MU-NLPC/Calc-aqua_rat huggingface dataset:
If a boat is rowed downstream for 600 km in 20 hours and upstream for 48 km in 4 hours, what is the speed of the boat and the river? Choose the correct choice: A) 21 , 21 B) 9 , 21 C) 21 , 9 D) 9 , 9 E) 20 , 8

Solution: Explanation:   If x: speed of boats man in still water   y: speed of the river   Downstream speed (Ds) = x + y   Upstream speed (Us) = x â€“ y   x = (Ds + Us) / 2   y = (Ds â€“ Us) / 2   In the above problem Ds = 30 ; Us = 12   x = (30 + 12) / 2 = 42/2= 
42/2 = 21
21 km/hr   y= (30 - 12)/2 = 18/2= 
18/2 = 9
9 km/hr   ANSWER: 21 , 9
Answer: C
If a, b and c are forming increasing terms of G.P., r is the common ratio then find the minimum value of (c-b), given that (log a+log b+log c)/log 6 = 6.Note that r can be any real no.	Choose the most appropriate option:
A) 23
B) 16
C) 17
D) 12
E) 62

Solution: Explanation:   a,b,c are in G.P. so let the first term of G.P. = arar, and common ratio = r.   Therefore, a = arar, b = aa, c = arar   Given, loga+logb+logclog6=6log⁡a+log⁡b+log⁡clog⁡6=6   ⇒logabclog6=6⇒log⁡abclog⁡6=6   ⇒log6abc=6⇒abc=66⇒log6abc=6⇒abc=66   put the value of a,b,c in gp format   ⇒ar×a×ar=66⇒ar×a×ar=66   ⇒a3=66⇒a=36⇒a3=66⇒a=36   Now a = 36r36r, b = 36, c = 36r.   We have to find the minimum value of c - b = 36r - 36.   r can be any number. So for r < 0, we get c - b negative.   When r = 1, c - b = 0   But none of the options are not representing it.   From the given options, r = 4/3, then c = 48. So option d satisfies this.   Answer: 12
Answer: D
One fourth of a solution that was 22% sugar by weight was replaced by a second solution resulting in a solution that was 35 percent sugar by weight. The second solution was what percent sugar by weight?	Pick one:
A) 74%  B) 24%  C) 22%  D) 18%  E) 8.5%

Solution: Say the second solution (which was 1/4 th of total) was x% sugar, then 3/4*0.22+1/4*x=1*0.35 --> x=0.74. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.22+25*x=100*0.35 --> x=0.74.   74%nswer: 74%.
Answer: A
Working alone, Mary can pave a driveway in 5 hours and Hillary can pave the same driveway in 3 hours. When they work together, Mary thrives on teamwork so her rate increases by 10%, but Hillary becomes distracted and her rate decreases by 10%. If they both work together, how many hours will it take to pave the driveway?  Choose the correct choice from the following options
A) 2 hours	B) 4 hours	C) 5 hours	D) 6 hours	E) 7 hours

Solution: Initial working rates:   Mary = 1/5 per hour   Hillary = 1/3 per hour   Rate when working together:   Mary = 1/5 + (1/10*1/5) = 2/9 per hour   Hillary = 1/3 - (1/10*1/3) = 3/10 per hour   Together they work 2/9 + 3/10 = 1/2 per hour   So they will need 2 hours to complete the driveway. The correct answer is 2 hours.
Answer: A
A and B together can do a piece of work in 1 days. If A alone can do the same work in 20days, then B alone can do the same work in? Choose the most appropriate option:	A) 0.35 days	B) 0.45 days	C) 0.55 days	D) 0.25 days	E) 0.95 days

Solution: B = 1/1 – 1/20 =0.95 days   ANSW0.95 daysR:0.95 days
Answer: E
In a classroom, if 6 students per bench are assigned to accommodate all students, one more bench will be required. However, if 7 students are accommodate per bench, there would be a space left for 5 students.What is the number of students in the class ? Choices.
A) 30 B) 45 C) 42 D) 72 E) 75

