MU-NLPC/Calc-aqua_rat huggingface dataset:
Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $5 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 18 percent, what is the discount rate on Pony jeans?  Choose the correct option:
A) 9%	B) 10%	C) 34.4%	D) 12%	E) 15%

Solution: You know that Fox jeans costs $15, and Pony jeans costs $18, you also know that 3 pairs of Fox jeans and 2 pairs of Pony jeans were purchased. So   3(15) = 45 - Fox   2(18) = 36 - Pony   The total discount discount is $5 and you are asked to find the percent discount of pony jeans,   so 45(18 - X)/100 + 36(X)/100 = 5 or 45*18 -45*x + 36*x =5*100 or 9x = -5*100 +45*18= 
-5*100 +45*18 = 310
310/9=34.4   34.4%
Answer: C
A cycle is bought for Rs.1000 and sold for Rs.2000, find the gain percent?	Select
A) 11  B) 20  C) 100  D) 77  E) 12

Solution: 1000 ---- 1000   100 ---- ? => 100%   Answer: 100
Answer: C
If abc = b^3 , which of the following must be true?
I. ac = b^2
II. b = 0
III. ac = 1	Choose the correct choice from the following options:
A) None
B) I only
C) II only
D) I and III
E) II and III

Solution: abc = b^3 implies abc - b^3 = 0   or b*(ac-b^2)=0   which implies either b=0 or ac=b^2   so, either of them or both of them can be true, but none of them must be true.   Nonenswer None
Answer: A
The age of man is three times the sum of the ages of his two sons. Seven years hence,his age will be double of the sum of the ages of his sons.The fatherâ€™s present age is :  Answers.
A) 40 years	B) 45 years	C) 50 years	D) 55 years	E) 63 years

Solution: Solution   Let the sum of present ages of the two sons be x years.   Then,father's present age = 3x years.   âˆ´ (3x + 7)=2 (x +14) â‡” 3x + 7 = 2x + 28â‡” x =21.   Hence,father's present age = 63 years. Answer 63 years
Answer: E
Jane and Ashley take 13 1/3 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ?
Choose the correct choice from the following answers
A) 10 Days B) 15 Days C) 16 Days D) 17 Days E) 20 Days

Solution: Let us assume that the work is laying 40 bricks.   Jane =3 bricks per day   Ashley = 1 brick per day   Together = 4 bricks per day   Let's say first 8 days Ashley works alone,   No of bricks = 8   Last 4 days Jane works alone,   No. of bricks = 12   Remaining bricks = 40 - 20= 
40 - 20 = 20
20   So together, they would take   20/4= 
  20/4 = 5
5   Total no. of days= 8 + 4 + 5= 
8 + 4 + 5 = 17
17   Answer is 17 Days
Answer: D
The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:11. If P invested the money for 5 months, find for how much time did Q invest the money?
Choose the correct choice from the following choices:  A) 19  B) 17  C) 13  D) 11  E) 12

Solution: 7*5: 5*x = 7:11   x = 11   Answer: 11
Answer: D
What is the smallest positive integer x, such that 5000x is a perfect cube?  Choose the correct choice from the following options:
A) 4
B) 6
C) 8
D) 25
E) 18

Solution: Take out the factors of 5000 that will come 10^3*5. for perfect cube you need every no. raise to the power 3. for 5000x to be a perfect cube, you need two 5 that means 25.   25 is the answer.
Answer: D
A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?	Answers:
A) 5/8 B) 5/9 C) 5/7 D) 5/2 E) 5/3

Solution: Two balls can be picked from nine balls in ⁹C₂ ways.   We select one white ball and one red ball from five white balls and four red balls. This can be done 4C2 . 4C1 ways.   The required probability = (5 * 4)/9C2 = 20/36 = 5/9   Answer: 5/9
Answer: B
The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent? Choose the correct choice:
A) 18 2/15
B) 18 2/11
C) 18 2/14
D) 18 2/16
E) 18 2/12

Solution: 13 CP = 11 SP   11 --- 2 CP   100 --- ? =>18 2/11%.Answer: 18 2/11
Answer: B
Which of the following is closer to (5!+4!)-(5!-4!)?
Choices.
A) 48  B) 84  C) 240  D) 420  E) 52

Solution: 5!+4!)-(5!-4!)=120+24-120+24= 
120+24-120+24 = 48
48   48nswer: 48
Answer: A
The total number of digits used in numbering the pages of a book having 346 pages is	Choose the most appropriate option
A) 732  B) 990  C) 1098  D) 930  E) 1405

