MU-NLPC/Calc-aqua_rat huggingface dataset:
A cyclist traveled for two days. On the second day the cyclist traveled 4 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day. If during the two days she traveled a total of 280 miles and spent a total of 10 hours traveling, what was her average speed on the second day?
Pick:  A) 5 mph  B) 10 mph  C) 20 mph  D) 30 mph  E) 40 mph

Solution: SOLUTION:   D = 280 Mi   T = 12 hrs   Day 1 time = T1   Day 2 time = T2   T2 - T1 = 4 hrs ----- (I)   T1 + T2 = 12 hrs ----- (II)   Adding I and II, T2 = 8 hrs and T1 = 4 hrs   Day 1 Rate = R1   Day 2 Rate = R2   R1 - R2 = 10 mph   i.e. R1 = 10 + R2   280 = 8R2 + 4R1   i.e. 280 = 8R2 + 4 (10 + R2)   i.e. R2 = 20 mph   ANSW40 mphR: 40 mph
Answer: E
If we listed all numbers from 100 to 10,000, how many times would the digit 3 be printed?  Select the correct option:	A) 3980	B) 3700	C) 3840	D) 3780	E) 3680

Solution: DETAILED SOLUTION   We need to consider all three digit and all 4-digit numbers.   Three-digit numbers: A B C. 3 can be printed in the 100’s place or 10’s place or units place.   => 100’s place: 3 B C. B can take values 0 to 9, C can take values 0 to 9. So, 3 gets printed in the 100’s place 100 times   => 10’s place: A 3 C. A can take values 1 to 9, C can take values 0 to 9. So, 3 gets printed in the 10’s place 90 times   => Unit’s place: A B 3. A can take values 1 to 9, B can take values 0 to 9. So, 3 gets printed in the unit’s place 90 times   So, 3 gets printed 280 times in 3-digit numbers   Four-digit numbers: A B C D. 3 can be printed in the 1000’s place, 100’s place or 10’s place or units place.   => 1000’s place: 3 B C D. B can take values 0 to 9, C can take values 0 to 9, D can take values 0 to 9. So, 3 gets printed in the 100’s place 1000 times.   => 100’s place: A 3 C D. A can take values 1 to 9, C & D can take values 0 to 9. So, 3 gets printed in the 100’s place 900 times.   => 10’s place: A B 3 D. A can take values 1 to 9, B & D can take values 0 to 9. So, 3 gets printed in the 10’s place 900 times.   => Unit’s place: A B C 3. A can take values 1 to 9, B & C can take values 0 to 9. So, 3 gets printed in the unit’s place 900 times.   3 gets printed 3700 times in 4-digit numbers.   So, there are totally  3700 + 280= 
 3700 + 280 = 3_980
3980 numbers.   CORRECT 3980NSWER : 3980
Answer: A
The price of rice falls by 20%. How much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously?  Select the correct option:
A) 5 kg
B) 15 kg
C) 25 kg
D) 30 kg
E) None

Solution: Solution: Let Rs. 100 be spend on rice initially for 20 kg.   As the price falls by 20%, new price for 20 kg rice,   = (100 -20% of 100) = 80   New price of rice = 80/20 = Rs. 4 per kg.   Rice can bought now at = 100/4= 
100/4 = 25
25 kg.   Answer: Option 25 kg
Answer: C
In a group of cows and chickens, the number of legs was 14 more than twice the number of heads. The number of cows was:
Select the correct option.
A) 5	B) 7	C) 10	D) 12	E) 14

Solution: Let the number of cows be x and their legs be 4x.   Let the number of chicken be y and their legs be 2x.   Total number of legs = 4x + 2y.   Total number of heads = x + y.   The number of legs was 14 more than twice the number of heads.   Therefore, 2 × (x + y) + 14 = 4x + 2y.   or, 2x + 2y + 14 = 4x + 2y.   or, 2x + 14 = 4x [subtracting 2y from both sides].   or, 14 = 4x – 2x [subtracting 2x from both sides].   or, 14 = 2x.   or, x = 7 [dividing by 2 on both sides].   Therefore, the number of cows = 7.   Correct Answer:7)7
Answer: B
If N = 1000x + 100y + 10z, where x, y, and z are different positive integers less than 4, the remainder when N is divided by 9 is  Choices.
A) 2
B) 4
C) 6
D) 8
E) 9

