MU-NLPC/Calc-aqua_rat huggingface dataset:
The ‘moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement Z for his trip along the moving walkway?  Choose the correct choice from the following:
A) 2 feet per second
B) 2.5 feet per second
C) 3 feet per second
D) 4 feet per second
E) 5 feet per second

Solution: I get E.   Their rate is 3 ft/sec and his is 6 ft/sec. Their distance is d-120 and his distance is d.   So we get two equations:   3t=d-120   6t=d   Substituting, we get 3t=6t-120, or t=40 which means that d=240 so Bill traveled 240 ft and they traveled 120 ft. (They were at 240 on the conveyor belt when they met.   So, Bill's average rate of movement is Z:   He traveled 6 ft/sec for 240 ft and 40 seconds. He traveled 3 ft/sec for the remaining 60 ft for 20 seconds.   (240+60)/(20+40)= 
(240+60)/(20+40) = 5
5 ft/sec=5 feet per second
Answer: E
The average of runs of a cricket player of 10 innings was 40. How many runs must he make in his next innings so as to increase his average of runs by 4? Choose the correct choice from the following:	A) 87	B) 16	C) 10	D) 84	E) 17

Solution: Average after 11 innings = 44   Required number of runs   = (44* 11) - (40* 10) = 484- 400= 
484- 400 = 84
84.   Answer: 84
Answer: D
The average age of the district level hockey team of eleven is 26 years.The average age gets increased by 2 year when the coach age is also included.what is the age of the coach ?  Answers:
A) 40 yrs.
B) 50 yrs.
C) 45 yrs.
D) 48 yrs.
E) 52 yrs.

Solution: Explanation:   Total age of players in team = 26 x 11 = 286   When coach is included, total members = 12, Avg age increases by two becomes 28   Total age when coach is included = 28x12 = 336   Age of coach = 336-286= 
336-286 = 50
50 yrs.   Answer: 50 yrs.
Answer: B
A glucose solution contains 20 grams of glucose per 1000 cubic centimeters of solution. If 500 cubic centimeters of the solution were poured into an empty container, how many grams of glucose would be in the container?
Pick one
A) 10.00 B) 15.00 C) 11.50 D) 10.50 E) 9.75

Solution: We are given that a glucose solution contains 20 grams of glucose per 1000 cubic centimeters of solution. Since we are dealing with a solution, we know that the grams of glucose is proportional to the number of cubic centimeters of solution. Thus, to determine how many grams of glucose would be in the container when we have 500 cubic centimeters of solution, we can set up a proportion.   We can say: “20 grams of glucose is to 1000 cubic centimeters of solution as x grams of glucose is to 500 cubic centimeters of solution.” Let’s now set up the proportion and solve for x.   20/1000 = x/500   When we cross multiply we obtain:   (20)(500) = 1000x   10000 = 1000x   10 = x   There are 10.00 grams of glucose in the solution in the container.   The answer is 10.00.
Answer: A
The area of a triangle is with base 3m and height 4m?  Choose the correct choice from the following choices:
A) 4 m2 B) 6 m2 C) 18 m2 D) 19 m2 E) 12 m2

Solution: 1/2 * 3 * 4= 
1/2 * 3 * 4 = 6
6 m2   Answer: 6 m2
Answer: B
Which of the following is divisible by the first six positive integer multiples of 19?
(i) 52440
(ii) 114600
(iii) 19038	Select:
A) None
B) i only
C) iii only
D) ii and iii only
E) i and ii only

Solution: A positive integer x is divisible by 19, 2*19,...,6*19 if and only if it is divisible by their least common multiple, which in this case is 3*4*5*19. In particular, x is divisible by 10, so iii is not divisible by the first six positive integer multiples of 19.   3*4*5*19=60*(20-1)= 
60*(20-1) = 1_140
1140. 1140*100=114000, so clearly (ii) is not divisible by the first six positive integer multiples of 19.   It remains to verify (i). 52440-40*1140=52440-45600= 
52440-45600 = 6_840
6840=6*1140, so (i) is divisible by 1140.   Answer i only.
Answer: B
Machine A and machine W are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine W. Machine W produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?  Choose one:	A) 6	B) 6.6	C) 60	D) 100	E) 110

Solution: [Reveal]Spoiler:   TimeW: 660/x   Time6: [660/x+10]   660/x = [660/x+10] *110/100   660/x =66*11/x+10   660x+10= 66*11*x   660x +6600 = 66*11*x   x= 100   plug in back to time6   660/100+10 => 660/110= 
660/110 = 6
6=6
Answer: A
A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B ?	Choose the correct option: A) 160 km B) 180 km C) 200 km D) 220 km E) 240 km