Solution: Total number of digits   = (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)   = (1 x 9 + 2 x 90 + 3 x 247) = (9 + 180 + 741)= 
(9 + 180 + 741) = 930
930.   ANSWER:930
Answer: D
The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @Rs.26.50 per metre is Rs.5300, what is the length of the plot in metres? Options
A) 55  B) 60  C) 65  D) 70  E) 75

Solution: Length of the fence =530026.50=200 m   ⇒ 2(length + breadth)=200 m   ⇒ 2(breadth + 20 + breadth)=200 m (∵ length = breadth+20)   ⇒ breadth + 20 + breadth =100 m   ⇒ breadth =40 m   length =40+20= 
40+20 = 60
60 m   Answer is 60.
Answer: B
A rich merchant had collected many gold coins. He did not want anybody to know about him. One day, his wife asked, " How many gold coins do we have?" After a brief pause, he replied, "Well! if I divide the coins into two unequal numbers, then 48 times the difference between the two numbers equals the difference between the squares of the two numbers." The wife looked puzzled. Can you help the merchant's wife by finding out how many gold coins the merchant has?  Choose the most appropriate option: A) 96 B) 53 C) 43 D) None of these E) Cannot be determined

Solution: Explanation :   Let the numbers of gold coins = x + y   => 48(x-y) = x2 - y2.   => 48(x-y) = (x- y)(x + y).   => x + y = 48.   Answer : None of these
Answer: D
How many days are there in x weeks x days	Choose the correct choice from the following answers:	A) 14x	B) 8x	C) 7x^2	D) 7	E) 6

Solution: Explanation:   x weeks x days =(7×x)+x = 7 x+x=8x days   Answer: Option 8x
Answer: B
How many two-element subsets of {6,7,8,9} are there that do not contain the pair of elements 8 and 9?
Select the correct option:
A) 5
B) 4
C) 3
D) 6
E) 7

Solution: Required subsets are = {6,7}, {6,8}, {6,9}, {7,8}, {7,9} = 5   5nswer: 5
Answer: A
A fast food restaurant sells chicken in orders of 6, 9, and 20.
What is the largest number of pieces of chicken you cannot order from this restaurant?  Options.
A) A)23 B) B)33 C) C)43 D) D)53 E) E)63

Solution: 43.   After 6 all numbers divisible by 3 can be ordered (because they can all be expressed as a sum of 6's and 9's). After 26, all numbers divisible by three when subtracted by 20 can be obtained. After 46, all numbers divisible by three when subtracted by 40 can be obtained. After 46, all numbers fit into one of these 3 categories, so all numbers can be obtained. 43 is the last number that doesn't fall into one of these categories (44 = 20 + 6 * 4, 45 = 6 * 6 + 9). answer is 43
Answer: C
The positive integer b is divisible by 5.
What is the remainder when dividing 3(6+b)(5+b) by 5?  Choose the correct choice from the following options:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: When we multiply any of these options: 3*11*10 (b=5) or 3*16*15 (b=10) we end up with numbers ending in 0 which are exactly divisible by 5 leaving no remainder.   Hence answer is 0.
Answer: A
A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
Pick one.
A) 250  B) 288  C) 276  D) 188  E) 112

Solution: CP1 = 100 SP1 = 90   CP2 = 80 SP2 = 80 * (140/100)= 
80 * (140/100) = 112
112   22 ----- 100   55 ----- ?=> Rs.250   250nswer: 250
Answer: A
Two pipes A,B can fill a tank in 24 min. and 32 min. respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min.?
Options:
A) 6 B) 7 C) 8 D) 9 E) 5

Solution: work done by A => 18/24   work done by B => x/32   18/24 + x/32 = 1   3/4 + x/32=1   24+x=32 => x=8   after 8 min b should be closed   ANSWER:8
Answer: C
The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary? Select:
A) 3% decrease  B) 5% decrease  C) 9% decrease  D) 8% decrease  E) 6% decrease

Solution: (30 * 30)/100= 
(30 * 30)/100 = 9
9% decrease   Answer: 9% decrease
Answer: C
The ratio of three numbers is 1:2:4 and the sum of their squares is 4725. The sum of the numbers is?  Choose the correct answer.
A) A)10  B) B)12  C) C)15  D) D)14  E) E)9

