MU-NLPC/Calc-aqua_rat huggingface dataset:
The speeds of three motor bikes are in the ratio 6 : 4 : 2. The ratio between the time taken by them to travel the same distance is : Choose the correct choice from the following answers
A) 2 : 5 : 6
B) 2 : 4 : 6
C) 2 : 3 : 6
D) 2 : 3 : 7
E) 1 : 3 : 6

Solution: Ratio of time taken :   1/6 :1/4 : 1/2 = 2 : 3 : 6   ANSWER:2 : 3 : 6
Answer: C
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good. Choose the correct choice from the following choices:
A) 20/65
B) 20/63
C) 20/68
D) 20/66
E) 20/29

Solution: Required probability   = (5C3 . 4C1)/9C4   = (10 * 4)/126   = 20/63   Answer:20/63
Answer: B
An arithemetic sequence of numbers begins p, 2p + 3, 4p + 4... What is the 12th member of this sequence? Choose the correct option.
A) A)57	B) B)40	C) + 13	D) D)53	E) + 13

Solution: Common difference of an arithmetic series is constant.   2p+3-p=4p+4-2p-3   p=2   1, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57   57ns:57
Answer: A
The sector of a circle has radius of 18 cm and central angle 135o. Find its perimeter?	Options.
A) 78.4 cm  B) 11.5 cm  C) 91.8 cm  D) 92.5 cm  E) 99.5 cm

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (135/360 * 2 * 22/7 * 18) + 2(18)   = 42.4 + 36= 
42.4 + 36 = 78.4
78.4 cm   78.4 cmnswer:78.4 cm
Answer: A
A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?  Choose the correct choice.
A) 59005
B) 59007
C) 59002
D) 59000
E) 59001

Solution: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.   Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.   Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)   Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.   Income of A = Twice the income of B   (2500 + 18000 + P) = 2(P)   P = 20500   Total profit = 2P + 18000   = 2*20500 + 18000= 
2*20500 + 18000 = 59_000
59000.Answer: 59000
Answer: D
Question: What is the remainder when I= (1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144?
Choose the correct answer:
A) 0
B) 25
C) 49
D) 81
E) 100

Solution: 144 =12 *12   (1!)^3=1   2!=2, therefore (2!)^3=2*2*2= 
2*2*2 = 8
8   3!=6, therefore (3!)^3=6*6*6= 
6*6*6 = 216
216   4!=24 therefore (4!)^3= 24*24*24 which is completely divisible by 144   thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0   now the remainder when I=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216= 
1+8+216 = 225
225 is divided by 144   now remainder when 225 is divided by 144 is 81. hence answer should be 81
Answer: D
A shop owner buys a 1280 ounce bag of sugar for resale. How many 1 pound containers can she sell?  Pick one:  A) 80  B) 90  C) 100  D) 110  E) 120

Solution: 1 pound = 16 ounces.   1280 ounces / 16 = 80 pounds.   80nswer: 80.
Answer: A
A hostess must seat 10 people around 2 circular tables. Table 1 can hold 6 people, table 2 can hold 4 people. If the hostess always seats people at Table 1 first and 2 seating arrangements are said to be different only when the positions of people are different relative to each other at the table, how many seating arrangements are possible?	Choose the correct choice from the following answers.
A) 5*210
B) 15!*210
C) 120*3!
D) 5!*3!*210
E) 5!*5!*3!

