MU-NLPC/Calc-aqua_rat huggingface dataset:
A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is? Choose the correct choice from the following
A) 677 m B) 456 m C) 500 m D) 663 m E) 757 m

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (800 + x)/60 = 65/3   x = 500 m.   Answer: 500 m
Answer: C
Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel two times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?	Choose the correct choice from the following options:
A) 4	B) 3	C) 8	D) 9	E) 12

Solution: W: the time for Wyane to do the job   S: the time for his son to do the job   We have 1/W + 1/S = 1/2 and W = 2S   Then we have 1/(2*S) + 1/S = 1/2 <=> 3/(2*S) = 1/2<=> S = 3   ANS: 3
Answer: B
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 S for his trip along the moving walkway?
Choose the correct choice.
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 S is:   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
A number when divided by a certain divisor left remainder 245, when twice the number was divided by the same divisor, the remainder was 112. Find the divisor?  Choose the most appropriate option:  A) 378  B) 365  C) 380  D) 456  E) 460

Solution: Easy solution:   N= Dq1+245   2N = 2Dq1 + 490 - (1)   2N = Dq2 + 112 - (2)   As (1) = (2) = 2N   D*(q2-2q1) = 378   D * Some integer = 378   Checking all options only (A) syncs with it.   378nswer 378
Answer: A
The cost price of 20 arƟcles is the same as the selling price of x arƟcles. If the profit is 25%, find out
the value of x  Choose the correct choice from the following answers.
A) 13 B) 14 C) 15 D) 16 E) 17

Solution: Explanation:   Let the Cost Price of one arƟcle = Rs. 1   CP of x articles = Rs. x   CP of 20 articles = 20   Selling price of x articles = 20   Profit = 25% [Given]   ⇒   (SP−CPCP)=25100=14   ⇒   (20−x)x=14   ⇒   80−4x=x   ⇒   5x=80   ⇒   x=805=16   Answer: 16
Answer: D
In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate	Choose the correct choice from the following answers.
A) 356000  B) 356500  C) 357000  D) 400000  E) None of these

Solution: Total number of invalid votes = 15 % of 560000   = 15/100 × 560000   = 8400000/100= 
8400000/100 = 84_000
84000   Total number of valid votes 560000 – 84000= 476000   Percentage of votes polled in favour of candidate A = 75 %   Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000   = 75/100 × 476000   = 35700000/100= 
35700000/100 = 357_000
357000   357000)
Answer: C
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?	Select:  A) 276 m  B) 167 m  C) 245 m  D) 167 m  E) 178 m

Solution: Speed = [45 X 5/18] m/sec   = [25/2] m/sec Time   = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30   = 25/2 => 2(130 + x) = 750 => x   = 245 m.   Answer:245 m
Answer: C
What is the area of a square field whose diagonal of length 10 m?	Pick one:
A) 50  B) 70  C) 60  D) 20  E) 25

Solution: d2/2 = (10 * 10)/2= 
(10 * 10)/2 = 50
50   50nswer:50
Answer: A
In a certain town, there are eight times as many people who were born in the town’s state as there are people who were born in another state or country. The ratio of those residents born in the town’s state to the town’s total population is  Choose one:  A) 1 to 4  B) 1 to 3  C) 1 to 2  D) 3 to 4  E) 8 to 9

Solution: Town state: 8 times the whole town or country   then ratio will be 8(times)/9 total(times)   So the answer is 8/9.   8 to 9
Answer: E
Find the sum of all odd numbers up to 100. Options
A) 2500	B) 2400	C) 2300	D) 2200	E) 2100

Solution: The given numbers are 1, 3, 5, 7, ..., 99.   This is an A.P. with a = 1 and d = 2.   Let it contain n terms. Then,   1 + (n - 1) x 2 = 99 or n = 50.   Required sum = n/2 (first term + last term)   = 50/2 (1 + 99) = 2500.   2500nswer is 2500.
Answer: A
If xy ≠ 0 and x^2y^2 − 2xy = 8, which of the following could be y in terms of x?
I. 4/x
II. -x/2
III. 3/x Choose the correct choice.
A) I only	B) II only	C) I and II	D) I and III	E) II and III

Solution: (x^2)(y^2) – 2xy - 8 = 0   (xy – 4)(xy + 2) = 0   xy – 4 = 0 or xy + 2 = 0   xy = 4 or xy = -2   Since we need y in terms of x, we can isolate y in both of our equations.   y = 4/x or y = -2/x   I onlynswer: I only
Answer: A
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 560 sq. feet, how many feet of fencing will be required?	Select the correct option:
A) 34 B) 40 C) 68 D) 76 E) 92