Solution: Let the numbers be x,2x,4x   then, x^2+4x^2+16x^2 = 4725   21x^2 = 4725   x^2 = 225   x=15   Answer is 15
Answer: C
One fourth of a solution that was 10% sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?
Choose the correct choice from the following answers: A) 34% 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*0.1+1/4*x=1*0.16 --> x=0.34. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.1+25*x=100*0.16 --> x=0.34.   34%nswer: 34%.
Answer: A
Tough and Tricky questions: Word Problems.
Mike, Sarah and David decided to club together to buy a present. Each of them gave equal amount of money. Luckily Sarah negotiated a 20% discount for the present so that each of them paid 4 dollars less. How much did they pay for a present? Pick one:  A) 20  B) 36  C) 48  D) 60  E) 72

Solution: Answer C.   We know that Sarah negotiated a discount of 20%, so each of them paid $4 less. Since there are three people, the 20% of the original price amounts to $12. 5 times 12$ is 60$, so the original price, before Sarah negotiated the discount, had been $60. They paid $12 less than the base price, so they spent $48.
Answer: C
Sudhir started a business with Rs.40,000 and after 8 months Ravi joined him with Rs.60,000. If they get a profit of Rs.28000 then ratio of their shares will be Choose the correct choice:
A) 3:2  B) 2:1  C) 4:3  D) 3:4  E) 3:5

Solution: 40000*12:60000*(12-8)   =480000 :240000   =2:1   ANSWER:2:1
Answer: B
The area of a triangle is with base 5.5m and height 6m?
Choose the correct choice from the following:	A) 11 m2	B) 16.5 m2	C) 18.5 m2	D) 19.5 m2	E) 12 m2

Solution: 1/2 * 5.5* 6= 
1/2 * 5.5* 6 = 16.5
16.5 m2   Answer: 16.5 m2
Answer: B
From the integer n, if n*n*n is odd, then what is true from below options?  Choose the most appropriate option
A) n is odd and n*n is even	B) n is odd	C) n is even	D) n*n is even	E) n*n is odd

Solution: n is odd and n*n is even   Option n is odd and n*n is even
Answer: A
Two trains of length 100 meters and 200 meters are 840 meters apart. They are moving towards each other on parallel tracks, at speeds of 54 km/h and 72 km/h. After how many seconds will the trains meet?
Select.
A) 20 B) 22 C) 24 D) 26 E) 28

Solution: The speeds are 54000/3600= 
54000/3600 = 15
15 m/s and 72000/3600= 
72000/3600 = 20
20 m/s   The relative speed is 35 m/s.   time= 840 / 35= 
840 / 35 = 24
24 seconds   The answer is 24.
Answer: C
How many three-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4?
Choose the correct choice from the following choices
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: Required subsets are = {1,2,3}, {1,3,4}= 2   Answer: 2
Answer: B
If a(a + 6) = 27 and b(b + 6) = 27, where a ≠ b, then a + b =  Choose the correct choice from the following choices:
A) −48
B) −6
C) 2
D) 46
E) 48

Solution: a(a + 6) = 27 and b(b + 6) = 27   => a, b must be integers and if a is -9 or 3, b will be 3 and -9 respectively   => a+b = -6   Ans: −6
Answer: B
A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
Choose the correct option.
A) 65 seconds
B) 46 seconds
C) 40 seconds
D) 97 seconds
E) 26 seconds

Solution: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   = 500 * (2/25)= 
500 * (2/25) = 40
40 seconds   Answer:40 seconds
Answer: C
A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 1 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold? Choose the correct choice from the following options.
A) 480  B) 120  C) 289  D) 270  E) 927

Solution: 1/x - 1/20 = -1/24   x = 120   120 * 1= 
120 * 1 = 120
120   Answer: 120
Answer: B
A palindrome is a word or a number that reads the same forward and backward. For example, 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits 1, 2, 3, 4, and 5, how many palindromes are possible? Choose the correct answer.
A) 25	B) 75	C) 125	D) 225	E) 625

Solution: There are 5 choices for each of the first three digits.   The number of possible palindromes is 5^3=125.   The answer is 125.
Answer: C
A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 2.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?
Choose the correct option:
A) (320 - y)/(5x)
B) (y +250)/(5x)
C) 5(80 - y)/(4x)
D) (y + 400)/(4x)
E) (4y + 250)/(5x)

Solution: Ans (y +250)/(5x)   Plug some numbers   Let y = 40 houses and x = 20   then they painted 20 houses per week   as painters were added to the group , the rate of the group increased to 2.25 x => 2.25 * 20= 
2.25 * 20 = 45
45 houses per week   total time they took= (40/20) + (40/45) = 2.9 weeks   Putting the values of x and y in equation (y +250)/(5x)   (y +250)/(5x) = (40+250)/5*20 = 290/100= 
290/100 = 29/10 = around 2.9
2.9
Answer: B
You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs.	Answers.
A) 180	B) 181	C) 182	D) 178	E) 168

