MU-NLPC/Calc-aqua_rat huggingface dataset:
A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 125, the runs scored by B are?
A. 15 B. 18
Answers:  A) 22  B) 18  C) 30  D) 77  E) 24

Solution: A:B = 2:3   B:30 = 2:5   A:B:30 = 4:6:15   6/25 * 125= 
6/25 * 125 = 30
30   Answer: 30
Answer: C
The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 22 years(the child was born during the interval). What is the present age of the child? Choose the most appropriate option:
A) 7 years
B) 9 years
C) 10 years
D) 4 years
E) 5 years

Solution: 28 * 2= 
28 * 2 = 56
56   22 * 3= 
22 * 3 = 66
66   -----------   10 years   Answer: 10 years
Answer: C
The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?	Choose the correct answer.
A) 12%	B) 14%	C) 16%	D) 20%	E) 22%

Solution: Explanation:   100 * 100= 
100 * 100 = 10_000
10000   80 * 110= 
80 * 110 = 8_800
8800   10000------- 1200   100 ------- ?= 12%   12%)
Answer: A
If the price of a certain bond on May 1st was 1/4 the price of the bond on June 1st and the price of the bond on July 1st was 25% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st?
Choices.
A) 100%  B) 150%  C) 155%  D) 300%  E) 355%

Solution: The price on June 1st = 12 (assume);   The price on May 1st = 1/4*12= 
1/4*12 = 3
3;   The price on July 1st= 3*1.25 = 3.75.   The average price of the bond on May 1st and July 1st = (3+3.75)/2 = 3.375.   The price of the bond on June 1st (12) is 32/9 times (355.55%) the average price of the bond on May 1st and July 1st.   Answer: 355%.
Answer: E
In a charity show, tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random (blindly) will have a number with a hundredth digit of 2?	Choose the correct choice from the following answers:	A) 0.285	B) 2/5	C) 99/225	D) 47/205	E) 3/5

Solution: Let S be the numbers between 101 and 350, i.e., n(S) = 250   Let E be the event when hundredth digit is 2.   n(E) = 100th digits of 2 = 299 − 199 = 100   P(E) = n(E)/n(S) = 100/250 = 2/5   ANSWER:2/5
Answer: B
Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 130 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond? Select:
A) 280
B) 400
C) 540
D) 650
E) 840

Solution: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month:   2/3*3/4 = 1/2 survived the first month.   Of the geese that survived the first month, 3/5 did not survive the first year:   (1-3/5)*1/2 = 1/5 survived the first year.   130 geese survived the first year:   1/5*(total) = 130 --> (total) = 650.   Answer: 650.
Answer: D
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one girl is included?  Choose the most appropriate option:
A) 145 B) 170 C) 195 D) 220 E) 245

Solution: The total number of ways to choose 4 children is 10C4 = 210   The number of ways to choose only boys is 6C4 = 15   The number of groups which include at least one girl is 195.   The answer is 195.
Answer: C
The banker's discount on Rs.1800 at 48% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time?	Choose the correct choice from the following answers
A) 1 months B) 4 months C) 5 months D) 6 months E) 7 months

Solution: Solution   S.I on Rs.1800 = T.D on Rs.1872.   P.W on Rs.1872 is Rs.1800.   Rs.72 is S.I on Rs. 1800 at 48%.   Time	=(100x72 / 48x1800)   = 1/12 year   = 1 months.   1 monthsnswer 1 months
Answer: A
If the cost price of 17 articles is same as the selling price of 25 articles. Find the gain or loss percentage?  Choose the correct option
A) 30% Gain	B) 30% Loss	C) 32% Loss	D) 40% Loss	E) 50% Loss

Solution: Explanation:   17 cp = 25 sp   32% Lossost price 32% LossP = 25   Selling price SP = 17   Formula = (SP-32% LossP)/32% LossP * 100 = (17 - 25)/25 * 100 = 32 % Loss   Answer: Option 32% Loss
Answer: C
A pool which was 2/3 full to begin with, was filled at a constant rate for 3/4 hours until it was until it was 3/4 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?
Answers.
A) 8 hrs 45 mins.  B) 9 hrs.  C) 9 hrs 30 mins.  D) 11 hrs 40 mins.  E) 15 hrs 30 mins