Solution: Down Stream Speed :(14+4)km/hr =18 km/hr   Up Stream Speed:(14-4)km/hr=10km/hr   (x/18)+(x/2/20)=19   x=180km   ANSWER:180 km
Answer: B
A cube has a volume of 27 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?  Answers:
A) 216 B) 48 C) 64 D) 80 E) 100

Solution: Volume = 27 = side^3   i.e. Side of Cube = 3   New Cube has dimensions 6, 6, and 6 as all sides are twice of teh side of first cube   Volume = 6*6*6= 
6*6*6 = 216
216 square feet   216nswer: option 216
Answer: A
Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion. In 16 years from now, Lyn the circus Lion will be exactly half as old as Ele, the circus Elephant. How old is Ele today? Pick:
A) 47
B) 48
C) 43
D) 42
E) 41

Solution: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion.   Ele = 3*Lyn   Usually, ages are integers so there is a good possibility that the age of Ele is 48 (the only option that is a multiple of 3).   Then age of Lyn would be 16. In 16 yrs, Ele would be 64 and Lyn would be 32 - so Lyn would be half as old as Ele.   Answer (48)
Answer: B
What is the smallest number which when increased by 3 is divisible by 18, 70, 100 and 21?	Choose the correct answer:	A) 5037	B) 5447	C) 5867	D) 6297	E) 6617

Solution: When increased by 3, the number must include at least 2^2*3^2*5^2*7 = 6300   The answer is 6297.
Answer: D
What is the probability of flipping a fair coin four times and the coin landing on heads on exactly three flips?
Choose the correct answer.
A) 1/3
B) 1/4
C) 2/3
D) 2/5
E) 1/8

Solution: Probability = (Favorable combination)/(Total combination)   Favorable combination = (HHHT, HHTH, HTHH,THHH) ==> 4   Total combination = 8 (2^4)   Probability = (4)/(16) = 1/4   (1/4)
Answer: B
Rectangular Floors X and Y have equal area. If Floor X is 14 feet by 18 feet and Floor Y is 9 feet wide, what is the length of Floor Y, in feet? Choose the correct choice from the following: A) 13 1/2 B) 18 C) 18 3/4 D) 21 E) 28

Solution: The area of a rectangle is: Area = length x width   We are given that floor X is 14 feet by 18 feet and that floor Y is 9 feet wide. So we can say:   length of X = 14   width of X = 18   width of Y = 9   length of Y = n   We also can say:   Area of Floor X = Area of Floor Y   (length of X)(width of X) = (length of Y)(width of Y)   (14)(18) = 9n   (14)(2) = n   28 = n   Answer 28.
Answer: E
There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability W that the number of men is equal to that of women?
Choose the correct answer
A) W=18/35	B) W=16/35	C) 14/35	D) 13/35	E) 12/35

Solution: METHOD-1:   Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6= 
6*6 = 36
36   Total ways of selecting 4 out of 8 Students= 8C4 = 8! / (4! * 4!) = 70   Probability = 36/70 = 18/35   A   METHOD-2:Also see the mistake done by the person who posted this question   Probability of First selected person being Man = 4/8   Probability of Second selected person being Man = 3/7   Probability of First selected person being Woman = 4/6   Probability of Second selected person being Woman = 3/5   i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35   The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here   When we take the probability of each case like we have have taken in this method then it always include W=18/35RRW=18/35NGEMENTS as well and so we have to take every arrangement of the events as well   The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!   W=18/35
Answer: A
If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many Z such committees are possible?  Choose the correct option
A) 20 B) 40 C) 50 D) Z=80 E) Z=120

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: 5C3=10.   But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.   Total # of ways: 5C3*2^3=80.   Answer: Z=80.
Answer: D
A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet? Choose the correct choice from the following:
A) 09:30 p.m B) 11:23 p.m C) 10:30 p.m D) 07:30 p.m E) 05:93 p.m

Solution: D = 70 * 1 ½ = 105 km   RS = 85 – 70 = 15   T = 105/15= 
105/15 = 7
7 h     3.30 + 7= 
  3.30 + 7 = 10.3
10.30 p.m.   Answer: 10:30 p.m
Answer: C
4, 5, 7, 11, 19, (...)  Answers:
A) 32
B) 22
C) 35
D) 27
E) 28