Solution: Let the number of benches in the class be x.   Then, 6(x + 1) = 7x - 5   x = 11.   Hence, number of students in the class	= 6 ( x + 1)   = 6 x 12   = 72.   ANSWER:72
Answer: D
75 boys can complete a job in 24 days. How many men need to complete the job twice in 20 days
Pick one:	A) 160	B) 170	C) 180	D) 190	E) 200

Solution: One man can complete the job in 24*75= 
24*75 = 1_800
1800 days   To complete the job twice he would need 3600 days.   Thus, to complete the job in 20 days, 3600/20=180 men are needed.   ANSWER:180
Answer: C
In a room there are 10 people. Each shake hands with every other person. How many hand shakes?	Choose the correct answer:
A) 50
B) 62
C) 75
D) 45
E) 61

Solution: Any pair of person = 10C2 = 10!/8!*2! = 45   Answer is 45
Answer: D
Consider four consecutive integers. What is the sum of the 2nd and fourth numbers if the first number is 13?	Choose the correct option.
A) 26 B) 19 C) 30 D) 43 E) None

Solution: 1st = x = 13   2nd = x+1   3rd = x+2   4th = x+3   ------   sum of 2nd and fourth numbers::   x+1+x+3 = 13+1+13+3= 
13+1+13+3 = 30
30   Answer 30
Answer: C
The ratio of the incomes of Chetan and Dinesh is 3:4. The ratio of their expenditures is 5:7. If each of them saves Rs.200, find the incomes of both?  Options:
A) Rs.1200,Rs.1800
B) Rs.1200,Rs.1000
C) Rs.8200,Rs.1600
D) Rs.1200,Rs.1960
E) Rs.1200,Rs.1600

Solution: The savings of Chetan and Dinesh are 3x - 5y and 4x - 7y respectively.   3x - 5y = 200 --- (1)   4x - 7y = 200 --- (2)   Multiplying (1) by 7 and (2) by 5 and subtracting the resultant equation (2) from resultant equation (1), we get x = 400.   The incomes of Chetan and Dinesh are 3x = Rs.1200 and 4x = Rs.1600 respectively.   Answer:Rs.1200,Rs.1600
Answer: E
The average of first 12 natural numbers is? Answers.
A) 5.2  B) 6.5  C) 5.3  D) 5.9  E) 5.1

Solution: Sum of 12 natural no. = 156/2= 
156/2 = 78
78   Average= 78/12= 
78/12 = 13/2 = around 6.5
6.5   Answer:6.5
Answer: B
A man can do a job in 15 days. His father takes 20 days and his son finishes it in 15 days. How long will they take to complete the job if they all work together?	Choose the correct option: A) 6.3 B) 6.9 C) 5.5 D) 6.1 E) 6.2

Solution: 1 day work of the three persons = (1/15 + 1/20 + 1/15) = 11/60   So, all three together will complete the work in 300/47 = 5.5 days.   Answer:5.5
Answer: C
On Sunday, Bill ran 4 more miles than he ran on Saturday. Julia did not run on Saturday, but she ran twice the number of miles on Sunday that Bill ran on Sunday. If Bill and Julia ran a total of 28 miles on Saturday and Sunday, how many miles did Bill run on Sunday?	Choices
A) 5  B) 6  C) 7  D) 8  E) 9

Solution: Let Bill run x on saturday, so he will run x+4 on sunday..   Julia will run 2*(x+4) on sunday..   totai= x+x+4+2x+8=28..   4x+12=28..   x=4..   ans =x+4= 
+4 = 4
4+4= 
4+4 = 8
8   Aswer 8
Answer: D
A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
Options: A) 1079 B) 1017 C) 1023 D) 1017 E) 1012