Solution: The pool was 2/3 full initially.   In 3/4 hrs, it was filled to 3/4 of its capacity.   Therefore, in 3/4 hrs, 3/4- 2/3 was the amount of volume filled.   So, 3/4 hrs = 3/4 - 2/3 = 1/12   Therefore, for filling the vessel from empty to full, you would require  3/4 * 12/1= 
 3/4 * 12/1 = 9
9 Hrs .   Hence 9 hrs.
Answer: B
The perimeter of a square and a rectangle is the same. If the rectangle is 12 cms. by 10 cms., then by what percentage is the area of the square more than that of the rectangle?
Choices.
A) 1	B) 3	C) 5/6	D) 1/2	E) 1/3

Solution: perimeter of rectangle=2*(12+10)= 
2*(12+10) = 44
44=perimeter of square   so side of square=44/4= 
44/4 = 11
11   area of rectangle=12*10= 
12*10 = 120
120   area of square=11*11= 
11*11 = 121
121   reqd%=(121-120)/120 *100=100/120=5/6   ANSWER:5/6
Answer: C
Alice can bake a pie in 5 minutes. Bob can bake a pie in 6 minutes. Compute how many more
pies Alice can bake than Bob in 60 minutes.	Choose the correct option:
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: Alice can bake 60/5= 
60/5 = 12
12 pies in 60 minutes. Bob can bake   60/6= 
  60/6 = 10
10 pies in 60 minutes.   Alice can therefore bake  12 - 10= 
 12 - 10 = 2
2 more pies than Bob.   correct answer 2
Answer: B
If Q + A < Q - A < A - Q, which of the following is correct?
Choose one.
A) A < Q < 0.	B) Q < A < 0.	C) Q < 0 < A.	D) 0 < B < A.	E) B > A > 0.

Solution: Check first inequality   Q + A < Q - A   A<-A   A is -ve   Check another equality   Q - A < A - Q   -2A<-2Q   A>Q   Combining both 0>A>Q   Option Q < A < 0. fits only   Ans Q < A < 0.
Answer: B
The captain of a cricket team of 11 members is 27 years old and the wicket keeper is 1 year older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?	Choose the correct option:
A) 20
B) 21
C) 22
D) 23
E) 24

Solution: Let the average age of the whole team be x years.   11x - (27 + 28) = 9 (x - 1)   11x - 9x = 46   2x = 46   x = 23.   The average age of the team is 23 years.   The answer is 23.
Answer: D
Some of the 50% solution of acid was removed and this was replaced with an equal amount of 20% solution of acid. As a result, a 35% solution of acid was obtained. What fraction of the original solution was replaced? Choose the correct choice from the following answers
A) 1/3 B) 1/2 C) 2/3 D) 3/5 E) 4/7

Solution: Let x be the fraction of the original solution that was replaced.   0.5*(1-x)+0.2(x)=0.35   0.3x=0.15   x=1/2   The answer is 1/2.
Answer: B
The area of a rectangle is 144 sq cm. Ratio of the breadth and the length of a rectangle 4:9.Find the area of the square whose side is equal to the length of the triangle?
Pick:  A) 525  B) 225  C) 400  D) 625  E) 324

Solution: Let the length and the breadth of the rectangle be l = 9x cm and b = 2x cm respectively. Let the side of the square be a cm.   4x*9x = 144   36x^2 = 144   x^2 = 4   x = 2   l = 9*2= 
9*2 = 18
18   area of the square= 18^2 = 324   Answer: 324
Answer: E
How many ways are there to award a gold, silver and bronze medal to 8 contending teams? Pick
A) 10 × 9 × 8
B) 8 * 7 * 6
C) 8!/3!
D) 876
E) 758