Solution: 1)since there are two tables, the hostess has to choose 6 out of 10 and the remaining 4 will go to other table..   so WAYS= 10C6=10!/6!4!=210..   2)now 6 on the Table 1 can be seated in (6-1)! ways   3)and 4 on the Table 1 can be seated in (4-1)! ways   TOTAL ways=210*5!*3!   5!*3!*210
Answer: D
The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 21 years and the average age of the last three persons is 34 years, then find the age of the person sitting in the middle of the row?  Choose the correct choice from the following choices
A) 21 years
B) 31 years
C) 44 years
D) 48 years
E) 75 years

Solution: Total age seven persons = (28 * 7)years   Total age of the first three persons and the last three persons are (21 * 3) years and (34 * 3) years respectively.   Age of the person sitting in the middle of the row   = 28 * 7 - 21 * 3 - 34 * 3 = 196 - 63 - 102= 
196 - 63 - 102 = 31
31 years.   Answer:31 years
Answer: B
If DHOOM is coded as 25 and RACE is coded as 14, then FASHION is coded as Choose the correct choice:
A) 12	B) 14	C) 36	D) 48	E) None

Solution: DHOOM = 4+8+15+15+13= 
4+8+15+15+13 = 55
55 i.e 5*5=25   RACE= 18+1+3+5= 
18+1+3+5 = 27
27 i.e 2*7=14   Fashion   6+1+19+8+9+15+14= 
  6+1+19+8+9+15+14 = 72
72 7*2=14   ANSWER:14
Answer: B
1=6,2=36,3=363,4=364,5=365, then 36=?
Choose the most appropriate option
A) 1  B) 2  C) 345  D) 445  E) 235

Solution: 1=6,2=36,3=363,4=364,5=365, then 36=?   36=2   check the second eqn.   ANSWER:2
Answer: B
Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 4200 envelopes.	Choose the correct choice:
A) 2
B) 3
C) 4
D) 6
E) 60/7

Solution: You can either take the amount of work done as the same as Karishma has done or take the work done by each in the same time. I will do the latter   1. Work done in 1 hr by A is 2000 envelopes   2. Work done in 1 hr by A and C is 3000 envelopes   3. So work done in 1 hr by C is 1000 envelopes   4. Work done in 1 hr by B and C is 2400 envelopes   5. So work done in 1 hr by B is 1400 envelopes   6. So to process 4200 envelopes 3 will take   4200/1400= 
  4200/1400 = 3
3 hrs   So the answer is choice 3
Answer: B
Truck P and Truck Q drive on the highway in the same direction at respective rates of 70 kph and 75 kph. If Truck Q is 5 km behind Truck P, by how much does Truck P need to increase the speed to catch up with Truck P in 20 minutes?	Choose the correct option:
A) 6 kph
B) 8 kph
C) 10 kph
D) 12 kph
E) 14 kph

Solution: Truck Q needs to gain 5 km in 20 minutes.   The relative speed difference needs to be 5 km / 20 minutes = 15 km/hour   Truck Q needs to increase up to 85 kph, thus an increase in 10 kph.   The answer is 10 kph.
Answer: C
A man can row 6 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.
Pick one
A) 2 km/hr  B) 12.5 km/hr  C) 1 2.6 km/hr  D) 22.5 km/hr  E) 22.6 km/hr

Solution: Given that, time taken to travel upstream = 2 × time taken to travel downstream   When distance is constant, speed is inversely proportional to the time   Hence, 2 × speed upstream = speed downstream   Let speed upstream = x   Then speed downstream = 2x   we have, 1/2(x+2x) = speed in still water   ⇒1/2(3x)=6   3x = 12   x = 4   i.e., speed upstream = 4 km/hr   Rate of stream = 1/2(2x−x)=x/2=4/2= 
4/2 = 2
2 km/hr   2 km/hrnswer is 2 km/hr
Answer: A
90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 50% of the total school population of x students, what is x?  Choose the correct choice from the following options.
A) 134 B) 150 C) 225 D) 250 E) 500

Solution: 90=x/100*50/100*x=>x^2 = 9*10000/5 = > x = 134   134
Answer: A
A train 100 m long crosses a platform 125 m long in 1 sec; find the speed of the train?  Options.
A) 810  B) 700  C) 930  D) 100  E) 200

