Rs. 6x.   Then, Gain = Rs. 4x   Required ratio = 4x : 2x = 2:1   2:1
Answer: E
A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 240 meter length?  Options: A) 65 seconds B) 46 seconds C) 40 seconds D) 97 seconds E) 48 seconds

Solution: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec   Total distance = 360+240= 
360+240 = 600
600 meter   Time= Distance/speed   = 600 * (2/25)= 
600 * (2/25) = 48
48 seconds   Answer:48 seconds
Answer: E
A line has a slope of 3/4 and intersects the point W (-12, -39). At which point does this line intersect the x-axis?
Choose the correct option.
A) (40,0)
B) (30,0)
C) (0,40)
D) (40,30)
E) (0,30)

Solution: Assume that the equation of the line is y=mx+c, where m and c are the slope and y-intercept.   You are also given that the line crosses the point (-12,-39), this means that this point will also lie on the line above.   Thus you get -39=m*(-12)+c , with m=3/4 as the slope is given to be 3/4.   After substituting the above values, you get c = -30.   Thus the equation of the line is y=0.75*x-30 and the point where it will intersect the x-axis will be with y coordinate = 0.   Put y=0 in the above equation of the line and you will get, x=40.   Thus, the point W of intersection is (40,0).   (40,0) is the correct answer.
Answer: A
5 persons working eight hours daily can complete a wall in 10 days. When they have Worked for 4 days, 5 more persons are brought to work. The wall can now be completed in?	Choose the correct choice from the following.
A) one more day  B) two more days  C) three more days  D) four more days  E) five more days

Solution: Let D be the number of required days   Using the chain rule,   M1 x T1 = M2 x T2 + M3 x T3   5 x 8 x 10 = (4 x 5 x 8) + (10 x 8 x D)   D = 3.   Hence, the wall will be completed in 3 more days.   ANSWER:three more days
Answer: C