Solution: we clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 8 ways   if gold medal is given to 1 of the teams then only possible 7 teams can be considered for silver medal. we can do selection in 7 ways   similarly if gold and silver medals are awarded then only remaining 6 teams can be considered for a bronze medal. we can do the selection in 6 ways   Total number of ways to select the 3 possible medal winners = 8 * 7 * 6   Correct answer - 8 * 7 * 6
Answer: B
Ajay can ride 50km in 1 hour. In how many hours he can ride 1000km?
Choose the correct choice from the following
A) 10hrs	B) 15hrs	C) 20hrs	D) 25hrs	E) 18hrs

Solution: 1 hour he ride 50km   he ride 1000km in = 1000/50 * 1= 
1000/50 * 1 = 20
20hours   Answer is 20hrs
Answer: C
The length of the bridge, which a train 145 m long and traveling at 45 km/hr can cross in 30 sec is?  Answers.
A) 230  B) 240  C) 245  D) 250  E) 255

Solution: Speed = 45 * 5/18 = 25/2 m/sec.   Time = 30 sec   Let the length of bridge be x meters.   Then, (145 + x)/30 = 25/2   x = 230 m.   230nswer: Option 230
Answer: A
At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years? Choose the correct choice from the following.
A) 6  B) 6.5  C) 7  D) 7.5  E) 8

Solution: Let the rate be R% p.a. Then, 1200 x (1 + R/100)*(1 + R/100) = 1348.32 (1 + R/100)*(1 + R/100) = 134832/120000 = 11236/10000 (1 + R/100)*(1 + R/100) = (106/100)*(106/100) 1 + R/100 = 106/100 R = 6%   6nswer 6
Answer: A
What is the sum of two consecutive even numbers, the difference of whose squares is 84? Choose the correct answer:
A) 42
B) 84
C) 48
D) 24
E) 43

Solution: Let the numbers be x and x + 2.   Then, (x + 2)2 - x2 = 84   4x + 4 = 84   4x = 80   x = 20.   The required sum = x + (x + 2) = 2x + 2 + (  + 2)= 
+ (  + 2) = 2
2x + 2= 42.   42NSWER 42 42
Answer: A
The engineers subjected the engine to exhaustive tests.  Choose the correct choice from the following answers.
A) Complicated
B) Thorough
C) Exclusive
D) Compulsory
E) Compulsory2

Solution: Exhaustive means thorough, complete or in-depth. Hence, option-b is synonym of exhaustive.   Complicatednswer:Complicated
Answer: A
Quentin's income is 60% less than Sid's income, and Sam's income is 25% less than Quentin's income. If Sid gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?  Choices
A) 8/9 B) 11/12 C) 8/13 D) 11/13 E) 12/13

Solution: We can take some easy numbers and make calculations simpler.   Let R ( Sid's income) = 100   Q (Quentin's income) = 40%R = 40   S (Sam's income) = 75% Q = (3/4)*40= 
(3/4)*40 = 30
30   Now, if Sid gives 40% to Quentin --> Q= 40 + 40= 
40 + 40 = 80
80   60% given to Sam --> S= 30+60= 
30+60 = 90
90   The ratio is : Q/S= 80/90 = 8/9=8/9
Answer: A
If there are 30 cans out of them one is poisoned. If a person tastes very little he will die within 14 hours. So if there are mice to test in 24 hours, how many mice’s are required to find the poisoned can?  Answers:
A) 5 B) 4 C) 1 D) 2 E) 3

Solution: first we drink one cane to every rat...   after one hour again drink one cane to every rat...   and so on till 10 hour... In 10 hour every rat drink 10 cans so all rat drink 30 cans...   if A OR B OR C died from poison in 14th hour so they died from 1st cane OR 2nd cane OR 3rd cane respectively   if died in 15th hour they died from 4th,5th,6th cans respectively....so on   In 24th hour they died from 28th,29th,30th cans respectively...   so we can determine which cane is poisoned..   ANSW3R:3
Answer: E
If xerox paper costs 5 cents a sheet and a buyer gets 10% discount on all xerox paper one buys after the first 200 papers and 20% discount after first 1000 papers, how much will it cost to buy 2500 sheets of xerox paper? Choose the correct choice from the following answers
A) $125 B) $106 C) $135 D) $90 E) $100