Solution: 4   4 × 2 - 3 = 5   5 × 2 - 3 = 7   7 × 2 - 3 = 11   11 × 2 - 3 = 19   19 × 2 - 3 = 35   Answer is 35
Answer: C
Two pyramids are thrown with faces 1,2,4,6. Find the probability to get a sum of even number on an their faces? Choose the correct answer.
A) 5/8  B) 3/4  C) 1/4  D) 7/4  E) 3/5

Solution: 1 pyramid can show 4 different kind of arrangements   1,2,4=7   1,2,6=9   1,4,6=11   2,4,6=12   So, out of 4 outcomes   3 are odd and 1 is even.   In question given two pyramids are thrown.   So, to make some of their faces as even   Condition 1: some of both individual faces of each pyramid is odd   3/4 * 3/4   =9/16   Condition 2: some of both individual faces of pyramid is even   1/4 + 1/4   =1/16   Total such conditions = 9/16 + 1/16   = 10/16   = 5/8   5/8NSWER:5/8
Answer: A
A certain number when divided by 39 leaves a remainder 17, what is the remainder when the same number is divided by 13?	Pick one:
A) 7  B) 8  C) 9  D) 6  E) 4

Solution: 4xplanation:     39 + 17= 
  39 + 17 = 56
56/13= 4 (Remainder)   Answer: 4
Answer: E
Average of all prime numbers between 30 to 50 Choose one.
A) 37 B) 37.8 C) 39 D) 39.8 E) 40

Solution: Explanation:   Prime numbers between 30 and 50 are:   31, 37, 41, 43, 47   Average of prime numbers between 30 to 50 will be   (31+37+41+43+47 / 5)=199 / 5= 
199 / 5 = 199/5 = around 39.8
39.8   Option 39.8
Answer: D
A snail, climbing a 42 feet high wall, climbs up 4 feet on the first day but slides down 2 feet on the second. It climbs 4 feet on the third day and slides down again 2 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall?	Choices.
A) 20	B) 26	C) 32	D) 39	E) 51

Solution: total transaction in two days = 4-2= 
4-2 = 2
2 feet   in 38 days it will climb 38 feet   on the 39th day , the snail will climb 4 feet , thus reaching the top   therefore , total no of days required=39   39
Answer: D
Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then	Choose the correct choice from the following:
A) XB > CD
B) XB < YD
C) AX > XB
D) AX < CD
E) AX > AB

Solution: A--X------B   C-----Y---D   AX < CD.   Answer: AX < CD.
Answer: D
The letters D, G, I, I , and T can be used to form 5-letter strings as DIGIT or DGIIT. Using these letters, how many 5-letter strings can be formed in which the two occurrences of the letter I are separated by at least one other letter?
Choose the correct choice from the following choices.
A) 12  B) 18  C) 24  D) 36  E) 48

Solution: Total no of ways arranging 5 letter with one letter redundant is 5!/2!=60   No of ways two I's can be together 4!=24   no of ways at least one alpha is between two I's =60-24= 
60-24 = 36
36   ANS:36
Answer: D
A 8% stock yields 20%. The market value of the stock is: Choose the correct choice:  A) Rs 48  B) Rs 45  C) Rs 40  D) Rs 50  E) Rs 55

Solution: Explanation:   For an income of Rs. 20, investment = Rs. 100.   For an income of Rs 8, investment =Rs.100/20 X8 =Rs 40   Market value of Rs. 100 stock = Rs 40   Answer is Rs 40
Answer: C
At what rate percent on simple interest will Rs.750 amount to Rs.825 in 5 years?  Select
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: 75 = (750*5*R)/100   R = 2%.2nswer: 2
Answer: A
In the formula V = 1/(2r)^3, if r is halved, then V is multiplied by?  Choose the correct choice from the following choices:
A) 16 B) 8 C) 1 D) 1/8 E) 1/64

Solution: Say r=1 => V1 = 1/8   when r=1/2; V2 = 1   V2 = 1*V1.   Answer : 8
Answer: B
If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
Choose the correct choice from the following options:  A) 0  B) 1  C) 2  D) 3  E) None of these

Solution: Explanation:   Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.   x = 2.   ANSWER IS 2
Answer: C
A vending machine randomly dispenses four different types of fruit candy. There are twice as many apple candies as orange candies, twice as many strawberry candies as grape candies, and twice as many apple candies as strawberry candies. If each candy cost $0.4, and there are exactly 90 candies, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy?  Choose the correct option
A) $3.00 B) $20.75 C) $33.20 D) $42.75 E) $45.00