Solution: add the max weights   52+50+78= 
52+50+78 = 180
180   180NSWER:180
Answer: A
The majority owner of a business received 25% of the profit, with each of 4 partners receiving 25% of the remaining profit. If the majority owner and two of the owners combined to receive $46,875, how much profit did the business make?	Select the correct option: A) $55,000 B) $75,000 C) $95,000 D) $115,000 E) $125,000

Solution: Let P be the total profit.   P/4 + 1/2*(3P/4) = P/4 + 3P/8 = 5P/8 = 46875   P = $75,000   The answer is $75,000.
Answer: B
When the price of an article was reduced by 40% its sale increased by 80%. What was the net effect on the sale?	Choose the correct choice from the following options:  A) 8% increase  B) 4% decrease  C) 6% increase  D) 66% increase  E) 66% decrease

Solution: if n items are sold for $p each, revenue is $np. If we reduce the price by 40%, the new price is 0.6p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.6p)(1.8n) = 1.08np, which is 1.08 times the old revenue, so is 8% greater.   8% increaseNSWER:8% increase
Answer: A
If (20)² is subtracted from the square of a number, the answer so obtained is 4321. What is the number?
Choose the correct choice from the following answers
A) 68 B) 69 C) 70 D) 71 E) 72

Solution: x^2=4321+400= 
4321+400 = 4_721
4721   4761=69*69   x=69   ANSWER:69
Answer: B
If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players? Select the correct option:
A) 1245	B) 1268	C) 1290	D) 1345	E) 1365

Solution: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.   =. Required number of ways = 14C10 = 14C4   = 14!/4!x19! = 1365   1365
Answer: E
In a certain large company, the ratio of college graduates with a graduate degree to non-college graduates is 1:8, and ratio of college graduates without a graduate degree to non-college graduates is 2:3. If one picks a random college graduate at this large company, what is the probability T this college graduate has a graduate degree?	Choose the correct choice:	A) 1/11	B) 1/12	C) 1/13	D) 3/19	E) 3/43

Solution: In believe the answer is D. Please see below for explanation.   0) we are told the following ratios   CG3/19 - College Graduate with 3/19egree   NCG - Non College Graduate   CGN - College Graduate no 3/19egree   CG3/19 NCG CGN   1 8   3 2   In order to make CG3/19 and CGN comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get   CG3/19 NCG CGN   3 24 16   If one picks a random college graduate at this large company, what is the probability this college graduate has a graduate degree?   Nr of CG3/19 = 3   Nr of CG = 3+ 16= 
3+ 16 = 19
19   Probability T of CG3/19 / (CG) -> 3/19   Answer 3/19
Answer: D
The greatest common factor of positive integers m and n is 14. What is the greatest common factor of (2m^2, 2n^2)? Choose the most appropriate option:	A) 14	B) 28	C) 196	D) 392	E) 784

Solution: m = 14j and n = 14k, where the greatest common factor of j and k is 1.   2m^2 = 2*14*14*j^2 and 2n^2 =  2*14*14= 
 2*14*14 = 392
392   The answer is 392.
Answer: D
A sun is divided among X, Y and Z in such a way that for each 5 rupees X gets, Y gets 3 rupees and Z gets 2 rupees. If the share of Z is RS. 200, what is the total amount of X and Y?
Options.
A) 650	B) 800	C) 600	D) 700	E) 900

Solution: x:y:z = 500:300200   5:3:2   2 --- 200   8 --- ? => 800   Answer: 800
Answer: B
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. -2  Choose the correct choice from the following.
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
If xy > 0, 1/x + 1/y = 15, and 1/xy = 5, then (x+y)/5 = ?  Choose the correct choice from the following options.
A) 1/25	B) 1/6	C) 3/5	D) 5	E) 6

Solution: (1/X+1/Y)=15 canbe solved as {(x+y)/xy}=5. Substituting for 1/xy=5, we get   x+y=15/5   ==> (x+y)/5= 15/(5*5)=3/5.   3/5
Answer: C
A farmer sells his strawberries through a distributor, which take a commission of 12% of the price set by the farmer. The distributor obtains the product from a farmer at the price of $35 per bushel. What is the price that the buyer observers if the distributor wants to maintain a 12% profit on the cost of a bushel? Answers:
A) 66.22
B) 44.55
C) 44.05
D) 66.02
E) 75.48

