MU-NLPC/Calc-aqua_rat huggingface dataset:
10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
Choose one:
A) 2267
B) 287
C) 268
D) 228
E) 225

Solution: 1 man's 1 day work = 1/100   (10 men + 15 women)'s 1 day work = 1/6   15 women's 1 day work = (1/6 - 10/100) = 1/15   1 woman's 1 day work = 1/225   1 woman alone can complete the work in 225 days.   Answer: 225
Answer: E
A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles?
Choose the correct choice from the following answers
A) 54 minutes  B) 34 minutes  C) 32 minutes  D) 21 minutes  E) 16 minutes

Solution: 8 minutes are needed to fill 150 bottles. How many groups of 150 bottles are there in 675 bottles?   675 * 150 = 4.5 = 4 and 1/2   For each of these groups 8 minutes are needed. For 4 groups and 1/2   8* 4 + 4 = 32 + 4= 
32 + 4 = 36
36 minutes. (4 is for 1/2 a group that needs half time)   We can also find the final answer as follows   4.5 x 8= 32 minutes correct answer 32 minutes
Answer: C
The average of runs of a cricket player of 10 innings was 37. How many runs must he make in his next innings so as to increase his average of runs by 4 ?	Select.
A) 76 B) 81 C) 85 D) 87 E) 89

Solution: Explanation:   Average = total runs / no.of innings = 37   So, total = Average x no.of innings = 37 x 10 = 370.   Now increase in avg = 4runs. So, new avg = 37+4= 
37+4 = 41
41runs   Total runs= new avg x new no. of innings = 41 x 11 = 451   Runs made in the 11th inning = 451 - 370= 
451 - 370 = 81
81 Answer: 81
Answer: B
How long does a train 145 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length? Options:
A) 52.66  B) 53.66  C) 54.66  D) 58.66  E) 59.66

Solution: T = (660 + 145)/54 * 18/5   T = 53.66   ANSWER:53.66
Answer: B
A train 100 m long can cross an electric pole in 20 sec and then find the speed of the train?  Pick one: A) 19 Kmph B) 18 Kmph C) 72 Kmph D) 17 Kmph E) 91 Kmph

Solution: Length = Speed * time   Speed = L/T   S = 100/20= 
100/20 = 5
5 M/Sec   Speed= 5*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 18 Kmph   Answer: 18 Kmph
Answer: B
A train covers a distance of 12 km in 10 min. If it takes 12 sec to pass a telegraph post, then the length of the train is?	Choose the correct option:
A) 100	B) 220	C) 120	D) 130	E) 240

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.   Length of the train = 20 * 12= 
20 * 12 = 240
240 m.   Answer: Option 240
Answer: E
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?  Choices: A) 128798 B) 134768 C) 153600 D) 168799 E) 156789

Solution: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.   60   Let length = 3x metres and breadth = 2x metres.   Then, 2(3x + 2x) = 1600 or x = 160.   Length = 480 m and Breadth = 320 m.   Area = (480 x 320) m2 = 153600 m   153600
Answer: C
A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is ?  Pick
A) 7/19 B) 7/15 C) 7/16 D) 7/12 E) 7/11

Solution: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.   Similarly from eight white balls two can be drawn in ⁸C₂ ways.   P = 7C2/15C2 + 8C2/15C2 = 7/15   Answer: 7/15
Answer: B
A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 4% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected.
What is the probability that a smartphone bundle that will be rejected by quality control?  Choose the correct choice from the following options
A) 0.25	B) .05^10	C) 1-0.95^10	D) 1-0.05^10	E) 1-0.96^10

Solution: Find the probability of the opposite event and subtract from 1.   The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.96^10.   P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.96^10.   Answer: 1-0.96^10.
Answer: E
The sale price sarees listed for Rs.600 after successive discount is 20% and 5% is?
Choose the correct choice from the following answers:  A) 227  B) 358  C) 456  D) 787  E) 191

