MU-NLPC/Calc-aqua_rat huggingface dataset:
One out of every 4000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch?	Choose the correct choice from the following:
A) 450  B) 900  C) 90,000  D) 1800,000  E) 900,000

Solution: (D) Read the whole question to get the feel of what they are asking you to find. Then start with the smallest amount and work your way outwards. We are told that two out of every 30 defective chips have a defective processor. Let x be the total number of defective processors in the batch. Because we know 2 out of every 30 defective chips will have defective processors, and the total number of defective processors in the batch is 30, we can write out an equation: (2/30)x = 30. This can be simplified to (1/15)x = 30. Multiplying each side by 15, we arrive at x = 450. This tells us that there are 450 defective chips in the whole batch. Because we know that 1 out of every 1000 chips is defective, we can set up a proportion. If 1 out of every 4000 chips is defective, then 450 out of y chips would be defective, where y is the total number of chips in the batch. This can be set up as an equation as follows: 1/4000 = 450/y. Solve for y and you will get the total number of chips in the batch: 1800,000.   The answer is (1800,000).
Answer: D
At an art exhibit the entrance costs is $1.15 per person, and every print sold costs $5. Assuming that you bought prints that came in a bag that could hold 12, and another that holds %50 more. How much money do you end up spending all together at the exhibition?  Pick.
A) 180  B) 181.15  C) 1.15  D) 81.15  E) 200.15

Solution: Entrance fee is $1.15.   total prints bought is 12 + (1.50*12)= 36   Total prints cost 36* $5= $180.   Total spent at exhibit is $1.15 + $18036*  5= 
36*  5 = 180
$180.   Total spent at exhibit is $1.15 + $180= $181.15   Answer is 181.15.1.15 +  180= 
1.15 +  180 = 181.15
$181.15   Answer is 181.15.
Answer: B
A 450 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 option.
A) 600 B) 525 C) 360 D) 370 E) 380

Solution: Speed = 450/18= 
450/18 = 25
25 m/sec.   Let the length of the platform be x meters.   Then, (x + 450)/39= 25   => x = 975 m.   L=975-450= 
975-450 = 525
525   Answer: Option 525
Answer: B
Look at this series: 7, 10, 8, 11, 9, 12, 10, 13, 11, ... What number should come next? Pick:
A) 12	B) 13	C) 14	D) 15	E) 16

Solution: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.   The answer is 14.
Answer: C
How many 1's are there preceded by 2 but not followed by 0?
5 9 3 2 1 7 4 2 6 9 7 4 2 1 3 2 8 7 0 1 3 8 3 2 5 6 7 4 3 9 5 8 2 2 1 0 7 4 6 3
Pick:  A) 4  B) 2  C) 6  D) 8  E) 9

Solution: 2 1 7   2 1 3   Only at these places 2 is preceded by 2 but not followed by 0   Answer: 2
Answer: B
Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?  Choose the correct option.
A) 13
B) 17
C) 18
D) 19
E) 12

Solution: Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/9   => 1/x = 1/6 - 1/9 = (3 - 2)/18 = 1/18   => x = 18.   Answer: 18
Answer: C
Three coins are tossed. What is the probability of getting at most two tails?  Choose the correct choice from the following answers.
A) 5/6 B) 2/3 C) 7/8 D) 8/7 E) 6/9

Solution: Explanation :   Total number of outcomes possible when a coin is tossed = 2 (∵ Head or Tail)   Hence, total number of outcomes possible when 3 coins are tossed, n(S) = 2 × 2 × 2 = 8   E = event of getting at most two Tails = {TTH, THT, HTT, THH, HTH, HHT, HHH}   Hence, n(E) = 7   P(E)=n(E)/n(S)=7/8   Answer:7/8
Answer: C
In the Olympic track represented above 8 runners are going to compete to reach the finish line in the shortest amount of time. Between Tom in line 1 and Jack in line 2 there's a distance of 1.2 meters, the same as in the subsequent lanes. If each runner is to race onto their assigned line (and not in the middle of the lane), and Tom is to run on line 1 and Bob on line 8. Bob will have to start-position himself approximately how many meters in front of Tom for the two to run the same distance before reaching the finishing line? Select:
A) 37  B) 51  C) 53  D) 64  E) 85