Solution: 30 sec approach - solve it using approximation   2500 sheet at full price, 5 cent = 125   2500 sheet at max discount price, 4 cent = 100   Your ans got to be between these two.   Ans $106 it is.
Answer: B
2 men dug a swimming pool in 30 days. If they used 15 men to dig another similar pool, how long will it take?  Select the correct option.
A) 5
B) 10
C) 6
D) 4
E) 2

Solution: M1*41=M2*42   2*30=15*42 => 42=4   Answer:4
Answer: D
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 16000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is Choose the most appropriate option:	A) 20	B) 21	C) 22	D) 35	E) NONE

Solution: Sol.   Let the total number of workers be x. Then,   8000x = (16000 × 7) + 6000 ( x – 7)   ‹=› 2000x = 70000   ‹=› x = 35.   Answer 35
Answer: D
A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets
Choose the correct choice from the following options
A) 30 %	B) 50 %	C) 60 %	D) 70 %	E) 80 %

Solution: Number of runs made by running = 110 - (3 x 4 + 8 x 6)   = 120 - (60)= 
120 - (60) = 60
60   Now, we need to calculate 60 is what percent of 120.=> 60/120 * 100= 
60/120 * 100 = 50
50 %   50 %
Answer: B
Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.
Year	Item of Expenditure
Salary	Taxes and Transport	Bonus	Interest on Loans	Fuel
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98
The total amount of Taxes paid by the company during the given period is approximately what percent of the total amount of salary paid during this period? Choose the correct choice from the following answers
A) A)0.5%  B) B)1.5%  C) C)1.25%  D) D)1%  E) E)4%

Solution: Required percentage   =	(288 + 342 + 324 + 336 + 420)   =	[	17	x 100	]	%   1710   ~= 1%.   Answer : 1%
Answer: D
In a zoo, there are deers and ducks. If the heads are counted, there are 180, while the legs are 448. What will be the number of deers in the zoo?  Choose the correct choice from the following.
A) 136	B) 68	C) 44	D) 22	E) NOne

Solution: Solution: Average legs per head = 448/180.   Deers: Ducks = 88: 272   Hence,the number of Deers = (180*88)/360= 
(180*88)/360 = 44
44.   Answer: Option 44
Answer: C
H.C.F of 3240, 3600 and a third number is 36 and their L.C.M is 24 * 35 * 52 * 72. The third number is:  Choices:
A) 22 * 35 * 72 B) 22 * 53 * 72 C) 25 * 52 * 72 D) 23 * 35 * 72 E) 23 * 35 * 78

Solution: 3240 = 23 * 34 * 5; 3600 = 24 * 32 * 52   H.C.F = 36 = 22 * 32   Since H.C.F is the product of lowest powers of common factors, so the third number must have (22 * 32 ) as its factor.   Since L.C.M is the product of highest powers of common prime factors, so the third number must have 35 and 72 as its factors.   Third number = 22 * 35 * 72   22 * 35 * 72NSWER:22 * 35 * 72
Answer: A
A is twice as good a work man as B and together they finish a piece of work in 14 days.The number of days taken by A alone to finish the work is :
Select
A) 11 B) 21 C) 28 D) 42 E) 45

Solution: Solution   (A’s 1 day’s work): (B’s 1 day’s work)= 2 : 1.   (A + B)'s 1 day’s work = 1/14   Divide 1/14in the ratio 2 : 1.   ∴ A’s 1 day’s work = (1/14 x 2/3)= 1/21   Hence,A alone can finish the work in 21 days.   Answer 21
Answer: B
A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?	Choose one:
A) 26.34 litres	B) 27.36 litres	C) 28 litres	D) 29.16 litres	E) 30 litres

Solution: Amount of milk left after 3 operations = [40(1 -4/40)^3] litres   =40 x 9/10 x 9/10 x 9/10	= 29.16 litres   Answer:29.16 litres
Answer: D
In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?  Answers:
A) 8 sec
B) 1 sec
C) 9 sec
D) 6 sec
E) 2 sec