Solution: D = 100 + 125= 
100 + 125 = 225
225   T= 15   S = 225/1 * 18/5= 
225/1 * 18/5 = 810
810 kmph   810nswer: 810
Answer: A
If a man buys 20 lollipops for $90 and sold them for $2 dollars determine his loss.	Pick.
A) $70	B) $40	C) $50	D) $30	E) $80

Solution: $50   $50   $50ost of 20 lollipops = $90   Sold each lollipop for $2   So he sold 20 lollipops for $(20 × 2) = $40   Loss = $(90 – 40) = $50   Therefore, loss = $ 50.
Answer: C
Assuming i have an infinite supply of coins.
What is the fewest number of coins would be required in order to make sure each and every coin touched exactly three other coins. Choose the correct choice from the following choices
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: Solution:   Four   three placed flat on the table in a triangle(touching each other) and put the fourth one on top of them in the middle.   Answer 4
Answer: D
If a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+5 ? Choose the correct choice from the following answers:
A) -1 B) -2 C) -3 D) 6 E) -5

Solution: let we put values. a=1, b=3, c=5   5-3-1= 
5-3-1 = 1
1   1+5= 
1+5 = 6
6   Answer :6
Answer: D
Kim bought a total of $1.82 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 3-cent stamps, what is the least number of 1-cent stamps she could have bought? Choose the correct choice:
A) 25  B) 32  C) 45  D) 60  E) 75

Solution: Let:   # of 5 and 25 cents stamps = n   # of 10 cent stamps = 2n   # of 1 cent stamps = m   Therefore:   5n + 25n + 10(2n) + m = 182 cents   50n + m = 182   Forleastnumber of 1 cents stamps, maximize 50n. Hence,   50*3 + m = 182   m = 32 i.e. 32 stamps 1 cents each   Answer: 32
Answer: B
A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit.
Choose the correct choice from the following choices:
A) 2288  B) 2778  C) 3000  D) 212  E) 28812

Solution: A:B:C = 5:6:4   Let the total profit = 100 - 30= 
100 - 30 = 70
70   5/15 * 70= 70/3   A share = 70/3 + 30 = 160/3   B + C share = 100 - 160/3 = 140/3   A-(B+C) = 160/3 - 140/3 = 20/3   20/3 ---- 200   100 ---- ? => 3000.Answer: 212
Answer: D
A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes
to cover a distance of 5 km upstream. Find the speed of the current.
Choose the correct choice from the following choices.
A) 1 km/hr
B) 2 km/hr
C) 3 km/hr
D) 4 km/hr
E) None of these

Solution: Explanation:   First of all, we know that   speed of current = 1/2(speed downstream - speed upstream) [important]   So we need to calculate speed downstream and speed upstream first.   Speed = Distance / Time [important]   Speed upstream =(15334)km/hr=15×415=4km/hrSpeed Downstream = (5212)km/hr=5×25=2km/hrSo   speed of current = 12(4−2)=1km/hr   1 km/hrnswer: 1 km/hr
Answer: A
Pipes A and B can fill a tank in 3 and 5 hours. Pipe C can empty it in 12 hours. If all pipes are opened together, then the tank will be filled in?  Answers
A) 60/17 hr B) 12/19 hr C) 20/9 hr D) 9/20 hr E) 63/19 hr

Solution: Net part filled in 1 hour = 1/3 + 1/5 - 1/12 = 9/20   The tank will be full in 20/9 hr   Answer is 20/9 hr
Answer: C
The value of (10^8-10^2)/(10^6-10^3) is closest to which of the following?
Choose the correct option:
A) 1
B) 10
C) 10^2
D) 10^3
E) 10^4

Solution: Because the question asks for what value isclosestthe question invites approximation.   Let's look at the numerator:   10^8 - 10^2   10^8 is HUGE compared to 10^2.   So 10^8 - 10^2 is very close to 10^8 itself. (Just as 100 - 0.0001 is very close to 100 itself).   Likewise, 10^6 is HUGE compared to 10^3.   So 10^6- 10^3 is very close to 10^6.   So we have:   10^8/10^6   or 10^(8-6) = 10^2.   10^2hoose 10^2.
Answer: C
A person got Rs.48 more when he invested a certain sum at compound interest instead of simple interest for two years at 8% p.a. Find the sum?  Choices:
A) 7500	B) 7528	C) 2789	D) 2668	E) 2088