Solution: Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.   Hence, the required number of ways = 45 - 1.   = 210 - 1 = 1024 - 1= 
1024 - 1 = 1_023
1023   Answer: 1023
Answer: C
Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 5 points more than the previous mock test. If he scored 760 on the GMAT and his average score for the mocks and the GMAT was 726.67, what was the difference in the score of his last mock and his GMAT score? Choose the correct choice from the following:
A) 20
B) 30
C) 40
D) 50
E) 60

Solution: One way to do this would be weighted average method..   1) let the average of 5 mocks be x...   so take it as a mix of5 quantitites of xand1 quantity of 760resulting in an average of 726.67...   By alligation/weighted average..   the difference in 760 and 726.67 is 5/6 of difference of 760 and x..   760-726.67 = 5/6 * (760-x)   760-x= 33.33*6/5=40...   so x = 720..   the last of mock test will be 720+5+5=730...   so ans = 760-730= 
760-730 = 30
30   30
Answer: B
Set D consists of all the prime numbers between 10 and 25. What is the range of set D?	Pick one.
A) 12 B) 13 C) 16.6 D) 17 E) 23

Solution: 12nswer of set D is 12=12
Answer: A
On a Monday in a certain restaurant, 20 percent of the 170 customers ordered the daily special. On Tuesday, only 10 percent of the 120 customers ordered the special. For the two days combined, what percent of the customers ordered the daily special?
Choose the correct option:	A) 15%	B) 16%	C) 18%	D) 23%	E) 30%

Solution: 20% of 170= 34   10% of 120=12   Total =46   percent for 2 days combined =46/300 ≈0.15. so it should be less than 0.15 so it is 15%   15%nswer:15%
Answer: A
How many integers n are there such that 1< 4n +4 < 20? Choose the correct choice from the following answers:
A) Five
B) Four
C) Three
D) Two
E) One

Solution: Solution:   1< 4n + 4 < 20   1< 4n + 4 < 20   We first subtract 4 from all three parts of the inequality, and we obtain:   -3 < 4n < 16   Next, we divide both sides of the inequality by 4 and we get:   -3/4 < n < 4   The answer is Four
Answer: B
A seller uses 800gm in place of 1kg to sell his goods. Find his actual % profit or loss, when he sells his article his article on 10% gain on cost price?
Pick one:
A) 32.5%	B) 37.5%	C) 35%	D) 40%	E) 50%

Solution: Selling price of 800gm = 100+10= 
100+10 = 110
$110   Profit= 110-80= 
110-80 = 30
$30   % of profit= 30*100/80= 
30*100/80 = 75/2 = around 37.5
37.5 %   Answer is 37.5%
Answer: B
A man sitting in a train which is traveling at 60 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?
Choose the correct choice from the following options:  A) 52 kmph  B) 58 kmph  C) 62 kmph  D) 65 kmph  E) 75 kmph

Solution: Relative speed = 280/9 m / sec = ((280/9)*(18/5))= 
((280/9)*(18/5)) = 112
112 kmph.   Speed of goods train= (112 - 60)= 
(112 - 60) = 52
52 kmph.   52 kmphnswer : 52 kmph
Answer: A
Zeynep (the lady of the rings) has 10 identical gold, 10 identical silver and 10 identical bronze rings. (total of 30) She always wears exactly 3 rings on each of her 10 fingers in a particular sequence: first gold, then silver and last bronze. In how many different orders can she wear her 30 rings?
Pick.
A) (10!)^3 / 2^10
B) (10!)^3 / 3^10
C) 30! / 2^10
D) 30! / 3^10
E) 30! / 6^10﻿

Solution: By convention, the answer choice letters are typically listed as capital letters, not lower case. Also, professional math notation is always preferable to plain text shortcuts.   30! / 6^10﻿   ANSW30! / 6^10﻿R:30! / 6^10﻿
Answer: E
The circumferences of two circles are 396 meters and 704 meters. Find the difference between the areas of the larger and the smaller circles?	Answers:
A) 29960 sq m
B) 26950 sq m
C) 43120 sq m
D) 27680 sq m
E) 27786 sq m