Solution: 600*(80/100)*(95/100)= 
600*(80/100)*(95/100) = 456
456   Answer: 456
Answer: C
A group of medical interns at Bohemus Medical School want to go on dates. There are 6 girls and 6 guys. Assuming girls go on dates with guys, how many possible ways can these 12 medical interns date each other?	Choose the correct answer:  A) A)320  B) B)420  C) C)520  D) D)620  E) E)720

Solution: 1st girl can go with 6 guys   2nd girl can go with remaining 5   3rd girl can go with remaining 4 and so on   so the total ways are 6!= 720   720 should be the answer
Answer: E
A grocer has a sales of Euro 520, Euro 320 , Euro 480, Euro 600 and Euro 800 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Euro 620?
Pick one
A) uro 4691	B) uro 4591	C) uro 2000	D) uro 7791	E) uro 1000

Solution: E   Euro 1000   Total sale for 5 months = Euro (520 + 320 + 480 + 600 + 800)= 
(520 + 320 + 480 + 600 + 800) = 2_720
Euro 2720.   Required sale= uro 1000uro [ (620 x 6) - 2720]   = uro 1000uro  (3720- 2720)= 
 (3720- 2720) = 1_000
uro 1000uro 1000.
Answer: E
It would take one machine 5 hours to complete a large production order and another machine 4 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?
Choose the correct answer
A) A 9/20 B) B 20/9 C) C 7/19 D) D 5/21 E) E 3/4

Solution: The rate of the first machine is 1/5 job per hour;   The rate of the second machine is 1/4 job per hour;   Thus, the combined rate of the machines is 1/5+1/4=9/20 job per hour, which means that it takes 1/(9/20)=20/9 hours both machines to do the job.   Answer: B 20/9.
Answer: B
Mixture A is 20 percent oil, and mixture B is 60 percent oil. If the two are poured together to create a 4-gallon mixture that contains 40 percent oil, approximately how many gallons of mixture A are in the mixture?
Answers
A) 1.0	B) 0.8	C) 0.7	D) 0.6	E) 0.5

Solution: (60-40)/(40-20) = Qa/Qb   20/20 = Qa/Qb   1 = Qa/Qb   Qa = (1/5) * 4 = 4/5= 
4/5 = 4/5 = around 0.8
0.8 approx   Answer : 0.8
Answer: B
A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 12 hours of the journey.  Select:
A) 342 km
B) 352 km
C) 642 km
D) 742 km
E) 492 km

Solution: The total distance covered by the car in the first 12 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 +48 +50 +52 = sum of 12 terms in AP whose first term is 30 and last term is 52 = 12/2 [30 + 52] = 492 km.   ANSW492 kmR:492 km
Answer: E
If a sum of money borrowed at 5 percent/annum SI amounts to Rs.1020 in 4 yrs, then the sum of money borrowed is? Answers:  A) Rs. 850  B) Rs. 960  C) Rs. 1000  D) Rs. 1200  E) Rs. 1230

Solution: Sol We have, A : Rs.1U2D   Let the pr xnpal be R5 x   Then mterest u — 12 : wzo — x   Therefore, by u xglurmula.   _umxx   ’ Rx’: (   , _ma>< 1nzn—xv   \4Ve|\a\e,Jc— 5“   :> ~(:51DD—S*(or6x:51UU   or, J: : w 350   . The sum of money burrowed : Rs. 850   Rs. 850)
Answer: A
3 pig’s and 10 hens are brought for Rs.1200. If the average price of a hen be Rs.30. What is the average price of a pig.  Choose the correct choice from the following options:
A) 300
B) 350
C) 400
D) 425
E) 275

Solution: Explanation:   Average price of a hen = Rs.30   total price of 10 hens = 10*30 = Rs.300   But total price of 3 pigs and 10 hens = Rs. 1200   Total price of 3 pigs is = 1200 - 300= 
1200 - 300 = 900
900   Average price of a pig= 900/3   = Rs. 300   300nswer: 300
Answer: A
A girl swims downstream 48 km and upstream 18 km taking 6 hours each time; what is the speed of the current? Choose the correct choice from the following choices:  A) 2.2  B) 2.3  C) 2.1  D) 2.5  E) 2.4