Solution: first perimeter:402 meters, second perimeter:455, for the two of them to run 402 meters the second athlete will have to start 53 meters ahead.   ANSWER:53
Answer: C
A man can row a boat three quarters of a kilometre in 11.25 minutes. What is the speed of the boat in still water?
Choose one
A) 4 kmph B) 8 kmph C) 6 kmph D) 5 kmph E) 12 kmph

Solution: Explanation:   Simple Division.   No stream current mentioned.   Trick question.   Speed= Distance/Time.   Speed= 3/4 km / (11.25/60) hr   Therefore, Speed = 4 km/hr   4 kmphNSWER:4 kmph
Answer: A
Two men Amar and Bhuvan have the ratio of their monthly incomes as 6 : 5. The ratio of their monthly expenditures is 3 : 2. If Bhuvan saves one-fourth of his income, find the ratio of their monthly savings?  Pick.
A) 4:10
B) 3:10
C) 3:17
D) 3:20
E) 3:60

Solution: Let the monthly incomes of Amar and Bhuvan be 6x and 5x respectively.   Let the monthly expenditure of Amar and Bhuvan be 3y and 2y respectively.   Savings of Bhuvan every month = 1/4(5x)   = (His income) - (His expenditure) = 5x - 2y.   => 5x = 20x - 8y => y = 15x/8.   Ratio of savings of Amar and Bhuvan   = 6x - 3y : 1/4(5x) = 6x - 3(15x/8) : 5x/4 = 3x/8 : 5x/4   = 3 : 10.   Answer:3:10
Answer: B
If u r genius solve it:-
40 * 14 = 11
30 * 13 = 12
20 * 12 = 6
10 * 11 = ?
Choose the correct choice: A) 2 B) 4 C) 6 D) 8 E) 10

Solution: 2   2   Logic :    40*14= 
 40*14 = 560
560=5+6+0= 
5+6+0 = 11
11   30*13= 
30*13 = 390
390=3+9+0= 
3+9+0 = 12
12   20*12= 
20*12 = 240
240=2+4+0= 
2+4+0 = 6
6   So 10*11= 
10*11 = 110
110=1+1+0= 
1+1+0 = 2
2
Answer: A
YES bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?
Choose one: A) 1:5 B) 625:3125 C) 100:105 D) 100^4:105^4 E) 725:3225

Solution: Hi Bunuel,   Here is my approach: is this correct?   YES bank offers an interest of 5% per annum compounded annually on all its deposits.   Interest earned in 4 year= 10000(1+0.05)^4   Interest earned in 5 year= 10000(1+0.05)^5   Ratio= {10000(1.05)^4}/{10000(1.05^5)} =>1.05^4/1.05^5 =>1/1.05 Multiplied by 100 in both numerator and denominator gives 100:105   Hence Ans:100:105
Answer: C
3 men and 2 women are lined up in a row. What is the number of cases where they stand with each other in turn? (The number of cases in which men (or women) do not stand next to each other) Pick:
A) 12
B) 15
C) 18
D) 21
E) 24

Solution: The list should be WMWMW. Hence, from women 2! And men 3!, we get (2!)(3!)=12. Therefore, the correct answer is 12.
Answer: A
The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?	Options
A) 1: 96 B) 1: 98 C) 1: 97 D) 1: 95 E) 1: 91

Solution: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.   (4x)(3x) = 6912   12x2 = 6912   x2 = 576 = 4 * 144 = 22 * 122 (x > 0)   => x = 2 * 12= 
2 * 12 = 24
24   Ratio of the breadth and the areas= 3x : 12x2 = 1 : 4x = 1: 96.   1: 96nswer:1: 96
Answer: A
Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? Pick one
A) 2 years
B) 4 years
C) 6 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 + 4)= 
(38 + 4) = 42
42 years.   Required difference= (42 - 36)= 
(42 - 36) = 6
6 years.   Answer: Option 6 years
Answer: C
A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 300 feet. What is its area, in square feet?
Choose the correct option:
A) 43,200	B) 19,600	C) 20,000	D) 20,400	E) 20,800