Solution: Since we cannot have more than one correct answers in PS questions, then pick some numbers for x, y, and z and find the reminder when 1000x + 100y + 10z is divided by 9.   Say x=1, y=2, and z=3, then 1000x + 100y + 10z = 1,230 --> 1,230 divide by 9 yields the remainder of 6 (1,224 is divisible by 9 since the sum of its digit is a multiple of 9, thus 1,230, which is 6 more than a multiple of 9, yields the remainder of 6 when divided by 9).   Answer; 6.
Answer: C
Three times a number is 20% more than twice another number when increased by 105. If twice the first number increased by 36 is 20% less than three times of the second number, then what is the first number?  Choose the most appropriate option:  A) 150  B) 162  C) 180  D) 170  E) 160

Solution: Let the two numbers be x and y.   3x = 1.2( 2y +105)   3x = 2.4y +126 ………………..(1)   2x +36 = 0.8(3y)   2x +36 =2.4y ………………..(2)   x = 162   ANSWER:162
Answer: B
Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?  Pick:
A) 2000
B) 2879
C) 2700
D) 2797
E) 2761

Solution: (10*10)/100= 
(10*10)/100 = 1
1%loss   100 --- 99   ? --- 1980=> Rs.2000   2000nswer:2000
Answer: A
A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 14 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?	Choose the correct choice from the following options.
A) 18/79	B) 1/6	C) 1/25	D) 1/50	E) 7/450

Solution: Everything is correct except that you assumed the letters can't be repeated. It can be repeated.   AA   BB   CC   AB, AC, BC, BA, CA, CB.   Thus; total government vehicles = (10)^2*(3)^2 = 100*9= 
100*9 = 900
900   Vehicles inspected within 3 hours= 60*3/14 = 14   P = 14/900 = 7/450   Ans:7/450
Answer: E
When a Mobile is sold for Rs. 24000, the owner loses 40%. At what price must that Mobile be sold in order to gain 40%? Choose one.
A) 54,000	B) 56,000	C) 58,000	D) 60,000	E) 62,000

Solution: 60 : 24000 = 140 : x   x = (24000 x 140)/60 = 56000.   Hence, S.P. = Rs. 56,000.   Answer: Option 56,000
Answer: B
A can empty the tank in 28 hrs, B can fill the tank in 14 hrs, and C takes 7 hrs for filling.
If all three pipes are opened simultaneously ,how long it will take to fill the tank?  Pick.
A) 4 hr 36 minutes  B) 5 hr 36 minutes  C) 6 hr 36 minutes  D) 7 hr 36 minutes  E) None of these

Solution: Solution:time taken=(28*14*7*)/(28*14 - 14*7 + 28*7)   To solve this quicker find out LCM(28,14,7)   we get 28   Time taken =28/(-28/28 +28/14 + 28/7)   =28/(-1+2+4)   =28/5= 
28/5 = 28/5 = around 5.6
5.6 hrs=5 hr 36 minutes   Answer 5 hr 36 minutes
Answer: B
Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 60%?	Answers:
A) 282  B) 229  C) 277  D) 380  E) 2812

Solution: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5   SP = CP[(100 + profit%)/100]   = 237.5 * [(100 + 60)/100] = Rs. 380.   Answer:380
Answer: D
If a and b are mixed in 3:5 ration and b and c are mixed in 8:5 ration if the final mixture is 35 liters, find the amount of b?
Choose one:
A) 13.73 ltrs
B) 14.73 ltrs
C) 15.73 ltrs
D) 16.73 ltrs
E) 17.73 ltrs

Solution: Ratio of abc will be 24 :40:25,   Amt of b in 35 litr of mixture of a,b,c = 40*35/89 =15.73 ltrs   ANSWER:15.73 ltrs
Answer: C
The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
Choose the correct option
A) 28  B) 68  C) 66  D) 51  E) 11