Solution: Let the radii of the smaller and the larger circles be s m and l m respectively.   2∏s = 396 and 2∏l = 704   s = 396/2∏ and l = 704/2∏   Difference between the areas = ∏l^2 - ∏s^2   = ∏{198^2/∏^2 - 352^2/∏^2}   = 198^2/∏ - 352^2/∏   = (198 - 352)(198 + 352)/∏   = (154)(550)/(22/7)   =26950 sq m   Answer:26950 sq m
Answer: B
John and Ingrid pay 30% and 40% tax annually, respectively. If John makes $56000 and Ingrid makes $72000, what is their combined tax rate?	Choose the correct choice from the following answers:
A) 32%  B) 34.4%  C) 35%  D) 35.6%  E) 36.4%

Solution: (1) When 30 and 40 has equal weight or weight = 1/2, the answer would be 35.   (2) When 40 has larger weight than 30, the answer would be in between 35 and 40. Unfortunately, we have 2 answer choices D and E that fit that condition so we need to narrow down our range.   (3) Get 72000/128000 = 72/128 = 9/16. 9/16 is a little above 8/16 = 1/2. Thus, our answer is just a little above 35.   Answer: 35.6%
Answer: D
George owns twelve audio compact discs. If he takes two of them to play on an upcoming car trip, how many different pairs of compact discs could he choose?  Choose the correct choice from the following.
A) 144 B) 132 C) 72 D) 66 E) 36

Solution: C212=66   Answer: 66.
Answer: D
The length of the bridge, which a train 250 metres long and travelling at 72 km/hr can cross in 30 seconds, is:	Options.
A) 200 m B) 225 m C) 245 m D) 350 m E) 240 m

Solution: Speed = [72 X 5/18] m/sec = 20 m/sec   Time = 30 sec   Let the length of bridge be x metres.   Then, (250 + x)/30 = 20 => 250 + x= 600 => x = 350 m.   ANSWER:350 m
Answer: D
An inspector rejects 0.0000008% of the meters as defective. How many will be examine to project ? Answers.
A) 2000	B) 230000000	C) 2700	D) 250000000	E) 250

Solution: Let the number of meters to be examined be x.   Then, 0.0000008% of x =2   [(8/10000000)*(1/100)*x] = 2   x = [(2*10000000*100)/8= 
(2*10000000*100)/8 = 250_000_000
250000000   Answer is 250000000.
Answer: D
Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?	Options:
A) 22 sec B) 88 sec C) 99 sec D) 20 sec E) 17 sec

Solution: Relative speed = (42 + 30) * 5/18 = 4 * 5= 
4 * 5 = 20
20 mps.   Distance covered in passing each other= 120 + 280= 
120 + 280 = 400
400 m.   The time required= d/s = 400/20= 
400/20 = 20
20 sec.Answer: 20 sec
Answer: D
A company gives bonus to retailer annually for a set target. This year the retailer has reached 1/4 of his target. If this year his target is increased to 20% from last year, how much target percentage of last year's target he should reach in order to get the bonus.	Answers: A) 5/20 B) 19/20 C) 6/5 D) 10/24 E) 2/3

Solution: Given 1/4 and 20% that is 1/5   Let the target of last year be 20   This year's target is 20% more of last year= 24   Target already reached is   1/4 *20= 
  1/4 *20 = 5
5   Remaining is  24-5= 
 24-5 = 19
19   Required 19/20   Answer is (19/20)
Answer: B
Rs. 900 becomes Rs. 956 in 3 years at a certain rate of simple interest.If the rate of interest is increased by 4% ,What amount will Rs. 900 become in 3 years ? Choose the correct choice from the following options:	A) Rs. 1020.80	B) Rs. 1025	C) Rs. 1064	D) Data inadequate	E) None of these

