MU-NLPC/Calc-aqua_rat huggingface dataset:
The area of a square field is 24200 sq m. How long will a lady take to cross the field diagonally at the rate of 6.6 km/hr?	Pick one:  A) 3 minutes  B) 0.04 hours  C) 2 minutes  D) 2.4 minutes  E) 2 minutes 40 seconds

Solution: Explanatory Answer   Step 1: Compute the length of the diagonal of the square   Let 'a' meters be the length of a side of the square field.   Therefore, its area = a2 square meters. --- (1)   The length of the diagonal 'd' of a square whose side is 'a' meters = √2 a --- (2)   From (1) and (2), we can deduce that the square of the diagonal = d2 = 2a2 = 2(area of the square)   Or d = √2 * area meters.   d =√2∗24200=48400 = 220 m.   Step 2: Compute the time taken to cross the field   The time taken to cross a distance of 220 meters while traveling at 6.6 kmph = 220 m/6.6 kmph   Convert unit of speed from kmph to m/min   1 km = 1000 meters and 1 hour = 60 minutes. So, 6.6 kmph = 6.6∗1000/60 m/min = 110 m/min   ∴ time taken = 220/110= 
220/110 = 2
2 minutes   2 minuteshoice 2 minutes
Answer: C
10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?	Choose the correct choice from the following answers
A) 8 days B) 6 days C) 7 days D) 9 days E) 1 days

Solution: 1 women's 1 day work = 1/70   1 child's 1 day work = 1/140   (5 women + 10 children)'s 1 day work   = (5/10 + 10/140) = (1/14 + 1/14) = 1/7   5 women and 10 children will complete the work in 7 days.   Answer: 7 days
Answer: C
A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1300, what is the reduced price for kg?	Pick one
A) s.40	B) s.65	C) s.49	D) s.41	E) s.42

Solution: 1300*(25/100)= 
1300*(25/100) = 325
325 ---- 5   ? ---- 1=> Rs.65   Answer: s.65
Answer: B
If 20 typists can type 46 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?
Options.
A) 63  B) 72  C) 144  D) 216  E) 207

Solution: 20 typists can type 46 letters, so 30 typists can type = 46*30/20   46*30/20 letters can be typed in 20 mins. In 60 mins typist can type= 46*30*60/20*20= 207   207 is the answer
Answer: E
If (A-B-C+D = 18) and (A+B-C-D = 6), what is the value of (B-D)^2? Choose the correct choice from the following options:
A) 4. B) 8. C) 12. D) 16. E) 36.

Solution: 36.Q1: A - B - C + D = 18   36.Q2: A + B - C - D = 6   (1) Subtract 36.Q1 from 36.Q2   A - B - C + D = 18   - A +B - C - D = 6   ------------------------   -2B + 2D = 12   (2) Simplify   -B + D = 6   B - D = -6   (B-D)^2 = (-6)^2 = 36   My answer: 36.
Answer: E
If n is a prime number and n ≠ 3, which of the following could be the remainder when 100! + n is divided by 3?
I. 2
II. 1
III. -3 Select
A) II only B) III only C) I and II only D) II and III only E) I, II and III

Solution: Notice that we are told that n is a prime number and n ≠ 3. Thus, n cannot be 1.   n also cannot be 6 or any other multiple of 3, thus the remainder cannot be 0.   It can be 1 for n=2 and 2 for n=5.   Answer: I and II only.
Answer: C
How many repeat sequence of three consecutive numbers are there in the given sequence?
6 9 6 2 4 2 9 6 2 9 2 6 9 4 9 6 2 6 9 2 4  Pick
A) 3 B) 2 C) 1 D) 4 E) 5

Solution: 962 repeated 3times   3NSWER:3
Answer: A
List I: 3, 6, 12, 19
List II: x, 3, 6, 8, 19  Choose the most appropriate option:
A) 6
B) 7
C) 8
D) 9
E) 10

Solution: We start by calculating the median of the numbers of list I: 3, 6, 12, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers.   median = (6 + 12)/2   median = 18/2= 
18/2 = 9
9   The median of list I is 9.   Looking at list II: x, 3, 6,12, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 9 and therefore x is 9.   The answer is 9.
Answer: D
Each shelf of a bookcase contained 11 books. If the librarian took out 31 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 4 books, how many shelves does the bookcase have?  Answers:  A) 5  B) 6  C) 7  D) 8  E) 9

Solution: Let x be the number of shelves.   11x - 31 = 7(x-1) + 4   4x = 28   x = 7   The answer is 7.
Answer: C
1804 x 1804 = ? Choose the most appropriate option:  A) A)3254416  B) B)3624216  C) C)3624316  D) D)3625116  E) E)3625216