Solution: Let number of Apple , Orange , strawberry and grape candies be A, O ,S and G respectively .   A= 2O   S= 2G   A= 2S   A= 4G   A+O+S+G = 90   =>A + A/2 + A/2 +A/4 = 90   => 9A/4 = 90   => A = 40   O = 20   S = 20   G = 10   Cost of each candy = .25 $   Mininum amount of money required to guarantee that you would buy at least three of each type of candy   We can buy 40 Apple candies , 20 orange candies , 20 strawberry candies and 3 grape candies to ensure atleast 3 of each type of candies .   Total = 83 candies   Amount required = 83 * .4= 
83 * .4 = 33.2
33.20 $   Answer $33.20
Answer: C
A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $5 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?	Choose the correct choice from the following answers:	A) $28	B) $82	C) $110	D) $138	E) $195

Solution: by the question, the equation would be 150 p - 85*150 - 16500 = 0   p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component.   solving the equation, we get p = $ 195. Answer $195 for me.
Answer: E
A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform? Choose the correct choice from the following choices.
A) 277 m  B) 240 m  C) 627 m  D) 892 m  E) 288 m

Solution: Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Length of the train= 15 * 20= 
15 * 20 = 300
300 m.   Let the length of the platform be x m . Then,   (x + 300)/36= 15 => x   = 240 m.   Answer: 240 m
Answer: B
If two positive numbers are in the ratio 1/9 : 1/5, then by what percent is the second number more than the first? Options:
A) 80%  B) 90%  C) 60%  D) 50%  E) 65%

Solution: Given ratio = 1/9 : 1/5 = 5 : 10   Let first number be 5x and the second number be 9x.   The second number is more than first number by 4x.   Required percentage = 4x/5x * 100 = 80%.   80%nswer:80%4 /5  * 100= 
4 /5  * 100 = 80
80%.   80%nswer:80%
Answer: A
A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 8:00 a.m., at what time was it one-eighth full? Choose the correct choice from the following options
A) 9:00 a.m.	B) 7:00 a.m.	C) 6:00 a.m.	D) 4:00 a.m.	E) 2:00 a.m.

Solution: To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/8*4=1/2, as it quadruples every hour then container was one-eighth full at 8:00 a.m -1 hour = 7:00 a.m.   Answer: 7:00 a.m..
Answer: B
C and D enter into partnership with capital as 7:9. At the end of 8 months, C withdraws. If they receive the profits in the ratio of 8:9 find how long D's capital was used? Choose the correct choice from the following:	A) months	B) months	C) months	D) months	E) months

Solution: 7 * 8 : 9 * x = 8:9 => x= 7   ANSWER:months
Answer: D
A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 1,600 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
Choose the correct option.
A) 5.55%  B) 5.65%  C) 5.75%  D) 5.85%  E) 5.95%

Solution: The amount of sodium chloride is 0.05*10,000 = 500 gallons   500/8400 = 5/84 which is about 5.95%   The answer is 5.95%.
Answer: E
The product of two successive numbers is 4160. Which is the smaller of the two numbers?  Pick one
A) 78 B) 64 C) 88 D) 67 E) 37

Solution: 64   4160   From the given alternatives,   64 × 65 = 4160   ∴ Smaller number = 64
Answer: B
A basket has 6 apples and 4 oranges. FOUR fruits are picked at random. The probability that at least 3 apples are picked is Choose the correct choice from the following choices
A) 25/42
B) 25/48
C) 19/42
D) 25/47
E) 25/43

Solution: Total fruits = 10Since there must be at least two apples,(619/423 * 419/421)/1019/424 + 619/424/1019/424 = 19/42.Answer:19/42
Answer: C
A man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?  Pick one:
A) 271 km
B) 224 km
C) 243 km
D) 222 km
E) 215 km

Solution: B   224 km   Let the total distance be x km.   Then, [(1/2 x) / 21 + (1/2 x) / 24] = 10   15x = 168 * 20 => x = 224 km.
Answer: B
The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
Select the correct option.
A) 16 2/3% loss B) 16 8/3% loss C) 19 2/3% loss D) 13 2/3% loss E) 26 2/3% loss

Solution: 15 CP = 18 SP   18 --- 3 CP loss   100 --- ? => 16 2/3% loss   16 2/3% lossnswer: 16 2/3% loss
Answer: A
A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
Choose the correct answer:
A) 288  B) 286  C) 298  D) 2776  E) 8811