Solution: Solution   S.I. = Rs.(956-900 )=Rs.56   Rate = (100x56/900x3) = 56/27%   New rate = (56/27 +4)% = 164/27%   New S.I. = Rs.(900 x 164/27 x 3/100) Rs. 164.   ∴ New amount = Rs.(900+164)= Rs. 1064.   Answer Rs. 1064
Answer: C
Replace X with the appropriate number in
2 , 4 , 6 , 30 , 32 , 34 , X  Select
A) 38
B) 8
C) 5
D) 36
E) 37

Solution: 36   list of consecutive numbers that does not contain a 'e' in the spelling
Answer: D
A train 190 m long passed a pole in 10 sec. How long will it take to pass a platform 1200 m long?  Choose the correct choice:
A) 80
B) 73
C) 78
D) 67
E) 56

Solution: Speed = 190/10= 
190/10 = 19
19 m/sec.   Required time= (190 + 1200)/19 = 73 sec.   Answer: Option 73
Answer: B
A person walks from one end to the other of a 60-meter long moving walkway at a constant rate in 30 seconds, assisted by the walkway. When this person reaches the end, they reverse direction and continue walking with the same speed, but this time it takes 120 seconds because the person is traveling against the direction of the moving walkway. If the walkway were to stop moving, how many seconds would it take this person to walk from one end of the walkway to the other?	Select the correct option:	A) 48	B) 60	C) 72	D) 84	E) 96

Solution: Let v be the speed of the person and let x be the speed of the walkway.   30(v+x)=60 then 120(v+x)=240   120(v-x)=60   When we add the two equations:   240v=300   v=5/4   time = 60 / (5/4)= 
60 / (5/4) = 48
48 seconds   The answer is 48.
Answer: A
A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is? Choose the correct answer:
A) 4:8
B) 4:1
C) 4:3
D) 4:2
E) 4:7

Solution: 12:9   = 4:3   Answer: 4:3
Answer: C
Machine P and Machine Q are each used to manufacture 990 sprockets. It takes Machine P 10 hours longer to produce 990 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?	Choose the correct choice from the following:  A) 5  B) 6  C) 7  D) 8  E) 9

Solution: P makes x sprockets per hour.   Then Q makes 1.1x sprockets per hour.   990/x = 990/1.1x + 10   1.1(990) = 990 + 11x   11x = 99   x = 9   The answer is 9.
Answer: E
Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
Pick one:
A) Rs. 9423  B) Rs. 10,250  C) Rs. 12,500  D) Rs. 14,000  E) None of these

Solution: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4   Simran's share = 24500 * 3/7 = Rs. 10500   ANSWNone of theseR:None of these
Answer: E
The average marks of 30 students in a class is 100. But a student mark is wrongly noted as 70 instead of 10 then find the correct average marks?
Options
A) A)78	B) B)82	C) C)98	D) D)91	E) E)85

Solution: correct avg marks = 100+(10-70)/30   avg = 100-2= 
100-2 = 98
98   Answer is 98
Answer: C
30 liters of a mixture contains milk and water in the ratio 2:1. If 5 liters of this mixture be replaced by 5 liters of milk, the ratio of milk to water in the new mixture would be?
Choose the most appropriate option:
A) 3:2	B) 3:1	C) 4:1	D) 5:2	E) 2:1

Solution: Quantity of milk in 30 liters if mix = 30*2/3= 
30*2/3 = 20
20 liters   Quantity of milk in 35 liters of new mix= 20+5= 
20+5 = 25
25 liters   Quantity of water in it= 35-25= 
35-25 = 10
10 liters   Ratio of milk and water in new mix= 25:10 = 5:2   Answer is 5:2
Answer: D
When 8 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads?
Choose the correct choice from the following answers:	A) 1	B) 3	C) 8	D) 31	E) 64

Solution: Total outcome is 2^8 = 256   Favourable cases = H_ _ _ _ _ _ H   The second to seventh places can be occupied by either H or T   There are 2^6 =64 ways that can be done.   Hence, the correct option is 64
Answer: E
Find the perimeter and area of a square of side 15 cm.	Choose the most appropriate option.
A) 144  B) 169  C) 196  D) 121  E) 225

