MU-NLPC/Calc-aqua_rat huggingface dataset:
Seven children — A, B, C, D, E,— are going to sit in seven chairs in a row. The children CE have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?  Pick:
A) 600	B) 720	C) 48	D) 4320	E) 4800

Solution: for such questions , we can treat both as one then total person=4..   these 4 can be arranged in 4! ways.. but within these 4, one consists of two people who can be arranged in 2 ways CF or FC.. so ans =4!*2=48   ans 48
Answer: C
It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is? Choose the correct choice from the following answers:  A) 3:9  B) 3:3  C) 3:4  D) 3:1  E) 3:2

Solution: Let the speed of the train be x km/hr and that of the car be y km/hr.   Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i)   And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii)   Solving (i) and (ii), we get x = 60 and y = 80   Ratio of speeds = 60:80 = 3:4   Answer: 3:4
Answer: C
A certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $120,000 and variables costs averaging $8 per item. If the manufacturer’s selling price per item is $12, how many items the manufacturer produce and sell to earn an annual profit of $140,000? Choose the correct choice from the following options:  A) 2,858  B) 18,667  C) 21,429  D) 35,000  E) 65,000

Solution: Let the items manufactured or sold bex   120000+8x = 12x-140000   4x = 260000   x = 65000   Ans:65,000
Answer: E
A can go round a circular path 8 times in 40 minutes. If the diameter of the circle is increased to 10 times the original diameter, then the time required by A to go round the new path once, travelling at the same speed as before is	Choose the correct choice from the following answers: A) 20 min B) 35 min C) 50 min D) 70 min E) none

Solution: Solution   Let original diameter be d metres. Then, its circumference = (Πd)metres.   Time taken to cover (8Πd)m = 40 min.   New diameter = (10d)m. Then, its circumference = (Π x 10d)m.   Time taken to go round it once   ‹=› [40 / 8Πd x 10Πd]m   ‹=›50 min.   Answer 50 min
Answer: C
In a jar there are 20 white balls, 24 green balls and 32 blue balls. How many balls must be taken out in order to make sure we have 22 balls of the same color? Options:  A) a)	23  B) b)	46  C) c)	57  D) d)	63  E) e)	67

Solution: Here, we need to find minimum number of marbles to be taken out to get 22 marbles of same color.   For a instance, if we take 21 white marbles 1st and followed by 22 Green and then 22 Blue.   Total will be   20 + 21+ 21= 
  20 + 21+ 21 = 62
62 draws.   If we choose either Green or Blue next time. This will bring the total of either of these colored marble to 22.   So Minimum we need to take 62+1= 
62+1 = 63
63 Times to get 22 marbles of same color(either Green or Blue).   Answer : d)	63.
Answer: D
Free notebooks were distributed in a class among all the students. Each student got notebooks which were one-eighth of the number of student. If number of student been half, then each child would have received 16 notebooks in total. Find the total number of books distributed among students?	Choose the most appropriate option:
A) 456
B) 534
C) 457
D) 567
E) 512

Solution: Let suppose total number of students in class are X.   Then from the question we can conclude it that,   X∗18X=X2∗16=>X=64Total notebooks,=18X2=(18∗64∗64)=512   512
Answer: E
In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case?
Choose the correct choice from the following answers
A) 568  B) 528  C) 567  D) 872  E) 623

Solution: Assume X soldiers join the fort. 1200 soldiers have provision for 1200(days for which provisions last them)(rate of consumption of each soldier)   = 1200(30)(3) kg   Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) kg   As the same provisions are available   => 1200(30)(3) = (1200 + x)(25)(2.5)   x = [1200(30)(3)]/[(25)(2.5)] - 1200   Answer: 528   x = 528
Answer: B
The variable x is inversely proportional to the square of the variable y. If y is divided by 5a, then x is multiplied by which of the following?
Answers
A) a. 1/25a B) b. 1/25a^2 C) 1/5a D) 25a E) 25a^2