Solution: 1804 x 1804 = (1804)2   = (1800 + 4)2   = (1800)2 + (4)2 + (2 x 1800 x 4)   = 3240000 + 16 + 14400.= 
3240000 + 16 + 14400. = 3_254_416
3254416.   3254416)
Answer: A
Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part?
Choose one
A) 27	B) 29	C) 30	D) 31	E) 33

Solution: Let $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation   larger number – smaller number = 7   which is equivalent to   Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31.   31
Answer: D
The Pinedale bus line travels at an average speed of 60 km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale Mall, which is 8 stops away. How far away, in kilometers, is Pinedale Mall away from Yahya's house?  Options:
A) 20 km
B) 30 km
C) 40 km
D) 50 km
E) 60 km

Solution: Number of stops in an hour: 60/5= 
60/5 = 12
12   Distance between stops: 60/12= 
60/12 = 5
5 km   Distance between Yahya's house and Pinedale Mall: 5 x 8= 40 km   IMO, correct answer is "40 km."
Answer: C
Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?  Choose the correct choice from the following options.
A) 271  B) 476  C) 277  D) 9898  E) 212

Solution: 3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x = 476   Answer: 476
Answer: B
Three coins are tossed. What is the probability of getting at most two tails? Choose the most appropriate option:
A) 7/8	B) 1/8	C) 1/2	D) 1/7	E) 2/5

Solution: 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   (∵ i.e., S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH})   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   7/8nswer is 7/8
Answer: A
A salesman`s commission is 5% on all sales upto Rs.10,000 and 4% on all sales exceeding this.He remits Rs.31,100 to his parent company after deducing his commission . Find the total sales.
Choose the correct choice
A) 32500 B) 2500 C) 22500 D) 30000 E) 40000

Solution: Let his total sales be Rs.x.Now(Total sales) – (Commission )=Rs.31,100   x-[(5% of 10000 + 4% of (x-10000)]=31,100   x-[((5/100)*10000 + (4/100)*(x-10000)]=31,100   x-500-((x-10000)/25)=31,100   x-(x/25)=31200  24x/25=31200x=[(31200*25)/24)=32,500.   Total sales=Rs.32,500   32500NSWER 32500
Answer: A
The length of the bridge, which a train 110 metres long and travelling at 45 km/hr can cross in 30 seconds, is?	Choices
A) 10 m	B) 16 m	C) 245 m	D) 265 m	E) 27 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(110 + x) = 750 => x   = 265 m.   Answer: 265 m
Answer: D
Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 2 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?	Choices.
A) 16 km
B) 20 km
C) 18 km
D) 15 km
E) 12 km

Solution: Distance = Relative Speed * Time   = (2 + 3) * 4= 
(2 + 3) * 4 = 20
20 km   [ They are travelling in the opposite direction, relative speed= sum of the speeds].   Answer: 20 km
Answer: B
In western Europe, P bicycles were sold in each of the years 1990 and 1993. The bicycle producers of Western Europe had a 42 percent share of this market in 1990 and a 33 percent share in 1993. Which of the following represents the decrease in the annual number of bicycles produced and sold in Western Europe from 1990 to 1993?  Choose the correct choice from the following choices: A) 9% of (x/100) B) 14% of (x/100) C) 75% of (x/100) D) 9% of P E) 14% of x

Solution: Moreover is't question actually asking the the difference between the {(Quantity Produced + Quantity Sold )P in 1990 - (Quantity Produced + Quantity Sold ) in 1993}   Though the Quantity sold in both the years is same it actually boils down to (Quantity Produced in 1990 ) in (Quantity Produced in 1993)=9% of P
Answer: D
A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year? Choose one:	A) 5512	B) 2800	C) 5550	D) 2787	E) 2309

Solution: Total production of salt by the company in that year   = 5000 + 5100 + 5200 + .... + 6100   = 66600.   Average monthly production of salt for that year = 66600/12= 
66600/12 = 5_550
5550.   Answer:5550
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:  Choose the correct option
A) 245 B) 225 C) 200 D) 250 E) 300

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.   245NSWER 245
Answer: A
Simple interest on a certain sum of money for 5 years at 8% per annum is half the compound interest on Rs. 8000 for 2 years at 15% per annum. The sum placed on simple interest is  Choose one.
A) Rs.3225  B) Rs.2580  C) Rs.8000  D) Rs.1290  E) None