Solution: Given that length and area, so we can find the breadth.   Length x Breadth = Area   20 x Breadth = 560   Breadth = 28 feet   Area to be fenced = 2B + L = 2 (28) + 20 = 76 feet answer : 76
Answer: D
If 1/(n – 2) = 1/(n + 2) + 1/(n – 1), which of the following is a possible value of n?
Choose the correct choice from the following.
A) -3 B) 0 C) 3 D) -4 E) 4

Solution: Multiply by (n-2)*(n+2)*(n-1) throughout to get:   (n+2)*(n-1) = (n-2)*(n-1) + (n+2)(n-2)   Of the given options, only n=0 satisfies this.   Answer : 0
Answer: B
Katie owned ten times as many cats as she did dogs. If she adopted 4 more dogs, the ratio of cats to dogs would be 1 to 1. How many dogs and cats does Katie have total after adopting the 4 more dogs. Choose the correct choice:
A) There is not enough information to solve the problem.	B) 10	C) 33	D) 99	E) None of the Above

Solution: By checking the answer choices:   Since we have an initial ratio of 10:1, the total count should be divisible by 11.   A. There is enough information to solve this problem, therefore A is not the correct choice.   B. Out, Since not divisible by 11.   C. 33/11=3, Cats = 30, Dogs = 3, Since 30-4 is not equal to 3+4, this is not the answer.   D. 99/11=9, Cats = 90, Dogs = 9, Since 90-4 is not equal to 9+4 this as well can not be the answer.   E. Since none of the choices above are correct, E is the answer.   None of the Above is the correct answer.
Answer: E
If A:B = 1/4: 1/3 B:C = 1/4:1/3 then A:B:C? Choose the correct choice from the following options:  A) 9:12:6  B) 9:2:16  C) 9:12:16  D) 9:12:14  E) 19:12:16

Solution: A:B = 1/4:1/3 = 3:4   B:9:12:16 = 1/4:1/3 = 3:4   --------------------   A:B:9:12:16 = 9:12:16   ANSWER:9:12:16
Answer: C
A and B together have $ 1210. If of A's amount is equal to of B's amount, how much amount does B have? Options:
A) $400 B) $489 C) $484 D) $365 E) %342

Solution: (4/15)A=(2/5)B   =>A=((2/5)*(15/4))B   =>A=(3/2)B   =>A/B=3/2   A:B=3:2   B's share=rs.(1210*(2/5))=$484   Option $484
Answer: C
There are two numbers. If 30% of the first number is added to the second number, then the second number increases to its five-fourth. What is the ratio of the first number to the second number?
Pick
A) 3 : 25
B) 25 : 8
C) 8 : 5
D) 5 : 6
E) 7 : 2

Solution: Let the two numbers be x and y.   (3/10) * x + y = (5/4) * y   (3/10) * x = (1/4) * y   x/y = 10/12 = 5/6   The answer is 5 : 6.
Answer: D
The area of a rectangle is 24 cm2. The width is two less than the length. What is the length and width of the rectangle? Choose the correct choice from the following answers
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: Solution   Let x be the length and let x - 2 be the width   Area = lenth × width = x × ( x - 2) = 24   x × ( x - 2) = 24   x2 + -2x = 24   x2 + -2x - 24 = 0   Since -24 = 4 × -6 and 4 + -6 = -2, we get:   (x + 4) × ( x + -6) = 0   This leads to two equations to solve:   x + 4 = 0 and x + -6 = 0   x + 4 = 0 gives x = -4. Reject this value since a dimension cannot be negative   x + -6 = 0 gives x = 6   Therefore, length = 6 and width = x - 2 = 6 - 2= 
6 - 2 = 4
4   Answer 4
Answer: B
The area of a rectangular field is 144 m2. If the length had been 6 metres more, the area would have been 54 m2 more. The original length of the field is Select:	A) 22 metres	B) 18 metres	C) 16 metres	D) 24 metres	E) None of these