Solution: you can avoid a lot of work in this problem by recognizing that, with the info provided, the diagonal forms a triangle inside the rectangle with sides that have a 3:4:5 ratio.   diagonal = 200   2x + 2y = 560, or x + y = 280   a^2 + b^2 = c^2 for each the sides of the triangle   using the ratio 3:4:5 for sides, and knowing c = 300, you can deduce the following   a=180   b=240   180x240=43,200   43,200 is the answer.
Answer: A
Right triangle ABC is the base of the prism in the figure above. If AB=AC=√2 and the height of the prism is 3, what is the volume of the prism?	Choose the correct choice from the following options:
A) 1
B) 3/2
C) 2
D) 3
E) 6

Solution: Volume of prism = Area of base * height = 1/2* (square root of 2) * (square root of 2)*3 = 3   Answer: 3
Answer: D
A,B,C invested the capitals in a business. If A invested Rs. 5000 more than B and C invested Rs.20,000 more than A, then how should a profit of Rs.36,000 be divided among A,B and C? Given : Capital of B is Rs.10,000
Choose the correct answer.
A) 3250, 2250, 6500  B) 3500, 2000, 6500  C) 3000, 2500, 6500  D) 3000, 2000, 7000  E) 3500, 2000, 6250

Solution: A==15,000   B==10,000   C==35,000   so, ration are 3:2:7   profit 14000   so,, 12000/12==1000   so,, A==3000, B==2000,, C==7000   ANSWER:3000, 2000, 7000
Answer: D
John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $30. What is the percent decrease?  Pick one
A) 20%
B) 30%
C) 40%
D) 70%
E) 80%

Solution: The is always the difference between our starting and ending points. In this case, it’s 100 – 30 = 70. The “original” is our starting point; in this case, it’s 100. (70/100)*100 = (0.7)*100= 
(0.7)*100 = 70
70%.   70%
Answer: D
The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?  Choose the correct answer.
A) 18	B) 19	C) 81	D) 16	E) 13

Solution: 1500 ---- 270   100 ---- ? => 18%   18nswer: 18
Answer: A
A man and his wife appear in an interview for two vacancies in the same post. The probability of husband's selection is (1/7) and the probability Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5? of wife's selection is (1/5). What is the probability that only one of them is selected ? Choose the correct option.
A) 9/19 B) 9/20 C) 11/21 D) 11/23 E) 12

Solution: Here, S = {1, 2, 3, 4, ...., 19, 20}.   Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.   P(E) = n(E)/n(S) = 9/20.   9/20)
Answer: B
A book club rented the party room of a local restaurant to meet and discuss its current novel over dinner. The total charge, including food and service, was $ 900. If each member of the club paid at least $ 40, then what is the greatest possible number of members in the club? Choose the correct choice from the following options
A) 19	B) 20	C) 21	D) 23	E) 25

Solution: Given: Each person spends $40   By looking at the options, we see that if there were 20 members, each person will spend atleast $40   Hence the greatest number of members = 22.5 Option 23
Answer: D
When 28 is divided by the positive integer a, the remainder is 1. What is the sum of all the possible values of a for which this is true? Choose one.
A) 2  B) 3  C) 9  D) 30  E) 39

Solution: The only possible values of the form 28=ap+1 are 3,9 or 27   The sum = 3+9+27= 
3+9+27 = 39
39. E is the correct answer. We dont need to look for values >28 as all these values will leave a remainder of 28 and not 1.
Answer: E
Aamir saves 32% of his monthly salary. If he spends Rs. 27200, then find his savings?
Select: A) 12877 B) 12817 C) 12171 D) 12800 E) 128722

Solution: Let the monthly salary of Aamir be Rs. x.   68% of x = 27200   => x = (27200 * 100)/68= 
(27200 * 100)/68 = 40_000
40000   His savings= 32/100 * 40000= 
32/100 * 40000 = 12_800
12800.   Answer:12800
Answer: D
If a sample of data has mean of 20 and SD of 3, which of the following values is more than 2.4 SDs from the mean?  Choose the correct choice from the following
A) 13  B) 20  C) 21  D) 22  E) 18

Solution: 2.4 SD's mean is equal to: +/- 2.4*3 = +/- 7.2   ie. 12.8 to 27.2   13nswer is: 13
Answer: A
If an object travels at 85 feet per second, how many feet does it travel in 30 minutes? Select the correct option
A) 3000
B) 1500
C) 1800
D) 9000
E) 2500