Solution: Solution   C.I.	=Rs[8000x(1+15/100)Â²-8000]   Rs.(8000x115/100x115/100-8000)	= Rs.2580.   Sum	=Rs. [1290x100 /5x8]   = Rs.3225.   Rs.3225nswer Rs.3225
Answer: A
Complete the series
13, 9, 5, 1, ...  Choose the correct option
A) -4  B) 0  C) 3  D) -2  E) 3

Solution: In the above series clearly we know we can get the next term by subtract 4 from the previous term so the answer is Option 3) -3
Answer: E
When processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 35% water? Choose one:
A) 1.3 kg
B) 1.5 kg
C) 1.7 kg
D) 1.9 kg
E) None of these

Solution: Explanation :   Flower-nectar contains 50% of non-water part.   In honey this non-water part constitutes 65% (100-35).   Therefore 0.5 X 1.3 kgmount of flower-nectar = 0.65 X 1.3 kgmount of honey = 0.65 X 1 kg   Therefore amount of flower-nectar needed =   (0.65/0.51)kg=1.3 kgs   1.3 kgnswer : 1.3 kg
Answer: A
To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced.How many parts the company made? Choose the correct choice from the following options:
A) 675
B) 778
C) 654
D) 412
E) 589

Solution: Let x be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made:   3⋅25+(x−3)⋅30=75+30(x−3)   Therefore: 25x=75+30(x−3)−100   25x=75+30x−90−100   190−75=30x−25   115=5x   x=23   So the company worked 23 days and they made 23⋅25+100=675 pieces.   correct answer is 675)675
Answer: A
A train 110 meters long completely crosses a 280 meters long bridge in 38 seconds. What is the speed of the train is?  Answers:
A) 32
B) 45
C) 40
D) 66
E) 09

Solution: S = (110 + 280 /38 = 390/38 * 18/5 = 40   Answer: 40
Answer: C
In a barrel of juice there is 15 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?	Options
A) 3:2.  B) 2:1.  C) 3:1.  D) 4:1.  E) 3:4.

Solution: Juice barrel : beer Barrel = 15:80 i.e. 3:8   price of Juice : Price of Beer = 3 : 4   so for 15/80 costs 3/4, ie 15J / 80B = 3/4.   Solving for J/B, we get 4:1   Answer 4:1..
Answer: D
A type of mixture is prepared by mixing brand at Rs.9 a kg with brand B at Rs.4 a kg.If a mixtue is worth rupees 7 a kg,how many kgs of brand A are needed to make 40 kgs of the mixture?	Pick one: A) 21 B) 22 C) 23 D) 24 E) 25

Solution: 9 4   7   (7-4) 3 2 (9-7)   thus ratio would be 3:2   and thus 3x+2x=40   so x=8 and 3x=24.   thus A type of mixture would be of 24 kg.   ANSWER:24
Answer: D
the cyclist going at a constant rate of 20 miles per hour is passed by a motor-cyclist traveling in the same direction along the same path at 60 miles per hour. the motor-cyclist stops to wait for the cyclist 10 minutes after passing her, while the cyclist continues to travel at constant rate, how many minutes must the motor-cyclist wait until the cyclist catches up? Choose the correct choice from the following answers:
A) 10 B) 20 C) 25 D) 30 E) 40

Solution: For the 10 minutes the motor-cyclist continues to overtake the cyclist, she is going at 40 miles per hour faster than the cyclist.   Once the motor-cyclist stops, the cyclist is going at 20 miles per hour while the motor-cyclist is at rest   So the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds. 40/20 * 10 or 20 minutes   Answer is (20)
Answer: B
Divide Rs.32000 in the ratio 3:5?	Choose the most appropriate option.
A) 12000, 20000  B) 12000, 200098  C) 12000, 20007  D) 12000, 20006  E) 12000, 20001

Solution: 3/8 * 32000= 
3/8 * 32000 = 12_000
12000   5/8 * 32000= 
5/8 * 32000 = 20_000
20000   12000, 20000nswer: 12000, 20000
Answer: A
A fraction bears the same ratio to 1/27 as 3/7 does to 5/9. The fraction is? Select the correct option.
A) 1/35
B) 2/35
C) 3/45
D) 4/25
E) 4/27

Solution: Let the fraction be x. Then,   x:1/27 = 3/7 : 5/9   x × 5/9 = 1/27 × 3/7   x × 5/9 = 1/9 × 1/7   x × 5/9 = 1/63   x × 5 = 9/63   5x = 1/7 = 1/35   1/35)
Answer: A
A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is? Select
A) 32
B) 82
C) 83
D) 89
E) 73

Solution: Explanation:   S = (100 + 300)/45 = 400/45 * 18/5= 
400/45 * 18/5 = 32
32   32nswer: Option 32
Answer: A
A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?	Answers.
A) 287 B) 891 C) 277 D) 666 E) 161