Solution: Length of the two trains = 600m + 400m   Speed of the first train = X   Speed of the second train= 48 Kmph   1000/X - 48 = 180   1000/x - 48 * 5/18 = 180   50 = 9X - 120   X = 68 Kmph   Answer: 68
Answer: B
The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 75 respectively. The sum is:	Select the correct option.
A) 1360 B) 637.5 C) 1600 D) 1800 E) None

Solution: Sol.   Sum = S.I. * T.D. / (S.I)-(T.D.) = 85 * 75 / (85 - 75) = Rs.637.5.   Answer 637.5
Answer: B
Ramu bought an old car for Rs. 42000. He spent Rs. 8000 on repairs and sold it for Rs. 64900. What is his profit percent?	Choose the most appropriate option:
A) 29.8%
B) 16%
C) 18%
D) 82%
E) 23%

Solution: Total CP = Rs. 42000 + Rs. 8000 = Rs. 50000 and SP   = Rs. 64900   Profit(%) = (64900 - 50000)/50000 * 100= 
(64900 - 50000)/50000 * 100 = 149/5 = around 29.8
29.8%   29.8%nswer:29.8%
Answer: A
a certain organization has three committees. only two persons are members of all committees, but every pair of committees have three members in common. what is the least possible no of member of members on any one committee?  Select:
A) 4	B) 5	C) 6	D) 7	E) 8

Solution: Total 4 members minimum required to serve only on one committee.   4NSWER:4
Answer: A
A sum of money is borrowed and paid back in two annual installments of Rs. 882 each allowing 5% C.I. The sum borrowed was? Pick:	A) 1277	B) 1640	C) 2877	D) 1882	E) 1811

Solution: Explanation:   Principal = (P.W. of Rs. 882 due 1 year hence) + (P.W. of Rs. 882 due 2 years hence)   = [882/(1 + 5/100) + 882/(1 + 5/100)2]   = (882 * 20)/21 + (882 * 400)/441 = Rs. 1640.   Answer: 1640
Answer: B
The present worth of a certain bill due sometime hence is Rs. 400 and the true discount is Rs. 20. What is the banker's discount?
Choose the most appropriate option.
A) Rs. 19  B) Rs. 22  C) Rs. 20  D) Rs. 21  E) None of these

Solution: Explanation :   BG = (TD)2/PW=202/400= Rs. 1   BG = BD – TD   => 1 = BD - 20   => BD = 1 + 20 = Rs. 21 Answer : Option Rs. 21
Answer: D
There are 11 person among whom 2 are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1 person sit between the brothers, is equal to?
Choose the correct choice from the following answers:  A) 4!*2!  B) 7!*2!  C) 6!*1!  D) 2!*1!  E) 8!*2!

Solution: Total number of ways = 8!*2!.   8!*2!
Answer: E
In how many years will a sum of money doubles itself at 5% per annum on simple interest? Choices
A) 80% B) 20% C) 29% D) 30% E) 60%

Solution: P = (P*5*R)/100   R = 20%   Answer: 20%
Answer: B
Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet? Answers
A) 7.16	B) 7.12	C) 7.11	D) 7.15	E) 7.13

Solution: T = (121 + 165)/ (80 + 65) * 18/5   T = 7.15   Answer: 7.15
Answer: D
From a total of 7 men and 3 women, how many ways to form a group of 5 men and 2 women ?	Answers
A) 53	B) 57	C) 61	D) 63	E) None of these

Solution: Explanation :   Required number of ways = (7C5 3C2)   = (21*3)= 
(21*3) = 63
63.   Answer : 63
Answer: D
Pipe A usually fills a tank in 2 hours. On account of a leak at the bottom of the tank, it takes pipe A 30 more minutes to fill the tank. How long will the leak take to empty a full tank if pipe A is shut?
Choose the correct choice
A) 7 hours	B) 8 hours	C) 9 hours	D) 10 hours	E) 11 hours