Solution: Let the length and breadth of the original rectangular field be x m and y m respectively.   Area of the original field = x × y = 144 m2   ∴ x = 144⁄y .....(i)   If the length had been 6 m more, then area will be   (x + 6) y = 144 + 54   ⇒ (x + 6)y = 198… (ii)   Putting the value of x from eq (i) in eq (ii), we get   (144⁄y + 6)y = 198   ⇒ 144 + 6y = 198   ⇒ 6y = 54 ⇒ y = 9m   Putting the value of y in eq (i) we get x = 16 m   Answer 16 metres
Answer: C
If Rs.440 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
Choose the correct choice:
A) s.575
B) s.595
C) s.590
D) s.580
E) s.585

Solution: 80 = (440*4*R)/100   R = 5.68%   I = (440*6*5.68)/100 = 150   440 + 150= 
440 + 150 = 590
590   ANSWER:s.590
Answer: C
The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.8000 and the average salary of the rest is Rs.6000. The total number of workers in the workshop is  Options:
A) 20	B) 21	C) 22	D) 7	E) 24

Solution: Solution   Let the toatl number of workers be x.   Then 8000x=(8000 x 7) + 6000 (x -7)   x= 7.   Answer 7
Answer: D
If both 5^2 and 3^3 are factors of n x (2^5) x (6) x (7^3), what is the smallest possible positive value of n?  Choose the correct choice from the following answers:
A) 75 B) 125 C) 145 D) 175 E) 225

Solution: (2^5) x (6) x (7^3) has one appearance of 3 (in the 6) and no appearances of 5.   Thus n must include at least 3^2 * 5^2 = 9 * 25= 
9 * 25 = 225
225   The answer is 225.
Answer: E
The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
Choose the correct choice from the following options
A) 7 yrs	B) 10 yrs	C) 18 yrs	D) 20 yrs	E) 25 yrs

Solution: Explanation:   9 * 2= 
9 * 2 = 18
18 years   ANSWER 18 yrs
Answer: C
There are three foam generators in the factory, each of the first two can generate 10 liters of foam in one hour and the third can generate 16 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated?	Choose the correct choice from the following
A) 120.
B) 121
C) 146.
D) 154.
E) 166.

Solution: Let the foam generators capacity be -   A = 10 lit/hr   B = 10 lit/hr   C = 16 lit/hr   Total foam generation in 1 hour will be 36 lit ( 10 + 10 + 16 ) ; since in 1 and 1/2 hr they will generate   36 + 18= 
  36 + 18 = 54
> 54 litres...   Now one of the first generators stops working ( Say A stops working ) , so we have -   B= 10 lit/hr   C = 16 lit/hr   Total foam generation in 2 hour will be 52 litres {2 (10+16)}   The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )...   Foam generated by 121 will be 3/2 * 10= 
3/2 * 10 = 15
> 15 litres   So, total foam generated will be 121 Litres ( 54 + 52 + 15 ) ; hence answer will be (121)
Answer: B
If the length of an edge of cube M is five times the length of an edge of cube N, what is the ratio of the volume of cube N to the volume of cube M?  Choose the correct choice:  A) 1/125  B) 1/25  C) 1/5  D) 1/16  E) 1/32

Solution: The length of cube N = 1;   The length of cube M = 5;   The ratio of the volume of cube N to the volume of cube M = 1^3/5^3 = 1/125   1/125nswer : 1/125
Answer: A
Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?	Answers.
A) 10  B) 12  C) 15  D) 20  E) 25

Solution: Explanation:   Speed of the first train =120/10 m/sec = 12 m/sec.   Speed of the second train =120/15 m/sec = 8 m/sec.   Relative speed = (12 + 8)= 
(12 + 8) = 20
20 m/sec.   Therefore Required time=(120+120)/20= 
(120+120)/20 = 12
12 sec.   ANSWER IS 12
Answer: B
Of 30 applicants for a job, 12 had at least 4 years' experience, 19 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?
Select the correct option.
A) 14
B) 13
C) 9
D) 7
E) 5

Solution: set A : people with more than 4 years exp   set B : people with degree   AUB = total - (less than 4 exp and no degree)   AUB = 30-6= 
30-6 = 24
24   AUB= A + B - AiB   AiB = 19+12-24= 
19+12-24 = 7
7   Answer 7
Answer: D
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is? Choose the correct choice from the following answers
A) 16 B) 19 C) 15 D) 22 E) 10

Solution: Let the son's present age be x years.   Then, man's present age = (x + 24) years.   (x + 24) + 2 = 2(x + 2) x + 26 = 2x + 4   => x = .   Answer: 22
Answer: D
The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 38 with him, what was the average amount with the group before his joining the group?
Pick one.
A) s.17	B) s.12	C) s.15	D) s.22	E) s.12