Solution: If an object travels at 85 feet per second it covers 85x60 feet in one minute, and 5x60x30 feet in 30 minutes.   Answer = 9000 Answer: 9000
Answer: D
The average marks of a class of 28 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?  Choose the correct choice from the following
A) 52.2	B) 59.5	C) 52.8	D) 52.5	E) 52.1

Solution: Sum of the marks for the class of 28 students = 28 * 40= 
28 * 40 = 1_120
1120   Sum of the marks for the class of 50 students= 50 * 60= 
50 * 60 = 3_000
3000   Sum of the marks for the class of 78 students=   1120 + 3000= 
1120 + 3000 = 4_120
4120   Average marks of all the students= 4120/78   = 52.8   Answer:52.8
Answer: C
100 liters of a mixture contains milk and water in the ratio 4:1. If 10 liters of this mixture be replaced by 10 liters of milk, the ratio of milk to water in the new mixture would be? Select the correct option:
A) 7:5
B) 9:2
C) 6:1
D) 5:4
E) 11:4

Solution: Quantity of milk in 100 liters if mix = 100*4/5= 
100*4/5 = 80
80 liters   Quantity of milk in 110 liters of new mix= 80+10= 
80+10 = 90
90liters   Quantity of water in it= 110-90= 
110-90 = 20
20 liters   Ratio of milk and water in new mix= 90:20 = 9:2   Answer is 9:2
Answer: B
A number is missing from the number series below.
Can you find it ?
?, 155, 258, 399 , 584, 819. Choose the correct choice from the following answers.
A) 275 B) 84 C) 399 D) 421 E) 449

Solution: B   The missing number is 84.   155 = 5^3 + 5^2 + 5   258 = 6^3 + 6^2 + 6   399 = 7^3 + 7^2 + 7   584 = 8^3 + 8^2 + 8   819 = 9^3 + 9^2 + 9   Thus,   84 = 4^3 + 3^2 + 4
Answer: B
-74x29+265=?  Choose the correct choice:
A) 2436
B) -1881
C) -2801
D) -2071
E) None of them

Solution: Given exp.=-74x(30-1)+265   =-(74x30)+74+265   =-2220+339   =-1881   Answer is -1881
Answer: B
A certain lab experiments with white and brown mice only. In one experiment, 2/3 of the mice are white. If there are 9 brown mice in the experiment, how many mice in total are in the experiment?  Choices:  A) 39  B) 33  C) 27  D) 21  E) 10

Solution: Let total number of mice = M   Number of white mice = 2/3 M   Number of brown mice = 1/3 M = 9   => M = 27   Answer 27
Answer: C
Every Monday, Marina eats one croissant and every Tuesday she eats two croissants. On each subsequent day of the week, she eats a number of croissants equal to the sum of the croissants eaten on the two previous days, with the exception that if she eats more than four croissants on any particular day, the next day she will eat only one croissant. At the end of the week (which runs from Monday through Sunday), the cycle resets, and Marina goes back to eating one croissant on Monday, two on Tuesday, and so forth. If a particular month begins on a Thursday, how many croissants will Marina eat on the 27th of that month? Options
A) 1
B) 2
C) 3
D) 5
E) 6

Solution: She eat as follow   Mon - 1   Tue - 2   Wed - 3   Thr - 5   Fri - 1(since she had more than 4 previous day)   sat - 6   sunday - 1 (since she had more than 4 previous day)   so 27th day of month she will have 2.   Answer is 2
Answer: B
A and B together do a work in 20 days.B and C together in 15 days and C and A in 12 days.then B alone can finish same work in how many days?	Choose the correct answer:
A) 50
B) 60
C) 45
D) 35
E) 48

Solution: (A+60) work in 1 day= 1/20,(60+C) work in 1 days = 1/15.,(C+A) work in 1 days=1/12   (1) adding=2[A+60+C] in 1 day work = [1/20+1/15+1/12]=1/5   (A+60+C) work in 1 day= 1/10   60 work in 1 days= [A+60+C] work in 1 days- work of (A+C) in 1 days   =[1/10-1/12]=1/60   60 alone finish work in 60 days   Answer 60
Answer: B
A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?	Pick.
A) 3:6  B) 3:4  C) 3:9  D) 3:3  E) 3:1