Solution: T = 60/36 * 18/5= 
60/36 * 18/5 = 6
6 sec   Answer:6 sec
Answer: D
500, 250, 750, 375...  Choose the correct option:  A) 875  B) 1050  C) 950  D) 1125  E) 925

Solution: 500/2= 
500/2 = 250
250 x 3= 750/2= 
750/2 = 375
375 x 3=1125   Answer is 1125
Answer: D
All of the students of the Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 112 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only?  Choose the correct choice from the following answers.
A) 48
B) 50
C) 52
D) 54
E) 56

Solution: 50% of students are in the band only, so 30% of students are in the orchestra only.   Since 20% of students are in both, then 70% of students are in the band which is 112 students.   The number of students in the orchestra is (30%/70%)*112 = 48.   The answer is 48. (30 /70 )*112= 
 (30 /70 )*112 = 48
48.   The answer is 48.
Answer: A
In what time will a train 100 m long cross an electric pole, it its speed be 54 km/hr?
Choose the correct choice from the following answers:
A) 2.5
B) 2.9
C) 6.67
D) 2.8
E) 2.1

Solution: Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec   Time taken= 100/15   = 6.67 sec.   Answer:6.67
Answer: C
For any triangle T in the xy–coordinate plan, the center of T is defined to be the point whose x–coordinate is the average (arithmetic mean) of the x–coordinates of the vertices of T and whose y–coordinate is the average of the y–coordinates of the vertices of T. If a certain triangle has vertices at the points (0,0) and (6,0) and center at the point (3,1), what are the coordinates of the remaining vertex?
Options
A) (3,3)	B) (3,6)	C) (4,9)	D) (6,4)	E) (9,6)

Solution: Let (a,b) be the remaining vertex.   x: 0 + 6 + a = 3*3. Then a = 3.   y: 0 + 0 + b = 3*1.= 
3*1. = 3
3.   The answer is (3,3).
Answer: A
The fourth proportional to 10, 20 and 25 is?
Options.
A) 21 B) 66 C) 88 D) 50 E) 26

Solution: (20*25)/10= 
(20*25)/10 = 50
50   Answer: 50
Answer: D
What least number should be subtracted from 13602 such that the remainder is divisible by 87 ?	Select the correct option.
A) 27  B) 29  C) 28  D) 30  E) 31

Solution: 13602 ÷ 87 = 156, remainder = 30   Hence 30 is the least number which can be subtracted from 13602 such that the remainder   is divisible by 87   Answer is 30
Answer: D
A retailer buys 40 pens at the market price of 36 pens from a wholesaler ,if he sells these pens giving a discount of 1% ,what is the profit % ? Choose the correct choice from the following options.
A) 2% B) 7% C) 9% D) 5% E) 10%

Solution: let the market price of each pen be Rs 1   then,C.P of 40 pens = Rs 36 S.P of 40 pens =99% of Rs 40=Rs 39.60   profit %=((3.60*100)/36)= 
((3.60*100)/36) = 10
10%   Ans: 10%
Answer: E
Of the 800 employees of Company X, 500 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 40 percent ?	Answers:  A) 200  B) 160  C) 112  D) 133.33  E) 56

Solution: The # oflong-termemployees is 50%*800=400.   After y of them retire new # oflong-termemployees would become 400-y.   Total # of employees would become 800-y.   We want 400-y to be 40% of 800-y --> 400-y=(800 -y)*40% --> y = 133.33.   Answer: 133.33.
Answer: D
In what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually?
Choose the correct choice from the following answers: A) 5 B) 3 C) 4 D) 2 E) 6

Solution: Principal = Rs. 1000; Amount = Rs. 1331; Rate = 10% p.a. Let the time be n years. Then,[ 1000 (1+ (10/100))^n ] = 1331 or (11/10)^n = (1331/1000) = (11/10)^3n = 3 years Answer : 3
Answer: B
An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m? Choices:
A) 4082.46  B) 4082.49  C) 4082.44  D) 4082.4  E) 4082.41