Solution: 2*12 : 3*12 : 4*24   1: 3: 4   1/8 * 3200= 
1/8 * 3200 = 400
400   Answer:2776
Answer: D
On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.6, what is the probability that Malachi will return home at the end of the day on the following Monday?
Choose the correct option
A) 0.096
B) 0.125
C) 0.128
D) 0.512
E) 0.64

Solution: Re-phrasing the question:   What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain   Probability of rain = 0.6   Therefore, probability of no rain = 0.4   0.6*0.6*0.4 = 0.096   Hence 0.096
Answer: A
How many combinations of three letters taken from letters (a, b, b, c, c, d) are possible?
Pick.
A) 10	B) 13	C) 35	D) 36	E) 56

Solution: So 4C3 for abcd - 4 choices   3 more for bb(a,c or d)   3 more for cc(a,b or d)   total 10   10ns :10
Answer: A
If x#y is defined to equal x^3/y for all x and y, then (-1#2)#3 =
Choose the correct choice from the following options.
A) 4/3	B) 1/3	C) 1/12	D) -1/12	E) 1/24

Solution: (-1)^3 / 2 = 1/2   (1/2)^3 / 3 = 1/24   so 1/24 is my answer
Answer: E
A part-time employee’s hourly wage was increased by 25%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased? Choose the correct answer
A) 9%
B) 15%
C) 20%
D) 50%
E) 100%

Solution: Let's plug in somenicenumbers and see what's needed.   Let's say the employee used to make $1/hour and worked 100 hours/week   So, the TOTAL weekly income was $100/week   After the 25% wage increase, the employee makes $1.25/hour   We want the employee's income to remain at $100/week.   So, we want ($1.25/hour)(new # of hours) = $100   Divide both sides by 1.25 to get:   new # of hours = 100/1.25   ≈ 80 hours   So, the number of hours decreases from 100 hours to (approximately) 80 hours.   This represents a 20% decrease (approximately) .   Answer : 20%
Answer: C
Find the median of the data 25, 37, 47, 18, 19, 26, 36. Choose the correct choice from the following options:
A) 22
B) 23
C) 24
D) 25
E) 26

Solution: Arranging the data in ascending order, we get 18, 19, 25, 26, 36, 37, 47   Here, the number of observations is odd, i.e., 7.   Therefore, median = (n + 1/2)th observation.   = (7 + 1/2)th observation.   = (8/2)= 
(8/2) = 4
4th observation.   4th observation is 26.   Therefore, median of the data is 26. ANSW26R :26
Answer: E
Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother three years younger to her was born. What is the difference between the ages of her parents?  Choose the correct answer
A) 2 years  B) 4 years  C) 5 years  D) 7 years  E) 8 years

Solution: Mother's age when Ayesha's brother was born = 36 years.   Father's age when Ayesha's brother was born = (38 + 3)= 
(38 + 3) = 41
41 years.   Required difference= (41 - 36)= 
(41 - 36) = 5
5 years.   Answer: Option 5 years
Answer: C
A batch of cookies was divided among three tins: 2/3 of all the cookies were placed in either the blue tin or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction E of the cookies that were placed in the other tins were placed in the green tin?
Choose one:  A) 15/2  B) 9/4  C) 5/9  D) 7/5  E) 9/7

Solution: Blue tin or red tin: 2/3 (N)   Red tin: (1/3)N   Blue tin: (1/4)N   What the last statment meant, is it wants this fraction: (# of cookies in green tin)/(# of cookies in red and green tin)   # of cookies in green tin = 2N/3 - N/4 = 8N- 3N/12 = 5N/12   # of cookies in red and green tin = N/3 + 5N/12 = 9N/12   Fraction E= 5N/12 * 12/9N = 5/9 (5/9)
Answer: C
If the cost price is 96% of the selling price, then what is the profit percent?	Choose the correct option.
A) 4.17% B) 5% C) 6.12% D) 3.25% E) 5.75%

Solution: Let S.P. = $100   C.P. = $96   Profit = $4   Profit% = 4/96 * 100 = 25/6 = 4.17%   4.17%nswer is 4.17%
Answer: A
It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is?  Choose the correct choice from the following answers.
A) 2:9
B) 3:1
C) 3:4
D) 3:9
E) 3:6

Solution: Let the speed of the train be x km/hr and that of the car be y km/hr.   Then, 120/x + 480/y = 8 or 1/x + 4/y   = 1/15 --- (i)   And, 200/x + 400/y = 25/3 or 1/x + 2/y   = 1/24 --- (ii)   Solving (i) and (ii), we get x = 60 and y   = 80   Ratio of speeds = 60:80 = 3:4   Answer:3:4
Answer: C