Solution: 48 --- 6 2.5S = 8   ? ---- 1   18 ---- 6 US = 3   ? ---- 1 S = ?   S = (8 - 3)/2= 
(8 - 3)/2 = 5/2 = around 2.5
2.5   Answer:2.5
Answer: D
Which of the following numbers is divisible by each one of 3, 7, 9 and 11 ?  Select the correct option
A) 2079	B) 456	C) 974	D) 562	E) 300

Solution: 639 is not divisible by 7   2079 is divisible by each of 3, 7, 9, 11.   2079NSWER 2079
Answer: A
If y ¤ q = y^(2q) for all positive integers, then (3 ¤ 4) ¤ 2 =
Choose the correct choice
A) 3^8	B) 3^12	C) 3^16	D) 3^24	E) 3^32

Solution: y ¤ q = y^(2q)   3 ¤ 4 = 3^(8)   (3 ¤ 4) ¤ 2 = (3^8) ¤ 2 = (3^8)^4 = 3^32   Correct Option: 3^32
Answer: E
Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 10 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?	Choose one.
A) 1:5
B) 9:25
C) 5:1
D) 25:9
E) Cannot be determined from the information provided

Solution: Same circumferential rate means that a point on both the gears would take same time to come back to the same position again.   Hence in other words, time taken by the point to cover the circumference of gear A = time take by point to cover the circumference of gear B   Time A = 2*pi*25/Speed A   Time B = 2*pi*5/Speed B   Since the times are same,   50pi/Speed A = 10pi/Speed B   SpeedA/Speed B = 50pi/30pi = 5/1   5:1orrect Option: 5:1
Answer: C
If x/y = 5/3, then (x + y)/(x - y) = ? Choose the most appropriate option
A) 4 B) 1/5 C) -1/6 D) -1/5 E) -5

Solution: Any x and y satisfying x/y = 5/3 should give the same value for (x + y)/(x - y).   Say x=5 and y=3, then (x + y)/(x - y) = (5 + 3)/(5-3)= 
(5 + 3)/(5-3) = 4
4.   4nswer: 4.
Answer: A
For all even numbers n, h(n) is defined to be the sum of the even numbers between 4 and n, inclusive. What is the value of h(12)/h(10) ?
Choose the correct choice from the following options
A) 1.8 B) 3 C) 6 D) 1.5 E) 60

Solution: CONCEPT: When terms are in Arithmetic Progression (A.P.) i.e. terms are equally spaced then   Mean = Median =(First+Last)/2   and Sum = Mean*Number of terms   h(12) = [(4+12)/2]*5 = 40   h(10) (4+12)/2 *5= 
(4+12)/2 *5 = 40
40   h(10)= (4+10)/2]*4 = 28   h(12)/h(10) (4+10)/2 *4= 
(4+10)/2 *4 = 28
28   h(12)/h(10)= (40) / (28) ~ 1.5   Answer : 1.5
Answer: D
Last year, sales at Company X were 10% greater in February than in January, 15% less in March than in Feb, 20% greater in April than in March, 10% less in May than in April, and 5% greater in June than in May. In which month were sales closest to Jan? Pick:
A) Feb
B) Mar
C) Apr
D) May
E) June

Solution: Jan = $100   10% greater in February than in January ---> Feb = 1.1 Jan = $110   15% less in March than in Feb ---> Mar = 0.85 Feb = $93.5   20% greater in April than in March ---> Apr = 1.2 Mar = $112   10% less in May than in April ---> May = 0.9 Apr = $101 (we have a winner)   5% greater in June than in May --->Jun = 1.05 May = $106   Ans May
Answer: D
A boat running downstream covers a distance of 12 km in 2 hours while for covering the same distance upstream, it takes 3 hours. What is the speed of the boat in still water?  Options:  A) 8 kmph  B) 5 kmph  C) 4 kmph  D) 6 kmph  E) 7 kmph