Solution: They should share the profits in the ratio of their investments.   The ratio of the investments made by A and 3:4   =6000 : 8000 => 3:4   Answer:3:4
Answer: B
Three brothers live in a farm. They agreed to buy new seeds: Adam and Ben would go and Charlie stayed to protect fields. Ben bought 75 sacks of wheat in the market whereas Adam bought 45 sacks. At home, they split the sacks equally. Charlie had paid 1400 dollars for the wheat. How much dollars did Ben and Adam get of the sum, considering equal split of the sacks? Choose the correct choice:
A) B$1150-A$180
B) B$1400-A$160
C) B$1225-A$175
D) B$1327-A$199
E) B$1876-A$250

Solution: Every farmer's part is 1/3(45+75) = 40 sacks.   Charlie paid $1400 for 40 sacks, then 1 sack costs $ 1400/40= 
 1400/40 = 35
$35/sack.   Adam got $35*(45-40)=35*5= 
35*5 = 175
$175.   Ben got $35*(75-40)=35*35= 
35*35 = 1_225
$1225.   Answer: Ben $1225, Adam $175
Answer: C
In how many E ways can the letters of the word JUPITER be arranged in a row so that the vowels appear in alphabetic order? Select:
A) 736 B) 768 C) 792 D) 840 E) 876

Solution: three letters can be arranged in 3! ways.   only one combination EIU is required.   7 letters can be arranged in 7! ways.   thus E=7!/ 3! * 1 = 840.   840
Answer: D
A man is facing northwest. He turns 90 degrees in the clockwise direction and then 135degrees in the anti-clockwise direction. Which direction is he facing now?	Select the correct option.
A) East	B) West	C) North	D) South	E) none

Solution: Turns 90 degrees from northwest in clockwise direction is ;His position is Northeast   From Northeast, turns 135 degrees in anticlock : his position is west   ANSWER:West
Answer: B
If two letters are taken at random from the word HOME, what is the probability that none of the letters would be vowels?
Choices.
A) 1/6  B) 1/9  C) 8  D) 2/2  E) 1/1

Solution: 1/6nswer: 1/6) 1/6
Answer: A
If LCM of two number is 693, HCF of two numbers is 11 and one number is 99, then find other
Select.
A) 34	B) 77	C) 12	D) 45	E) 67

Solution: Explanation:   For any this type of question, remember   Product of two numbers = Product of their HCF and LCM   So Other number =   693×11/99   = 77   Option 77
Answer: B
A man bought 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is
Choose the correct choice
A) 12
B) 14
C) 15
D) 16
E) 17

Solution: Dividend on 20=(9/100*20)   =9/5   12 is an income on 100   9/5 is an income on   (100/12*9/5)= 
  (100/12*9/5) = 15
15   Option 15
Answer: C
Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for his new house. Each TV costs $200 more than the size below it. Alan spends a total of $4,400. How much would he have spent if he had bought only the 28 inch and 30 inch TVs?	Choose the correct choice from the following answers:
A) 850 B) 1,100 C) 1,700 D) 2,200 E) 3,400

Solution: Assume the cost of the least sized (26 Inch) TV = x   Cost of 28 inches TV = x + 200   Cost of 30 inches TV = x + 400   Cost of 32 inches TV = x + 600   Total cost = 4x + 1200 = 4400   Therefore x = 3200/4= 
3200/4 = 800
800   Price of 28inch + 30 inch= 1000 + 1200= 
1000 + 1200 = 2_200
2200   Option 2,200
Answer: D
If a and b are integers and (2^a)(3^b) is a factor of 900^40, what is the largest possible value of ab?
Options.
A) 2a
B) 5a
C) 20a
D) 40a
E) 80a

Solution: (2^a)(3^b) is a factor of 900^40   We need to find the largest possible value of ab.   We know that 900 = 2^2*5^2*3^2   Therefore 900^40 will have 2 powers of 3 in it.   Hence in (2^a)(3^b), b has to 2   Therefore value of ab = 2a   Correct Option: 2a
Answer: A
Aarti can do a piece of work in 9 days. In how many days will she complete three time of work of same type?	Choose the correct choice from the following options:
A) 6 days  B) 18 days  C) 21 days  D) 27 days  E) 13 days