Solution: P = (d * 1002) / R2   => (48 * 100 * 100) / 8 * 8 = Rs.7500   7500nswer: 7500
Answer: A
What is the average of three tenths and five thousandths
Choose one
A) 0.2022	B) 0.3325	C) 0.1525	D) 0.2012	E) 0.2114

Solution: Explanation:   three tenths = 0.3   Five thousandths = 0.005   The average is (0.3 + 0.005)/2= 
(0.3 + 0.005)/2 = 0.1525
0.1525   Answer: 0.1525
Answer: C
A , B , and C started a partnership business by investing $45,000 , $63,000 , and $72,000 respectively. At the end of the year, the profit was distributed among them. If C's share of profit is $24,000, what is the total profit?	Choose the correct choice from the following choices
A) $48,000	B) $52,000	C) $56,000	D) $60,000	E) $64,000

Solution: A:B:C = 45000:63000:72000 which is a ratio of 5:7:8.   Let the total profit be x.   x * 8/20 = 24000   x = 24000*20/8 = 60,000.   The answer is $60,000.
Answer: D
Which of the following is not divisible by 8?
Pick.
A) 10032
B) 21192
C) 47816
D) 91232
E) 72034

Solution: Divisibility rule of 8: Last three digits of the number should be divisible by 8   Option A: 10032, last three digits = 032. Divisible by 8   Option B: 21192, last three digits = 192. Divisible by 8   Option C: 47816, last three digits = 816. Divisible by 8   Option D: 91232, last three digits = 232. Divisible by 8   Option E: 72034, last three digits = 034. Not divisible by 8. Hence 72034 is not divisible by 8
Answer: E
At garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 15th highest price and the 25th lowest price among the prices of the items sold, how many items were sold at the garage sale? Choose the correct choice from the following answers: A) 33 B) 34 C) 35 D) 39 E) 37

Solution: 14+24+1= 
14+24+1 = 39
39   Answer: 39
Answer: D
A 4 digit number 8a43 is added to another 4 digit number 3121 to give a 5 digit number 11b64, which is divisible by 11, then (a+b)=?	Choose the correct choice from the following answers:
A) 3 B) 4 C) 7 D) 5 E) 9

Solution: Solution: a+1=b   => b-a=1.   and 11b64 is divisible by 11   => (4+b+1)-(6+1)=0   => b-2=0   => b=2.   so, a=1   =>(a+b)= 3.   3nswer 3
Answer: A
A man sitting in a train which is travelling at 80 kmph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed?	Options:	A) 52 kmph.	B) 62 kmph.	C) 72 kmph.	D) 80 kmph.	E) 32 kmph.

Solution: Solution   Relative Speed	= (280 / 9)m/sec   = (280/9 x 18/5)   = 112 kmph.   Speed of the train	= (112 - 80)= 
(112 - 80) = 32
32 kmph.   Answer 32 kmph.
Answer: E
A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
Choose the correct answer.
A) 12.8 kmph  B) 23.9 kmph  C) 21.9 kmph  D) 12.5 kmph  E) 13.8 kmph

Solution: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.   Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b)   = 7   Solving the equation, the speed of man in still water is   12.5 kmph.   Answer: 12.5 kmph
Answer: D
A women has 3 purse and 4 paper. In how many ways can he put the paper in her purse?
Pick:
A) 78
B) 80
C) 81
D) 82
E) 85