Solution: Pipe A fills the tank normally in 2 hours. Therefore, it will fill ½ of the tank in an hour.   Let the leak take x hours to empty a full tank when pipe A is shut. Therefore, the leak will empty of the tank in an hour.   The net amount of water that gets filled in the tank in an hour when pipe A is open and when there is a leak = of the tank. — (1)   When there is a leak, the problem states that Pipe A takes two and a half hours to fill the tank. i.e. hours. Therefore, in an hour, of the tank gets filled. – (2)   Equating (1) and (2), we get => => x = 10 hours.   The problem can also be mentally done as follows.   Pipe A takes 2 hours to fill the tank. Therefore, it fills half the tank in an hour or 50% of the tank in an hour.   When there is a leak it takes 2 hours 30 minutes for the tank to fill. i.e hours to fill the tank or or 40% of the tank gets filled.   On account of the leak, (50 - 40)% = 10% of the water gets wasted every hour. Therefore, the leak will take 10 hours to drain a full tank.   ANSWER:10 hours
Answer: D
A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 1, 6, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following?
Choose one
A) 1/7  B) 1/14  C) 1/28  D) 2/49  E) 2/81

Solution: There are 7*7= 
7*7 = 49
49 possibilities.   Bob has 2 chances so the probability is 2/49.   The answer is 2/49.
Answer: D
5n + 7 > 12 and 7n - 5 < 44; n must be between which numbers?  Answers:
A) 1 and 8  B) 2 and 6  C) 0 and 9  D) 1 and 7  E) 2 and 9

Solution: 5n > 5 --> n > 1   7n < 49 --> n < 7   1 < n < 7   Answer: 1 and 7
Answer: D
A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?  Choose the correct choice from the following choices
A) 35 hrs B) 20 hrs C) 10 hrs D) 15 hrs E) 50 hrs

Solution: Pipe 35 hrs alone take x hrs   then pipe B and C will take x/2 and x/4 hrs   =>1/x+2/x+4/x=1/x=>7/x=1/5   x = 35 hrs   35 hrsNSWER 35 hrs
Answer: A
The weight of four dogs is determined to be 25 pounds, 31 pounds, 35 pounds and 33 pounds respectively. The weight of a fifth dog is determined to be y pounds. If the average (arithmetic mean) weight of the first four dogs is the same as that of all five dogs what is the value of y?  Select:
A) 31 B) 33 C) 35 D) 37 E) 39

Solution: Total weight of the 4 dogs = (25+31+35+33)= 
(25+31+35+33) = 124
124   Avg= 124/4= 
124/4 = 31
31   Total weight of 5 dogs= 124+y or 4(31)+y   Average of 5 dogs as per Question = 31   Equation:   4(31) + y = 5 (31), or y = 31.   Choose 31
Answer: A
The sum of three consecutive even numbers is 42. Find the middle number of the three?	Choose the correct answer:
A) 5	B) 8	C) 96	D) 32	E) 14

Solution: Explanation:   Three consecutive even numbers (2P - 2), 2P, (2P + 2).   (2P - 2) + 2P + (2P + 2) = 42   6P = 42 => P = 7.   The middle number is: 2P = 14.   Answer 14
Answer: E
200 liters of a mixture contains milk and water in the ratio 4:1. If 20 liters of this mixture be replaced by 20 liters of milk, the ratio of milk to water in the new mixture would be? Choose the correct choice from the following:	A) 6:1	B) 1:6	C) 2:3	D) 3:2	E) 4:1

Solution: Quantity of milk in 200 liters if mix = 200*4/5= 
200*4/5 = 160
160 liters   Quantity of milk in 210 liters of new mix= 160+20= 
160+20 = 180
180 liters   Quantity of water in it= 210-180= 
210-180 = 30
30 liters   Ratio of milk and water in new mix= 180:30 = 6:1   6:1nswer is 6:1
Answer: A
A car dealership has 40 cars on the lot, 30% of which are silver. If the dealership receives a new shipment of 80 cars, 40% of which are not silver, what percentage of total number of cars are silver? Choose the correct choice from the following choices: A) 35% B) 37.5% C) 45% D) 47.5% E) 50%