Solution: Total members in the group = 7   Average amount = Rs. 20   Total amount with them = 7 * 20 = Rs. 140   One number has Rs. 38. So, the amount with remaining 6 people = 140 - 38 = Rs. 102   The average amount with them = 102/6 = Rs.17.   s.17nswer:s.17
Answer: A
If 1*548 is divisible by 3, which of the following digits can replace *?  Choose the correct choice from the following options:
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: Solution   1 + x + 5 + 4 + 8 = (18 + x).   Clearly, when x=0, then sum of digits divisible by 3.   Answer 3
Answer: D
A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability T that the sum of the two integers will equal 9 ?
Choices.
A) 0.15	B) 0.20	C) 0.25	D) 0.30	E) 0.33

Solution: Rearrange the first set:   A = {5,4,3,2}   B = {4,5,6,7, 8}   As you can see numbers in each column (the numbers of the same color) give the sum of 9. So there are 4 such pares possible, total # of pairs is 4*5= 
4*5 = 20
20. T=favorable/total=4/20=0.2.   Answer: B.   Or: we can select ANY number from set A (4/4=1) but in this case we must select its matching pair from set B (the number of the same color) and since there are only one matching pair of this particular number in B then the probability of this is 1/5. So, overall: T=1*1/5.   Answer: 0.20.
Answer: B
3*15 + 3*16 + 3*19 + 11 = ?
Choose the correct option.
A) 125 B) 126 C) 130 D) 148 E) 161

Solution: 3*15 + 3*16 + 3*19 + 11 = 45 + 48 + 57 + 11= 
45 + 48 + 57 + 11 = 161
161   The answer is 161.
Answer: E
A fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans. A customer bought the pair of jeans for 10 percent more than the retailer paid for them. The price the customer paid was what percent greater than the cost of manufacturing the jeans?	Pick.
A) 54%  B) 70%  C) 75%  D) 85%  E) 95%

Solution: find the product of the two increases: (1.4) * (1.1), which is 1.54 and a 54% increase.   54%
Answer: A
The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area? Select.
A) 288 B) 240 C) 267 D) 299 E) 162

Solution: 4a = 68 => a = 17   172 – 82 = 152   1/2 * 16 * 30= 
1/2 * 16 * 30 = 240
240   Answer:240
Answer: B
In what time will a train 100 meters long cross an electric pole, if its speed is 180 km/hr	Choices: A) 5 seconds B) 4.5 seconds C) 3 seconds D) 2 seconds E) None of these

Solution: Explanation:   First convert speed into m/sec   Speed = 180*(5/18)= 
180*(5/18) = 50
50 m/sec   Time= 2 secondsistance/speed   = 100/50= 
100/50 = 2
2 seconds   Answer: 2 seconds
Answer: D
In Mike's opinion, his weight is greater than 65kg but leas than 72 kg. His brother does not agree with Mike and he thinks that Mike's weight is greater than 60kg but less than 70kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Mike?  Choose one:
A) 45.5 kg  B) 50.5 kg  C) 55.5 kg  D) 66.5 kg  E) 72.5 kg

Solution: Let Mike's weight be X kg.   According to Mike, 65 < X < 72.   According to Mike's brother, 60 < X < 70.   According to Mike's mother, X < 68.   The values satisfying all the above conditions are 66 and 67.   Required average = (66 + 67) / 2= 
(66 + 67) / 2 = 133/2 = around 66.5
66.5 kg   66.5 kg
Answer: D
Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 37 pages per hour. If Tom starts reading a novel at 4:00, and Jan begins reading an identical copy of the same book at 4:56, at what time will they be reading the same page?  Choose the correct choice from the following options.
A) 7:26
B) 7:56
C) 8:26
D) 8:56
E) 9:26

Solution: Since Tom reads an average of 1 page every 2 minutes, Tom will read 28 pages in the first 56 minutes. Jan can catch Tom at a rate of 7 pages per hour, so it will take 4 hours to catch Tom.   The answer is 8:56.
Answer: D
There are 50 students in a class. If 10 % are absent on a particular day, find the number of students present in the class. Choose the most appropriate option:
A) 43
B) 36
C) 28
D) 45
E) 11