Solution: We have the important relation, More work, More time (days)   A piece of work can be done in 9 days.   Three times of work of same type can be done in 9 x 3   = 27 days   Answer 27 days
Answer: D
50 men do a work in 100days. How many men are needed to finish the work in 20days? Choices
A) 50
B) 100
C) 250
D) 300
E) 400

Solution: men required to finish the work in 2days = 50*100/20= 
50*100/20 = 250
250   Answer is 250
Answer: C
Pipe A can fill a tank in 9 hours. Due to a leak at the bottom, it takes 12 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?	Choose the correct choice:  A) 36  B) 88  C) 18  D) 26  E) 12

Solution: Let the leak can empty the full tank in x hours 1/9 - 1/x = 1/12   => 1/x = 1/9 - 1/12 = 1/12   => x = 36. 36nswer:36
Answer: A
85% of a number is added to 24, the result is the same number. Find the number?	Choose the correct choice from the following choices
A) 28	B) 288	C) 279	D) number=160	E) 232

Solution: ( 85/100) * X + 24 = X   3X = 480   X = 160   Answer:number=160
Answer: D
In how many ways can 21 books on English and 19 books on Hindi be placed in a row on a shelf so that two books on Hindi may not be together?	Pick.
A) 3990	B) 1540	C) 1995	D) 3672	E) 2314

Solution: We must place all these books as under:   XEXEX….XEX   There are 21 books on English, 19 books on Hindi   19 places out of 22 can be chosen 22C19=22C3=1540 ways   ANSWER 1540 1540
Answer: B
The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 20 with him, what was the average amount with the group before his joining the group?  Select the correct option.
A) s.17 B) s.12 C) s.15 D) s.29 E) s.20

Solution: Total members in the group = 7   Average amount = Rs. 20   Total amount with them = 7 * 20 = Rs. 140   One number has Rs. 20. So, the amount with remaining 6 people = 140 - 20 = Rs. 20   The average amount with them = 120/6   = Rs.20.   Answer:s.20
Answer: E
If 1 tic equals 4 tacs and 5 tacs equal 8 tocs, what is the ratio of one tic to one toc?  Pick one
A) 15/2 B) 6/5 C) 5/6 D) 32/5 E) 1/15

Solution: Tic=4*Tac and 5*Tac=8*Toc;   5*Tic=20*Tac and 20*Tac=32*Toc --> 5*Tic=32*Toc --> Tic/Toc=32/5.   Answer: 32/5.
Answer: D
In a class there are 20 boys and 30 girls. In how many ways can a boy and a girl be selected?	Choose the most appropriate option:
A) 400	B) 500	C) 600	D) 530	E) 630

Solution: Explanation:   We can select one boy from 20 boys in 20 ways.   We select one girl from 30 girls in 30 ways   We select a boy and girl in 20 * 30 ways i.e., = 600 ways.   Answer: Option 600
Answer: C
Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank? Choose one: A) 22 B) 10 minutes C) 88 D) 566 E) 222

Solution: 4/12 + x/15 = 1   x = 10.Answer: 10 minutes
Answer: B
Man1 alone can do a piece of work in 6 days and Man2 alone in 8 days. Man1 and Man2 undertook to do it for Rs. 3200. With the help of Man3, they completed the work in 3 days. How much is to be paid to Man3?
Pick.
A) 400
B) 200
C) 100
D) 150
E) 500

Solution: Man3 1 day work = 1/3-(1/6+1/8) = 1/3-7/24 = 1/24   Man1 : Man2: Man3 = 1/6:1/8:1/24 ==>4:3:1   Man3 share = 3*1/24*3200= 
3*1/24*3200 = 400
Rs 400   400NSWER 400
Answer: A
A ratio between two numbers is 7:9 and their L.C.M. is 189. The Second number is
Choose the correct choice from the following choices:  A) 35  B) 25  C) 20  D) 27  E) None

Solution: Sol.   Let the required numbers be 7x and 9x. Then, their L.C.M. is 63x.   ∴ 63x = 189⇔ x = 3. Hence, the Second number is 27.   Answer 27
Answer: D