Solution: Number of silver cars before shipment = 30% of 40 = 12   Number of silver cars after shipment = 60% of 80 = 48   Total number of silver cars out of 120 = 48+12= 
48+12 = 60
60, which is 50%   50% is my answer.
Answer: E
a, b, c, and d are positive integers where a is a factor of b and c is a factor of d. Which of the following is NOT necessarily an integer?	Choose the correct choice from the following answers:
A) (ac)/(bd)
B) (bd)/(ac)
C) (bcd)/a
D) d/c + b/a
E) (a + b)d/c

Solution: As per the question, let a = 2, b = 6, c = 5, and d = 10. Plugging these into the answer choices, only (ac)/(bd) does not yield an integer.
Answer: A
Operation#is defined as adding a randomly selected two digit multiple of 14 to a randomly selected two digit prime number and reducing the result by half. If operation#is repeated 10 times, what is the probability that it will yield at least two integers?
Choices:  A) 0%  B) 10%  C) 20%  D) 30%  E) 40%

Solution: Any multiple of 14 is even.   Any two-digit prime number is odd.   (even+odd)/2 is not an integer. Thus # does not yield an integer at all.   Therefore P=0.   0%nswer: 0%.
Answer: A
An bus covers a certain distance at aspeed of 180 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of?  Choose the most appropriate option
A) 560 km/h
B) 567 km/h
C) 779 km/h
D) 723 km/h
E) 540 km/h

Solution: Distance = (180 x 5) = 900 km.   Speed = Distance/Time   Speed = 900 /(5/3) km/hr. [We can write 1 hours as 5/3 hours]   Required speed = 900 x 3/5 km/hr = 540 km/hr.   540 km/h
Answer: E
Kim finds a 4-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains? Choose the correct choice from the following options
A) 2/5  B) 7/5  C) 3/5  D) 8/15  E) 1/2

Solution: 3 pieces of 1/5 length and two piece each of 1/15 and 2/15 lengths. removing one piece each from pieces of each kind of lengths the all that will remain will be   2 pieces of 1/5 i.e 2/5, 1 piece of 1/15, and 1 piece of 2/15   Which gives us 2/5 + 1/15 + 2/15 -----> 3/5   Answer is 3/5
Answer: C
A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?  Choose the correct choice from the following answers.
A) 22C10 - 6 B) 22C10 - 4 C) 22C12 - 1 D) 22C10 - 1 E) 12C10 - 1

Solution: The total number of ways of forming the group of ten representatives is 22C10.   The total number of ways of forming the group that consists of no seniors is 10C10 = 1 way   The required number of ways   = 22C10 - 1   Answer: 22C10 - 1
Answer: D
A 750 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform? Choose the correct choice from the following answers.
A) 300 B) 875 C) 360 D) 770 E) 380

Solution: Speed = 750/18 = 125/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 750)/39 = 125/3   => x = 1625 m.   L=1625-750= 
1625-750 = 875
875   Answer: Option 875
Answer: B
The average age of a group of 12 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
Choose the correct choice from the following answers:
A) 22 years
B) 30 years
C) 34 years
D) 32 years
E) None of these

Solution: Answer   The average age of a group of 12 students is 20.   Therefore, the sum of the ages of all 12 of them = 12 * 20= 
12 * 20 = 240
240   When two new students join the group, the average age increases by 2.   New average= 22.   Now, there are 14 students.   Therefore, the sum of the ages of all 14 of them = 14 * 22= 
14 * 22 = 308
308   Therefore, the sum of the ages of the two new students who joined= 308 - 240= 
308 - 240 = 68
68   And the average age of each of the two new students= 68/2= 
68/2 = 34
34 years.   Answer 34 years
Answer: C
An design manager has 10patterns of chairs & 10patterns of tables. In how many ways can he make a pair of table & chair?	Choose the correct choice from the following
A) 20
B) 40
C) 80
D) 90
E) 100

Solution: He has has ten patterns of chairs and eight patterns of tables   Hence, A chair can be arranged in 10 ways and   A table can be arranged in 10 ways   Hence one chair and one table can be arranged in 10 x 10 ways = 100 ways   100
Answer: E
A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:  Choose the correct choice from the following answers:
A) 22 B) 23 C) 24 D) 26 E) 27