Solution: Farmer price = $35;The distributor wants to maintain a 12% profit on the cost of each strawberry bushel, thus he must get $ 35*1.12= 
 35*1.12 = 39.2
$39.20 after the distributor takes a commission of 12% of the final price --> (final price)*0.88= $39.20 --> (final price) = $44.55Answer: 44.55.
Answer: B
A train passes a man standing on the platform. If the train is 160 meters long and its speed is 72 kmph, how much time it took in doing so?	Choose one
A) 5 sec B) 6 sec C) 8 sec D) 9 sec E) 7 sec

Solution: D = 160   S = 72 * 5/18= 
72 * 5/18 = 20
20 mps   T= 160/20= 
160/20 = 8
8 sec   ANSWER:8 sec
Answer: C
Length of a rectangular plot is 12 mtr more than its breadth. If the cost of fencing the plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
Choose the correct option.
A) 56 m
B) 60 m
C) 80 m
D) 82 m
E) 84 m

Solution: Let breadth = x metres.   Then, length = (x + 12) metres.   Perimeter = 5300 m = 200 m.   26.50   2[(x + 12) + x] = 200   2x + 12 = 100   2x = 88   x = 44   Hence, length = x + 12 = 56 m   56 m
Answer: A
How much time does a train 125 metres long running at 60 km/hr take to pass a pole?  Select the correct option
A) 7.9s	B) 2.5s	C) 7.5s	D) 7.6s	E) 7.4s

Solution: Explanation:   60 km/hr = 60 * 5/18 = 16.67 m/s   Speed = distance/time; v = d/t   16.67 = 125/t   t = 7.5s   ANSWER: 7.5s
Answer: C
A car travels uphill at 30 km/hr and downhill at 90 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car? Answers:  A) 32kmph  B) 39kmph  C) 34kmph  D) 35kmph  E) 36kmph

Solution: avg speed=total distance/total time.   total distance traveled=100+50= 
100+50 = 150
150km;   time taken for uphill journey=100/30=10/3;   time taken for down hill journey=50/90=5/9;   avg speed=150/(10/3+5/9)=39kmph   ANSWER:39kmph
Answer: B
On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction R of the total distance did he cover while the sun was shining on him?  Choose the most appropriate option.
A) 1/4
B) 4/5
C) 1/5
D) 1/6
E) 1/7

Solution: If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is R=2/14 = 1/7. Answer: 1/7
Answer: E
The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches? Select the correct option:
A) 31
B) 66
C) 55
D) 77
E) 81

Solution: Total score of the batsman in 20 matches = 800.   Total score of the batsman in the next 10 matches = 130.   Total score of the batsman in the 30 matches = 930.   Average score of the batsman = 930/30= 
930/30 = 31
31.   31nswer: 31
Answer: A
Two men and three women can repair a bridge in 10 days while three men and two women can do same work in 8 days. If two men and one woman are used to finish this work, in how many days they will complete it?	Answers:
A) 9.7 days
B) 12.5 days
C) 10 days
D) 11.3 days
E) 12.7 days

Solution: Work done by 2 men and 3 women in 1 day = 1/10   Work done by 3 men and 2 women in 1 day = 1/8   Let 1 men does m work in 1 day and 1 women does w work in 1 day. The above equations can be written as   2 m + 3 w = 1/10 ---(1)   3 m + 2 w = 1/8 ---(2)   Solving equation (1) and (2) , we get m=14/200 and w=1/100   2 men and 1 woman together can finish the work in =14/200+1/100=2/25=12.5 days   12.5 days
Answer: B
A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?  Choices:  A) 16  B) 13  C) 15  D) 18  E) 12

Solution: Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.   1/x + 1/(x - 5) = 1/(x - 9)   (2x - 5)(x - 9) = x(x - 5)   x2 - 18x + 45 = 0   (x- 15)(x - 3) = 0 => x = 15   Answer: 15
Answer: C
Andrew is selling fruit to be able to buy a new bike. The bike costs 400. He sells a large bag of fruit for $8. He so far has sold 32 bags, how many more need to be sold in order to buy the bike.  Pick one:
A) 3  B) 18  C) 15  D) 12  E) 2

Solution: 8*32= 
8*32 = 256
256   400-256= 
400-256 = 144
144   144Ã·8=18   18 more bags of fruit need to be sold in irder for the bike to be purchased.   Therefore answer 18 is correct.
Answer: B