Solution: Speed downstream =12/2= 
12/2 = 6
6 kmph   Speed upstream=12/3= 
12/3 = 4
4 kmph   Speed of the boat in still water= 6+4 / 2= 5 kmph   ANSWER:5 kmph
Answer: B
The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:
Pick:
A) 101	B) 107	C) 111	D) 185	E) none

Solution: EXPLANATION   Let the numbers be 37a and 37b.   Then, 37a x 37b = 4107   ab = 3.   Now, co-primes with product 3 are (1, 3).   So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).   Greater number = 111.   Answer 111
Answer: C
A person walking takes 26 steps to come down on a escalator and it takes 30 seconds for him for walking. The same person while running takes 18 second and 34 steps. How many steps are there in the escalator?  Answers:	A) 45 steps	B) 46 steps	C) 47 steps	D) 48 steps	E) 49 steps

Solution: 26+30n=18+34n   12n=8   n=2/3 substitute n valve   26+30(2/3)=46 steps   ANSWER:46 steps
Answer: B
The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:  Choose the correct choice from the following:
A) 12 years	B) 14 years	C) 16 years	D) 18 years	E) 20 years

Solution: Let the present age of son =x   present age of father (60 -x)   Then, (60 - x) - 6 = 5(x - 6)   54 - x = 5x - 30   6x = 84   x = 14.   Son's age after 6 years = (x+ 6) = 20 years   Answer :20 years
Answer: E
A man can row upstream at 8kmph and downstream at 13 kmph. The speed of the stream is
Choices: A) 2.5 km/hr B) 4.2 km/hr C) 5 km/hr D) 10.5 km/hr E) None

Solution: Sol.   Speed of stream = 1/2(13 -8) kmph = 2.5 kmph.   2.5 km/hrnswer 2.5 km/hr
Answer: A
How much water must be mixed in 300 ml of sugar solution which contains 40% sugar by Weight, such that it becomes a 30% sugar solution?  Answers:
A) 50 ml	B) 75 ml	C) 90 ml	D) 100 ml	E) 120 ml

Solution: Total Quantity = 300 ml   Sugar by weight = 120 ml   Water= 180 ml   Let x be the amount of water added to the solution   Then 120/(300 + x)=30/100   =>1200 = 900 + 3x   =>x= 100 ml   ANSWER:100 ml
Answer: D
The harmonic mean of two numbers xx and yy, symbolized as h(x,y)h(x,y), is defined as 2 divided by the sum of the reciprocals of xx and yy, whereas the geometric mean g(x,y)g(x,y) is defined as the square root of the product of xx and yy (when this square root exists), and the arithmetic mean m(x,y)m(x,y) is defined as x+y2x+y2. For which of the following pairs of values for xx and yy is g(x,y)g(x,y) equal to the arithmetic mean of h(x,y)h(x,y) and m(x,y)m(x,y)?	Select the correct option:
A) x=−2 y=−1	B) x=−1, y=2	C) x=2, y=8	D) x=8, y=8	E) x=8, y=64

Solution: A. x=−2 , y=−1   B. x=−1 , y=2   C. x=2 , y=8   D. x=8 , y=8   E. x=8 , y=64   The arithmetic mean, the geometric mean and the harmonic mean of two equal numbers are equal((x+x)/2=x, sqrt(x*x)=x, (2x*x)/(x+x)=x).   So without tedious calculation, (x=8, y=8) should be answer.
Answer: D
Two pipes A and B can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank? Choose the correct choice from the following choices:
A) 14 min 49 sec B) 14 min 70 sec C) 14 min 41 sec D) 14 min 40 sec E) 24 min 40 sec

Solution: Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15   Remaining part = 1 - 7/15 = 8/15   Part filled by B in 1 minute = 1/20   1/20 : 8/15 :: 1 ; x   x = 8/15 * 1 * 20 = 10 2/3 min = 10 min 40 sec.   The tank will be full in (4 min. + 10 min. 40 sec) = 14 min 40 sec.   Answer:14 min 40 sec
Answer: D
The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 60%?
I will see what is the quickest way to solve it then I will provide the explanation	Choose the correct choice from the following choices: A) 6 B) 7 C) 9 D) 4 E) 11