Solution: We know that the perimeter of square = 4 Ã— side   Side= 15 cm   Therefore, perimeter = 4 Ã— 15 cm = 60 cm   Now, area of the square = (side Ã— side) sq. units   = 15 Ã— 15 cmÂ²   = 225 cmÂ²   ANSW225R : 225
Answer: E
At what rate percent on simple interest will Rs.750 amount to Rs.975 in 5 years?	Choose the correct answer.
A) 2  B) 3  C) 4  D) 5  E) 6

Solution: 225 = (750*5*R)/100   R = 6%.Answer: 6
Answer: E
At the beginning of 1992, Maria's stock portfolio was worth $600,000. During 1992, the portfolio's value increased by 95%. During the next year, the portfolio increased its worth by only 5%. What was Maria's portfolio worth, in dollars, by the end of 1993? Choose the correct choice from the following
A) 1,180,000 B) 1,200,000 C) 1,200,300 D) 1,228,500 E) 1,330,000

Solution: By the end of 1992, the port folio worth is 1.95 * ($600K)   By 1993, the portfolio is 1.05 * (1.95 * $600K)   =$ 1,228,500   ANSWER:1,228,500
Answer: D
If A:B = 1/3: 1/4 B:C = 1/3:1/4 then A:B:C?
Choose the correct choice from the following options
A) 1:2:3	B) 16:12:9	C) 4:12:16	D) 9:6:18	E) 4:6:8

Solution: A:16:12:9 = 1/3:1/4= 4:3   16:12:9:C = 1/3:1/4 =4:3   --------------------   A:16:12:9:C = 16:12:9   Answer: 16:12:9
Answer: B
David biked 16 1/3 miles in 2 hours and 20 minutes. What was his average rate of speed in miles per hour?	Choose the correct choice from the following
A) 7
B) 7 2/3
C) 8 1/3
D) 9
E) 9 1/3

Solution: D = 16(1/3) = 49/3   T = 2(1/3) = 7/3   S = D/T = 7   7nswer = 7
Answer: A
What distance will be covered by a bus moving at 72 kmph in 30 seconds?
Select the correct option.
A) 238  B) 600  C) 299  D) 277  E) 1211

Solution: 72 kmph = 72 * 5/18= 
72 * 5/18 = 20
20 mps   D= Speed * time = 20 * 30= 
20 * 30 = 600
600 m.Answer: 600
Answer: B
Which of these numbers is different from the others?
Choose the correct choice:	A) 678	B) 690	C) 696	D) 702	E) 708

Solution: All of the numbers are multiples of 6. 702 is the only number that is also a multiple of 9.   Answer: 702
Answer: D
A coin is tossed live times. What is the probability that there is at the least one tail?
Answers.
A) 31/32  B) 31/39  C) 31/99  D) 31/77  E) 16/99

Solution: Let P(T) be the probability of getting least one tail when the coin is tossed five times.   = There is not even a single tail.   i.e. all the outcomes are heads.   = 1/32 ; P(T) = 1 - 1/32 = 31/32   31/32nswer: 31/32
Answer: A
The lenght of a room is 5.5 m and width is 4 m. Find the cost of paving the floor by slabs at the rate of Rs. 850 per sq. metre.	Choose the correct choice from the following: A) s. 15,550 B) s. 15,600 C) s. 16,500 D) s. 17,600 E) s. 18,700

Solution: Area of the floor = (5.5 Ã— 4) m2 = 22 m2.   Cost of paving = Rs. (850 Ã— 22) = Rs. 18700   Answer: Option s. 18,700
Answer: E
A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 12:00 a.m., at what time was it one-eighth full? Choose the correct choice from the following options:
A) 9:00 a.m.  B) 7:00 a.m.  C) 6:00 a.m.  D) 4:00 a.m.  E) 11:00 a.m.