Solution: First paper can be put in 3 ways, similarly second, third and forth paper also can be put in 3 ways.   So total number of ways = 3 x 3 x 3 x 3 = 34 = 81   81
Answer: C
19 persons went to a hotel for a combined dinner party. 13 of them spent Rs 79 each for the dinner and the rest spent Rs 4 more than the average expenditure of all the 19. What was the total money spent by them?	Select the correct option
A) Rs1628.40  B) Rs1536  C) Rs1492  D) Rs1498  E) none of these

Solution: (13*79)+(6(x+4)) = 19x   1027 + 6x + 24 = 19x   1051 = 13x   x = 1051/13   total money = 19x = 1536   ANSWER:Rs1536
Answer: B
If 10 gallons of grape juice are added to 50 gallons of a mixture, which contains 10 percent grape juice then what percent of the resulting mixture is grape juice?  Choose the correct choice from the following answers.
A) 14% B) 25% C) 28% D) 34% E) 50%

Solution: OFFICIAL SOLUTION:   If we start with 40 gallons of a mixture that is 10% grape juice, then we have:   50 × 0.10 = 5 gallons of grape juice.   50 × 0.90 = 45 gallons of other components.   If we add 10 gallons of grape juice, we will end up with 15 gallons of grape juice and 45 gallons of other components, and we will have a total of 60 gallons of the mixture.   So 15/60 of the new mixture is grape juice. Now we convert this to a percent:Percent Grape Juice = 25/100= 25%.   The correct answer is choice (25%)
Answer: B
In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 10 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can? Pick one:
A) 40 B) 44 C) 48 D) 55 E) None of these

Solution: Let the capacity of the can be T litres.   Quantity of milk in the mixture before adding milk = 4/9 (T - 10)   After adding milk, quantity of milk in the mixture = 6/11 T.   6T/11 - 10 = 4/9(T - 10)   10T = 990 - 440 => T = 55.   ANSWER:55
Answer: D
The L.C.M of two numbers is 48. The numbers are in the ratio 1:3. The sum of numbers is:  Choose the correct option:
A) 28  B) 30  C) 40  D) 50  E) 64

Solution: Let the numbers be 1x and 3x.   Then, their L.C.M = 3x. So, 3x = 48 or x = 16.   The numbers are 16 and 48.   Hence, required sum = (16 + 48)= 
(16 + 48) = 64
64.   ANSW64R:64
Answer: E
The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 25 years. What is the age of the new member ?	Options:	A) 20 years	B) 21 years	C) 40 years	D) 23 years	E) 24 years

Solution: The average age of a group of 5 members is 20 years --> the sum of the ages is  5*20= 
 5*20 = 100
100;   Two years laterthe sum of the ages of these 5 members would be 100+5*2= 
100+5*2 = 110
110;   Now, say the age of the new member is x years, so the sum of the ages of a new 6 member group is 110+x. Since given that the average age of this group of 6 members is 25 years then: 25*6=110+x --> x=40.   Answer: 40 years.
Answer: C
A student needed to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What is the value of x? Pick
A) 5  B) 4  C) 3  D) 7  E) 6

Solution: 3+11+7+9+15+13+8+19+17+21+14+x/12=12   137+x/12=12   137+x=144   x=144-137= 
144-137 = 7
7   Option 7
Answer: D
Every year an amount increases by 1/9th of itself. How much will it be after two years if its present value is Rs.64000?	Choose the correct choice from the following answers:
A) 81000
B) 81007
C) 81008
D) 79012.3
E) 81022

Solution: 64000* 10/9 * 10/9 = 79012.3   Answer:79012.3
Answer: D
The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue, in dollars, from the sale of cars priced at $ 12,000?  Choices
A) 50,000 B) 750,000 C) 850,000 D) 7,500,000 E) 2,400,000,000

Solution: number of cars sold = x=800000-50y   y=12000   x=800000-600000= 
800000-600000 = 200_000
200000   revenue from 50000 cars=12000*200000= 
12000*200000 = 2_400_000_000
2400000000   Answer 2,400,000,000
Answer: E
certain office 1/3 of the workers are women ½ of the women are married and 1/3 of the married women have children if ¾ of the men are married and 2/3 of the married men have children what part of workers are without children?
Select the correct option:
A) 11/8 of all workers  B) 1/18 of all workers  C) 11/18 of all workers  D) 13/18 of all workers  E) 4/18 of all workers