Solution: The following approach might be the easiest one and less error prone.   We need on-time departure rate to be higher than 6/10, so it should be at least 7/11, which means that 7 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then  7-3= 
 7-3 = 4
4 subsequent flights need to depart on-time.   Answer: 4
Answer: D
How many liters of water must be added to 20 liters of milk and water containing 10% water to make it 50% water? Choose the correct choice from the following options:
A) 10	B) 12	C) 14	D) 16	E) 18

Solution: By rule of alligation:   50% - 10% = 40%   100% - 50% 50  - 10= 
50  - 10 = 40
40%   100% - 50% = 50%   Quantity of pure water : Quantity of the mixture  100  - 50= 
 100  - 50 = 50
50%   Quantity of pure water : Quantity of the mixture= 4 : 5   There are 20 liters of mixture, so we need to add 16 liters of pure water.   The answer is 16.
Answer: D
If x and y are integers and 3^(x-5) = 3^(y+2), what is y in terms of x?
Choose the correct answer
A) x - 6
B) x - 7
C) x - 2
D) x + 2
E) x + 6

Solution: Answer: A   3^(x-5) = 3^(y+2)   Since the base is the same, I isolated the equations and solved for y.   x-5 = y+2   y=x-7   Ans : x - 7
Answer: B
Each of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum Q in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her original investment is  Choices.
A) 90% B) 80% C) 70% D) 60% E) 40%

Solution: The problem asks for the approximate chance that no more than 1/3 of the original investment is lost. We can apply the “1 – x” technique: what’s the chance that more than 1/3 of the original investment is lost? There are two outcomes we have to separately measure:   (a) All 3 investments become worthless.   (b) 2 of the 3 investments become worthless, while 1 doesn’t.   Outcome (a): The probability is (0.2)(0.2)(0.2) = 0.008, or a little less than 1%.   Outcome (b): Call the investments X, Y, and Z. The probability that X retains value, while Y and Z become worthless, is (0.8)(0.2)(0.2) = 0.032. Now, we have to do the same thing for the specific scenarios in which Y retains value (while X and Z don’t) and in which Z retains value (while X and Y don’t). Each of those scenarios results in the same math: 0.032. Thus, we can simply multiply 0.032 by 3 to get 0.096, or a little less than 10%.   The sum of these two probabilities is   0.008 + 0.096= 
  0.008 + 0.096 = 0.104
0.104, or a little more than 10%. Finally, subtracting from 100% and rounding, we find that the probability we were looking for is approximately 90%.   The correct answer is A.   This problem illustrates the power of diversification in financial investments. All else being equal, it’s less risky to hold a third of your money in three uncorrelated (independent) but otherwise equivalent investments than to put all your eggs in one of the baskets. That said, be wary of historical correlations! Housing price changes in different US cities were not so correlated—and then they became highly correlated during the recent housing crisis (they all fell together), fatally undermining spreadsheet models that assumed that these price changes were independent.
Answer: A
Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 8160, how much money did he borrow?	Choose the correct choice from the following:
A) 8000
B) 80288
C) 2668
D) 2600
E) 2781

Solution: Let the sum be Rs. x. Then,   [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 8160   18x + 45x + 39x = (8160 * 100)   102x = 816000 => x = 8000.   8000nswer:8000
Answer: A
The ratio between the sale price and the cost price of an article is 12:7. What is the ratio between the profit and the cost price of that article?
Pick
A) 2:9  B) 2:5  C) 3:6  D) 5:7  E) 2:1

Solution: Let C.P. = Rs. 7x and S.P. = Rs. 12x.   Then, Gain = Rs. 5x   Required ratio = 5x : 7x = 5:7   Answer:5:7
Answer: D
For the past n days, the average (arithmetic mean) daily production at a company was 60 units. If today's production of 90 units raises the average to 62 units per day, what is the value of n ? Choose the correct choice from the following answers
A) 30
B) 14
C) 10
D) 9
E) 7