Solution: EXPLANATION   Let the number of hens be x and the number of cows be y.   Then, x + y = 48 …. (i)   and 2x + 4y = 140 x + 2y = 70 …. (ii)   Solving (i) and (ii) we get: x = 26, y = 22.   The required answer = 26.   Answer 26
Answer: D
What will be the compound interest on a sum of Rs. 30,000 after 3 years at the rate of 12% p.a.?	Choices
A) s.10123.77
B) s.10123.21
C) s.10123.20
D) s.12147.84
E) s.10123.21

Solution: Amount = [30000 * (1 + 12/100)3]   = 30000 * 28/25 * 28/25 * 28/25   = Rs. 42147.84   C.I. = (42147.84 - 30000)   = Rs. 12147.84   Answer:s.12147.84
Answer: D
Lionel left his house and walked towards Walt's house, 48 miles away. Two hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 3 miles per hour and Walt's 3 miles per hour, how many miles had Lionel walked when he met Walt?
Choose the correct option.
A) 12	B) 16	C) 20	D) 27	E) 28

Solution: In the first 2 hours Lionel at the rate of 3 miles per hour covered distance=rate*time=3*2= 
3*2 = 6
6 miles. So, the distance between him and Walt was 48-6= 
48-6 = 42
42 miles when Walt left his house. Now, their combined rate to cover this distance was 3+3= 
3+3 = 6
6 miles per hour, hence they will meet (they will cover that distance) in time=distance/rate=42/6= 
42/6 = 7
7 hours. Total time that Lionel was walking is 2+7= 
2+7 = 9
9 hours, which means that he covered in that time interval distance=rate*time=3*9= 
3*9 = 27
27 miles.   Answer: 27.
Answer: D
In a box, there are 12 red, 6 blue and 5 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?	Pick one
A) 12/23	B) 10/21	C) 7/12	D) 11/31	E) 13/17

Solution: Total number of balls = 10+6+5 = 23   E = event that the ball drawn is neither red nor green   = event that the ball drawn is red   n(E) = 12   P(E) = 12/23   12/23nswer is 12/23
Answer: A
A and B can do a piece of work in 18 days; Band C can do it in 24 days A and C can do it in 36 days. In how many days will A, Band C finish it together? Choose the correct choice from the following choices: A) 16 days B) 12 days C) 3 days D) 5 days E) 9 days

Solution: Sol. (A + B)'s 1 day's work = (1/18) (B + C)'s 1 day's work = (1/24)   and (A + C)'s 1 day's work = (1/36)   Adding, we get: 2 (A + B + C)'s 1 day's work =¬(1/18 + 1/24 + 1/36)   =9/72 =1/8   (A +B + C)'s 1 day's work =1/16   Thus, A, Band C together can finish the work in 16 days.   16 daysns: 16 days
Answer: A
A, Band C can do a piece of work in 11 days, 20 days and 67 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days?
Select:  A) 7.1 days  B) 8.1 days  C) 9.1 days  D) 10 days  E) 11 days

Solution: (A+8.1 days)'s 1 day's work = 1/11+1/20 = 31/220   (A+C)'s 1 day's work = 1/11+1/67 = 78/737   work done in 2 day's = 31/220+78/737 = 19/77   19/77th work done in 2 days   work done= 77/19*2 = 8.1 days   ANSWER:8.1 days
Answer: B
After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope? Options:  A) 1/12  B) 0  C) 12/212  D) 11/12  E) 11/13

Solution: 0   If one letter is in wrong envelope, the letter corresponding to that letter will also be in wrong envelope.   ANSWER:0
Answer: B
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was Choose the correct option
A) 2500 B) 2700 C) 3000 D) 3100 E) Nobe

Solution: Solution   Number of valid votes = 80% of 7500   = 6000.   Valid votes polled by other candidates	= 45% of 6000   (45/100×6000)   = 2700.   Answer 2700
Answer: B
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions?
Choose the correct answer.
A) 287 m  B) 704 m  C) 278 m  D) 298 m  E) 286 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.   = 500 * 2 * 22/7 * 22.4= 
500 * 2 * 22/7 * 22.4 = 70_400
70400 cm= 704 m   Answer:704 m
Answer: B