Solution: Speed = 240/24= 
240/24 = 10
10 m/sec.   Required time= (240 + 650)/10= 
(240 + 650)/10 = 89
89 sec.   Answer:891
Answer: B
In an examination, 25% of total students failed in Hindi, 50% failed in English and 25% in both. The percentage of these who passed in both the subjects is :	Choices:
A) 23 B) 37 C) 28 D) 40 E) 50

Solution: Explanation:   Formula n(aâˆªb) = n(a) + n(b) âˆ’ n(aâˆ©b)   Fail in Hindi or English = 25 + 50 â€“ 25 = 50   Therefore students who passed = 100 â€“ 50 = 50.   Answer: 50
Answer: E
Which of the below number is the odd one out?
Choose the correct answer.
A) 36142	B) 36119	C) 84129	D) 50246	E) 72927

Solution: D   50246   All the others are three digit numbers followed by their square root, eg 361 followed by its square root, 19.   Answer is 50246
Answer: D
The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?  Choose the correct choice from the following.
A) 240	B) 235	C) 245	D) 250	E) 260

Solution: Speed = 45 * 5/18 = 25/2 m/sec.   Time = 30 sec   Let the length of bridge be x meters.   Then, (130 + x)/30 = 25/2   x = 245 m.   Answer: Option 245
Answer: C
P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?
Choose the most appropriate option
A) 9(3/5) days B) 9(1/5) days C) 9(2/5) days D) 10 days E) 10(1/5) days

Solution: Explanation :   9(3/5) daysmount of work P can do in 1 day = 1/16   9(3/5) daysmount of work Q can do in 1 day = 1/12   9(3/5) daysmount of work P, Q and R can together do in 1 day = 1/4   9(3/5) daysmount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48   => Hence R can do the job on 48/5 days = 9 (3/5) days   9(3/5) daysnswer : Option 9(3/5) days
Answer: A
If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between?  Pick one
A) 0 and 3/20
B) 3/20 and 1/5
C) 1/5 and 1/4
D) 1/4 and 3/10
E) 3/10 and 1/2

Solution: A. 0 and 3/20 - covers 0 to 3/20 but leaves out 3/20 to 10/20. So in essence, covers only 3 parts out of 10 parts   B. 3/20 and 1/5 - covers 3/20 to 4/20 (= 1/5). So in essence, covers only 1 part out of 10 parts   C. 1/5 and 1/4 - covers 4/20 to 5/20. So in essence, covers only 1 part out of 10 parts   D. 1/4 and 3/10 - covers 5/20 to 6/20. So in essence, covers only 1 part out of 10 parts   E. 3/10 and 1/2 - covers 6/20 to 10/20. So in essence, covers 4 parts out of 10 parts. Since this range is the widest, so the probability of the number lying in this range is the highest.   Answer (3/10 and 1/2)
Answer: E
Sohan purchased a horse for Rs.2000 and sold it to Mohan at a loss of 10 percent. Mohan sold it to Sham at a loss of 10 percent while sham sold it to Gopi at a gain of 10 percent. The amount Gopi paid for it would be Pick one:  A) 2399  B) 788  C) 1782  D) 67591  E) 1122

Solution: Explanation:   Cost price = 2000   Selling price = 90% (2000) = 1800.   Mohan sold this to Sham at a loss of 10%. So selling price = 90% (1800) = 1620   Sham sold this at 10% profit. So selling price = 110% (1620) = 1782   Answer:1782
Answer: C
A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 200 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour?	Choose the correct answer:
A) 1	B) 2	C) 3	D) 4	E) 6

Solution: The distance between the nest and the ditch is 200 meters.   15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds.   So the distance is  30 * 200= 
 30 * 200 = 6_000
6000.   4= ST   6000/1.5 = T , I think we can take 6000 meters as 6 km, then only we get T = 4.( 1000 meters = 1 km)   4)
Answer: D
If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b + c ?  Choose one:
A) 12  B) 2  C) -1  D) -3  E) -4

Solution: consectutive even , X , X + 2 , X + 4 where X = Even   now subtract X + (X+2) + (X+4)   doing this leaves us with 3X + 6   what even number can we substitute in X to yield an answer choice   12 works 12 (plug in 2 for X)
Answer: A
A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit?
Options:
A) 1400
B) 1500
C) 1600
D) 1200
E) None of these