Solution: (average production for n days) * n = (total production for n days) --> 60n=(total production for n days);   (total production for n days) + 90 = (average production for n+1 days) * (n+1) -->60n + 90 = 62 * (n+1) --> n=14.   Or as 30 extra units increased the average for n+1 days by 2 units per day then 30/(n+1)=2 --> n=14.   Answer: 14.
Answer: B
During a certain week, a seal ate 45% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?  Options: A) 32 B) 48 C) 55 D) 64 E) 80

Solution: Total smelt = x.   Then, 0.45*80+0.3(x-80)=0.4*x --> x=120 --> 0.4*x=48.   Answer: 48.
Answer: B
At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
Choose the correct choice:
A) 77 years	B) 15 years	C) 66 years	D) 88 years	E) 55 years

Solution: Let the present ages of Arun and Deepak be 4x and 3x years respectively.   Then, 4x + 6 = 26 => x = 5   Deepak's age = 3x = 15 years.   Answer: 15 years
Answer: B
The mean of four integers A will not change if all the integers are multiplied by any constant. What is always true about this set of numbers?
I. The mean of the set is 0
II. The sum of the largest member and the smallest member of the set is 0
III. The set contains both positive and negative integers
Choices:
A) I only B) II only C) III only D) I and II only E) I, II, and III

Solution: If we consider a set {1,2,3,4}, when multiplied with a constant we take that constant as 1 and multiply resulting set will contain the same numbers as the original. so how can the answer be I only.....I only
Answer: A
The average of five numbers is 281. The average of the first two numbers is 280 and the average of last two numbers is 178.5. What is the third number?	Pick.
A) 27
B) 88
C) 16
D) 19
E) 11

Solution: Answer:88
Answer: B
a is an integer greater than 9 but less than 21, b is an integer greater than 19 but less than 31, what is the range of a/b?
Choose the correct choice from the following choices:
A) 1/4 B) 1/2 C) 2/3 D) 1 E) 5/4

Solution: min value of a/b will be when b is highest and a is lowest ---> a=10 and b=30   So, a/b = 1/3   max value of a/b will be when b is lowest and a is highest ---> a=20 and b=20   So, a/b = 1   Range is 1-(1/3) = 2/3.   Answer should be 2/3
Answer: C
A certain manufacturer increased its gross profit on a product from 10 percent of the cost of the product to 15 percent of the cost by changing the selling price. If the new selling price was $92.00 and the cost of the product remained the same, what was the old selling price?  Choose the correct choice
A) $77.40
B) $80.00
C) $83.64
D) $87.40
E) $88.00

Solution: Given that {cost of the product}*1.15=$92 --> {cost of the product}=$80.   The old price was $ 80*1.1= 
 80*1.1 = 88
$88.   Answer: $88.00.
Answer: E
Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? Pick one.
A) 11  B) 77  C) 60  D) 12  E) 14

Solution: Let the speed of the slower train be x m/sec.   Then, speed of the train = 2x m/sec.   Relative speed = ( x + 2x) = 3x m/sec.   (100 + 100)/8 = 3x => x = 25/3.   So, speed of the faster train = 50/3 = 50/3 * 18/5= 
50/3 * 18/5 = 60
60 km/hr.   Answer:60
Answer: C
A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:5, and the ratio of soap to salt is four times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is quartered by water evaporation. At that time, what is the ratio of water to salt in the solution? Choose the correct choice from the following answers:  A) 9:100  B) 100:9  C) 12:100  D) 12:20  E) 13:100

Solution: Water:soap = 3:5   Soap:Salt=12:20   => For 12 soap, salt = 20   => For 5 Soap, salt = (20/12)*5 = 100/12=25/3   So, water:soap:salt = 3:5:25/3 = 9:15:25   9:100fter open container, water:soap:salt = 2.25:15:25   So, water:salt = 2.25:25 = 9:100   9:100NSWER:9:100
Answer: A