Solution: Length of the first carpet = (1.44)(6) = 8.64 cm   Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)   = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m   Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40.Answer: 4082.4
Answer: D
A train 250m long passes a man, running at10 km/hr in the same direction in which the train is going, in 20 seconds. The speed of the train is: Choose the correct answer
A) 100  B) 60  C) 55  D) 50  E) 45

Solution: Speed of the train relative to man =250/20 m/sec   =25/2 m/sec.   =25	/2x18/5km/hr   = 45 km/hr.   Let the speed of the train be x km/hr. Then, relative speed = (x -10) km/hr.   x - 10= 45 =55 km/hr.   Answer:55
Answer: C
A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?	Select:
A) 228 m
B) 150 m
C) 276 m
D) 255 m
E) 212 m

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 100)/25 = x/15 => x   = 150 m.   Answer:150 m
Answer: B
In a game of 40 points; A can give B 5 points and C 15 points. Then how many points B can give C in a game of 35 ?
Options
A) can give C 10 points B) can give C 4 points C) can give C 2 points D) can give C 6 points E) can give C 8 points

Solution: A: B = 40 : 35, A : C = 40 : 25.   B/C = ( B/ A * A/C) = (35 / 40 * 40 / 25) = 35/25 = 7/5 = 35: 25   Therefore ,In a game of 35, B can give C 10 points.   can give C 10 pointsnswer is can give C 10 points.
Answer: A
By how much is two-fifth of 350 greater than four- seventh of 210 ?  Choose the correct choice
A) 95	B) 110	C) 20	D) None of these	E) Cannot be determined

Solution: Solution   2/5of 350 - 4/7of 210 = 20.   Answer 20
Answer: C
A certain tire company can produce tires at a cost of $22,500 per batch plus $7 per tire. The company can sell tires to the wholesaler at a cost of $20 per tire. If a batch of 15,000
tires is produced and sold, what is the company’s profit per tire?	Choose the correct choice from the following choices:
A) $9.00
B) $9.50
C) $11.00
D) $11.50
E) $20.00

Solution: CP(15000 tires) = $22500 +($7×15000) =$127500   SP (15000 tires) = $20×15000 = $300000   Profit = SP-CP   = $300000-$127500= $172500   PROFIT/TIRE 300000- 127500= 
300000- 127500 = 172_500
$172500   PROFIT/TIRE= $172500/15000= 
172500/15000 = 23/2 = around 11.5
$11.50   Answer $11.50
Answer: D
A farmer spent $37 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 20% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined? Pick one.
A) $37.80
B) $38.50
C) $39.20
D) $39.50
E) $40.70

Solution: A farmer spent 40% money on chicken feed, so he spent 0.4*$37=$14.8 on chicken feed, thus he spent the remaining 37-14.8 0.4* 37= 
 0.4* 37 = 14.8
$14.8 on chicken feed, thus he spent the remaining   37-14.8= 
  37-14.8 = 22.2
$22.2 on goat feed.   Now, since he bought chicken feed at a 20% discount then the original price of it was x*0.8=$14.8 --> x=$18.5.   Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 18.5+22.2=$40.7.   Answer: $40.70
Answer: E
A husband and wife can complete a certain task in 1 and 2 hours respectively. Their children, Rae and Herman, can complete the same task in 5 and 6 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task?  Choose the correct answer
A) a)11:45  B) b)3:10  C) c)12:23  D) d)5:18  E) e)10:3

Solution: couples one hour work=1/1+1/2=3/2   so total time=2/3..   now, kids one hour work=1/5+1/6=11/30   so total time=30/11..   ratio=2/3:30/11=11/45   ans a)11:45
Answer: A
For what values of k will the pair of equations 3x + 4y = 12 and (kx + 12y)/2 = 15 does not have a unique solution?  Select.
A) 12
B) 9
C) 3
D) 7.5
E) 2.5

Solution: we have 2 equations   1. 3x + 4y = 12 -- > 9x + 12y = 36   2. (kx + 12y)/2 = 15 --> kx + 12y = 30   substract 1-2, we get (9-K)x = 6   i.e. x = 6/(9-k)   then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is 9
Answer: B