Solution: To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/8*4=1/2, as it quadruples every hour then container was one-eighth full at 12:00 a.m -1 hour = 11:00 a.m.   Answer: 11:00 a.m..
Answer: E
In given series 7 8 16 46 107 232 448 only one number is incorrect. Find out that wrong number.	Choose the correct choice
A) 8 B) 16 C) 46 D) 107 E) 232

Solution: (N+1)th term = Nth term +(N)^3   8=7+1^3   16=8+2^3   43= 16+3^3............. so 46 is wrong.   107= 43+4^3   232= 107+5^3   448= 232+6^3   ANSWER:46
Answer: C
If 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is?	Options: A) 1:1 B) 2:1 C) 3:1 D) 4:1 E) 5:1

Solution: B   2:1   Let 1 man's 1 day work = x and 1 boy's 1 day work = y.   Then, 12x + 16y = 1/5 and 13x + 24y = 1/4   Solving these two equations, we get:   x = 1/100 and y = 1/200   Required ratio = x:y = 1/100 : 1/200 = 2:1.
Answer: B
A committee of 6 persons is to be formed from 3 company secretaries, 4 economists and 1 chartered accountant. What is the probability that each of the three professions is represented in the committee?
Select the correct option:
A) 1/28  B) 3/28  C) 1/14  D) 360/14  E) 3/14

Solution: 3/8*4/7*1/6*6! = 3/14. We are multiplying by 6! because we can choose secretary,economist, and accountant is several way:   Answer: 360/14.
Answer: D
If 6 - 12/X = 7 - 7/X, then X =
Choices: A) -5 B) 19 C) -7/5 D) 1 E) 5/6

Solution: We're given the equation 6 - 12/X = 7 - 7/X. We're asked for the value of X.   The common-denominator of these 4 numbers is X, so we need to multiply both sides of the equation by X, giving us...   6X - 12X/X = 7X - 7X/X   We can then eliminate that denominator, which gives us....   6X - 12 = 7X - 7   -5 = X   -5
Answer: A
If y ¤ s = y^(2s) for all positive integers, then (3 ¤ 4) ¤ 2 =  Choose the correct choice from the following choices.
A) 3^8  B) 3^12  C) 3^16  D) 3^24  E) 3^32

Solution: y ¤ s = y^(2s)   3 ¤ 4 = 3^(8)   (3 ¤ 4) ¤ 2 = (3^8) ¤ 2 = (3^8)^4 = 3^32   Correct Option: 3^32
Answer: E
Faiza has 7 purses, she gives 3 purse as gift. Now how many purse did she have ? Select:
A) 2
B) 5
C) 11
D) 9
E) 4

Solution: 7-3= 
7-3 = 4
4. Answer is 4
Answer: E
If shares of two persons in profits are Rs.400 and Rs.800 then ratio of their capitals is
Pick one:  A) 3:4  B) 2:3  C) 4:3  D) 1:3  E) 1:2

Solution: profit=time*capital   so 400:800=1:2   ANSW1:2R:1:2
Answer: E
Sam invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?  Choose the correct choice from the following options:
A) 16537.52
B) 16537.29
C) 16537.5
D) 16537.2
E) 16537.11

Solution: P = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year   = 2 half-year   Amount = [15000 * (1 + 5/100)2]   = (15000 * 21/20 * 21/20)   = Rs.16537.50   Answer:16537.5
Answer: C
A shopkeeper forced to sell at cost price, uses a 750 grams weight for a kilogram. What is his gain percent?
Pick
A) 10%  B) 9%  C) 33.33%  D) 12 %  E) None of these

Solution: Shopkeeper sells 750g instead of 1000g.   So, his gain = 1000 - 750= 
1000 - 750 = 250
250g.   Thus, %Gain= (250 *100)/750 = 33.33%.   answer : OPTION 33.33%
Answer: C