Solution: Let the total no of workers be x   No of women =x/3   No of men =x-(x/3)=2x/3   No of women having children =1/3 of ½ ofx/3=x/18   No of men having children=2/3 of ¾ of2x/3=x/3   No of workers having children = x/8 +x/3=7x/18   Workers having no children=x-7x/18=11x/18=11/18 of all workers   Option 11/18 of all workers is answer
Answer: C
A tyre has two punctures. The first puncture alone would have made the tyre flat in 12 minutes and the second alone would have done it in 8 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?  Options:
A) 4 4/5min
B) 3 2/5min
C) 3 3/5min
D) 3 4/5min
E) 3 min

Solution: Explanation:   Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute.   Lets Solve it:   1 minute work done by both the punctures =   (1/12+1/8)=(5/24)   So both punctures will make the type flat in   (24/5)mins=4 4/5mins   Option 4 4/5min
Answer: A
(0.96)(power 3) - (0.1)(power 3)/ (0.96)(power 2) + 0.096 + (0.1)(power 2) is:	Choose the most appropriate option: A) 0.86 B) 0.68 C) 0.96 D) 0.69 E) 0.76

Solution: Given expression   = (0.96) (power 3) - (0.1)(power 3) / (0.96)(power 2) + (0.96 x 0.1) + (0.1)(power 2)   = a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)   = (a - b)   = (0.96 - 0.1)= 
(0.96 - 0.1) = 0.86
0.86   0.86nswer is 0.86.
Answer: A
What is the value of the following expression?
(1/ (2^2 – 1)) + (1/ (4^2 – 1)) + (1/ (6^2 – 1)) + .... + (1/ (18^2 – 1))	Select the correct option:
A) a. 9/19  B) b. 10/19  C) c. 10/21  D) d. 11/21  E) e. 11/19

Solution: it can be written into   1/3+1/15+ 1/35.....1/323   i.e   1/3+1/2*(1/3-1/5)+1/2*(1/5-1/7).... til last term - 1/2*(1/19)   all terms from 1/5 .. to second last term get cancelled   left with   1/3+1/6-1/42=1/2-1/38=18/38=9/19   a. 9/19
Answer: A
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 30 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?  Choose one.
A) 20 B) 34 C) 30 D) 40 E) 46

Solution: Nice question +1   We have that X/24 - (60-X)/2R = 30   Also X/R - (60-X)/2R = 120   So we get that 2x - 60 = 80R   3x - 60 = 240R   Get rid of R   120 = 3x   x = 30   Hence answer is 30
Answer: C
At what rate percent on simple interest will Rs.750 amount to Rs.900 in 10 years? Choose the correct choice from the following choices
A) 6%  B) 2%  C) 4%  D) 5%  E) 3%

Solution: 150 = (750*10*R)/100   R = 2%   Answer: 2%
Answer: B
A and B go around a circular track of length 900m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
Choose the correct answer:
A) 120 sec  B) 165 sec  C) 186 sec  D) 180 sec  E) 168 sec

Solution: Time taken to meet for the first time at the starting point   = LCM { length of the track / speed of A , length of the track / speed of B}   = LCM { 900/ (36 * 5/18) , 900/ (54 * 5 /18) }   = LCM (90, 60)   =180 sec.   Answer:180 sec
Answer: D
If 7^n is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of n?
Choose one:
A) 12
B) 13
C) 14
D) 15
E) 16

Solution: So the question just means that we have to find all the multiples of 7 between 1 to 100   there are 14 multiples of 7 ( 7 - 98)   But 49 and 98 contain two 7's as factors   so we have to add  14 + 2= 
 14 + 2 = 16
16   ANSW16R:16
Answer: E