Solution: Explanation :   Assume that the total profit is x.   Since 5% goes for charity, 95% of x will be divided between A and B in the ratio 3: 2   => A's profit = (95x/100) * (3/5) = 855   => 95x/100 = 855*5/3 = 285*5= 
285*5 = 1_425
1425=> x = 1425 * 100/95 = 285 * 100/19= 
285 * 100/19 = 1_500
1500   Hence the total profit= 1500. Answer : Option 1500
Answer: B
A box contains eight 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:
A) 10/35 B) 11/35 C) 9/35 D) 8/35 E) 6/35

Solution: Required probability = (4C3 . 4C1)/8C4 = (4 * 4)/70   = 8/35   Answer:8/35
Answer: D
Two thirds of the roads from A to B are at least 5 miles long, and 1/2 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long?  Options:
A) 5/6	B) 1/4	C) 2/3	D) 3/4	E) 11/12

Solution: So please:   Find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long: P=1-1/3*1/2=5/6.   5/6nswer: 5/6.
Answer: A
I came across this problem in the GMATprep software and got it totally wrong!
A company consists of 6 senior and 4 junior staff officers. If a committee is created with 1 senior and 1 junior staff officers, how many possible committees are there?
Choose the correct choice from the following choices
A) 12	B) 44	C) 56	D) 24	E) 200

Solution: 6C1*4C1   =24=24
Answer: D
A train 360 m long is running at a speed of 42 km/hr. In what time will it pass a bridge 140 m long? Choose the correct choice:  A) 40 sec  B) 29 sec  C) 26 sec  D) 27 sec  E) 43 sec

Solution: Speed = 42 * 5/18 = 35/3 m/sec   Total distance covered = 360 + 140= 
360 + 140 = 500
500 m   Required time= 500 * 3/35   = 43 sec   Answer:43 sec
Answer: E
Some people are standing square. From them 32 are removed and then form a small square and
then 8 more removed. now we cannot form the square. so how many people are there at the
beginning?  Select the correct option: A) 31 B) 32 C) 33 D) 34 E) can't be determined

Solution: We should find the two square numbers whose difference is 32. Starting from 9,16,25,36,49,64,81,100,....   We observe   81-49= 
  81-49 = 32
32 & 49-8= 
49-8 = 41
41 which is not a square.   ANSWcan't be determinedR:can't be determined
Answer: E
28% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?
Answers
A) 25 B) 30 C) 50 D) 55 E) 70

Solution: I came up with (E) 70   Think of 100 people total:   From the first fact, 28 of these are women with fair hair.   From the second fact, these 20 women make up 40% of the total fair haired population.   We can then make a ratio of 60:40 fair haired men to fair haired women.   This means that (60/40)*28 equals the number of fair haired men, which is 42 men with fair hair.   Add this 42 to the 28 women and get 70 fair haired men and women out of 100 total men and women.   70%70
Answer: E
The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:  Choose the correct answer:
A) 12  B) 16  C) 24  D) 48  E) 60

Solution: Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.   So, the numbers 12 and 16.   L.C.M. of 12 and 16 = 48.   Answer: Option 48
Answer: D
Working simultaneously at their respective constant rates, machine A and B produces 20 widgets in c hours. Working alone at its constant rate, Machine A produces 20 widgets in 'a' hours.In terms of a and c, how many hours does it take Machine B, working alone at its constant rate, to produce 10 widgets  Options:
A) ac/a+c
B) 2ac/a+c
C) ac/2a+2c
D) ac/2a-2c
E) ac/2c-2a

Solution: Let the individual rates be R(a) and R(b) for machines a and b respectively. Given than combined rate is 20 widgets in c hours => 20/c   R(a) + R(b) = 20/c   Also given is the individual rate for machine a = R(a) = 20/a   Therefore, R(a) + R(b) = 20/c => 20/a + R(b) = 20/c => R(b) = 20/c - 20/a = 20(a-c)/ac = 20/(ac/(a-c)), which basically means that b produces 20 widgets in ac/a-c Hrs. We have to calculate how much does it take to produce 10 widgets. So divide the rate by 2 which gives us ac/2(a-c).   Hence the answer is ac/2a-2c
Answer: D
Three cannons are firing at a target. If their individual probabilities to hit the target are 0.6, 0.7, and 0.8 respectively, what is the probability that none of the cannons will hit the target after one round of fire?
prob. that all the cannons will hit the target = .06
prob. that none of the cannons will hit = 1 - .06 = .94  Choose one:
A) 0.006
B) 0.012
C) 0.024
D) 0.029
E) 0.904

Solution: The probability that eachdoesn'thit is: 0.4, 0.3, and 0.2. When we have multiple independent events, we multiply the probabilities:   .4*.3*.2 = 0.024.   Option: 0.024
Answer: C