Solution: Number of students absent on a particular day = 10 % of 50   i.e., 10/100 × 50 = 5   Therefore, the number of students present = 50 - 5= 
50 - 5 = 45
45 students.   Answer:45
Answer: D
How many rectangles can be formed out of a chess board ?  Choose the correct choice from the following choices.
A) 204  B) 1230  C) 1740  D) 1296  E) none of these

Solution: A chess board consists 9 parallel lines x 9 parallel lines.   For a rectangle we need to select 2 parallel lines and the other two parallel lines that are perpendicular to the first set.   Hence, 9C2 x 9C2 = 1296 rectangles   ANSWER:1296
Answer: D
A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
Choose the correct choice:
A) 399	B) 238	C) 200	D) 288	E) 291

Solution: A:B:200 = 2/3:1/6:1/6 = 4:1:1   x * 2/100 * 2/3 = 200   B capital = 15000*1/6= 
15000*1/6 = 2_500
2500 .Answer: 200
Answer: C
Look at this series: 36, 34, 30, 28, 24, ... What number should come next? Choose one:  A) 20  B) 24  C) 22  D) 26  E) 30

Solution: alternating no subtraction series first 2 is subtracted and then 4 and 2 so on   22 is the next one   ANSWER 22
Answer: C
Bradley owns b video game cartridges. If Bradley’s total is one-third the total owned by Andrew and seven times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?  Select the correct option
A) (16/3)b	B) (17/4)b	C) (13/4)b	D) (19/12)b	E) (29/7)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   (1/7)b = Charlie’s total   Add each total   b + 3b+ (1/7)b = 4b + (1/7)b = (29/7)b   Therefore,choose (29/7)b.
Answer: E
A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?  Choose the correct choice from the following answers.
A) 5 kmph
B) 1kmph
C) 7 kmph
D) 9 kmph
E) 11 kmph

Solution: Explanation:   DS = 6   US = 4   S = ?   S = (6 - 4)/2= 
(6 - 4)/2 = 1
1 kmph   Answer: 1kmph
Answer: B
What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12% p.a.?	Choose the correct choice from the following: A) 10123.298 B) 10123.22 C) 10123.2 D) 10123.21 E) 10123.54

Solution: Amount = [25000 * (1 + 12/100)3]   = 25000 * 28/25 * 28/25 * 28/25 = Rs. 35123.20   C.I. = (35123.20 - 25000) = Rs. 10123.20   Answer: 10123.2
Answer: C
A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 11.30 a.m. ?  Choose the correct choice from the following options
A) 7 B) 5 C) 9 D) 17 E) 12

Solution: D   17   Relative speed = 2 + 3= 
2 + 3 = 5
5 rounds per hour.   So, they cross each other 5 times in an hour and 2 times in half an hour.   Hence, they cross each other 17 times before 11.30 a.m.
Answer: D
A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour and returns along the same road at an average speed of 8 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?
Options
A) (a) 24/5 B) (b) 5 C) (c) 26/5 D) (d) 27/5 E) (e) 16/3

Solution: from the uphill we can find out the distance = 4*2= 
4*2 = 8
8   average speed= total distance/total time   = 16/ (2+ (8/8)) = 16/3   Answer is (e) 16/3.
Answer: E
A jar contains 10 marbles consisting of an equal number of red, green, and blue marbles. Three marbles are removed from the jar and discarded. What is the probability that only two colors will remain in the jar after the Three marbles have been removed?
Answers.
A) 1/40  B) 1/165  C) 1/81  D) 1/30  E) 1/20

Solution: Jar contains {3-red, 3-green, 3-blue} marbles. We are asked to find the probability that after removing 3 marbles only 2 colours remain in the jar, i.e., the probability of removing EITHER red, OR green, OR blue.   Sample space = 10C3 = 120.   Probability of choosing 3 red = 3C3/10C3 = 1/120.   Probability of choosing 3 green = 3C3/10C3 = 1/120.   Probability of choosing 3 blue = 3C3/10C3 = 1/120.   Required probability = 1+1+1/120 = 3/120 = 1/40. 1/40ns (1/40).
Answer: A
A,B,C together can earn $600 per day. while A and C together earn $400 and B and C together can earn $300. The daily earnings of C?  Select:  A) $100  B) $200  C) $250  D) $300  E) $500

Solution: B's daily earnings = 600-400= 
600-400 = 200
$200   $100's daily earnings= 600-300= 
600-300 = 300
$300   C's daily earnings= 600-200-300= 
600-200-300 = 100
$100   $100nswer is $100
Answer: A