Solution: initially - did x= 1/y^2   But this yielded the wrong answer,   I then re examined the question and tried y^2/x =1   Which I then got y = SQR(X)   subbing into y/5a I got answer 25a^2)
Answer: E
If the terms of a series are either2or24and the sum of all the terms G of the series is 124, then which of the following could be the number of2sin the series?  Choose the correct choice from the following answers:
A) 26	B) 29	C) 35	D) 40	E) 48

Solution: Ans: A   Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms G is 124 means  24*5= 
 24*5 = 120
120 so number of 24 can't be more than 5   so 24x +2y= 124   24*5 + 2y =124 then y=2   24*4 + 2y = 124 then y=14   24*3 +2y = 124 then y= 26   24*2 +2y =124 then y = 38   24 +2y = 124 then y= 50   26 is the ans.26
Answer: A
A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 820 in 4 years. The
rate on interest per annum is.  Choose the most appropriate option
A) 0.4%  B) 5.0%  C) 2.5%  D) 7%  E) 8%

Solution: Explanation:   S.I. on Rs 800 for 1 year = 20   Rate = (100*20)/(800*1)= 
(100*20)/(800*1) = 5/2 = around 2.5
2.5%   Answer: 2.5%
Answer: C
Consider a sequence of numbers given by the expression 7 + (q - 1) * 5, where n runs from 1 to 80.What is the sum of this series ?
Pick:
A) 409
B) 1636
C) 16360
D) 16000
E) 15360

Solution: terms in this sequence are 7,12,17----402   now since this is an a.p. with a common difference of 5. therefore its sum can be given as   q(a+l)/2----------------1)   q= total no. of terms =80   a= first term=7   l= last term=402   subsituting values in the expression 1 we have   80(7+402)/2   = 40(409)   =16360=16360
Answer: C
Find all integers x NOT EQUAL TO 3 such that X-3|X^3-3  Choose the correct choice from the following choices
A) 1,2,3,4,5
B) -21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27
C) 1
D) 6
E) -1,0,1

Solution: Let x-3=t. Thus, t is an integer not equal to such'that t|(t+3)^2-3,   which is equivalent to the condition t|3^3-3, or t|24. Therefore, it is necessary   and sufficient for t to be an integer divisor of 24, hence t must be equal   to one of the numbers +or-1, +or-2, +or-3, +or-4, +or-6, +or-8, +or-12, +or-24. For x   = t+3 we obtain the values -21, -9, -5, -3, -1,0,1,2,4,5,6,7,   9, 11, 15, and 27.   Correct Answer -21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27 -21,-9,-5,-3,-1,0,1,2,4,5,6,7,9,11,15,27
Answer: B
How long does a train 140 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?	Choose the correct option:
A) 13.6 sec B) 12.1 sec C) 17.9 sec D) 16.8 sec E) 14.9 sec

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec   Total distance covered= 140 + 132= 
140 + 132 = 272
272 m.   Required time= 272/20= 
272/20 = 68/5 = around 13.6
13.6 sec.   13.6 secnswer: 13.6 sec
Answer: A
a is what percent of b percent of c, in terms of a, b and c?	Choose the correct choice from the following answers:  A) 10^4*a/bc  B) abc  C) bc*10^4  D) 1/abc  E) abc/1000

Solution: Algebraically, b% of c is just (b/100)*c, or bc/100. So we want to answer the question: a is what percent of bc/100? Say a is equal to m% of bc/100; then we have:   a = (m/100)*(bc/100)   10,000a/bc = m   10^4*a/bc
Answer: A
A 20 kg metal bar made of alloy of tin and silver lost 2 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar?  Choose the correct choice:
A) 1/4  B) 2/5  C) 1/2  D) 3/5  E) 2/3

Solution: The bar lost certain percentage of its weight. We don't know how much tin was lost and how much silver was lost but in all 2 kg was lost with is 10% of its overall weight.   Tin loses 1.375 kg in 10 kg so 13.75% of its weight when it is put in water.   Silver loses .375 kg in 5 kg so  .375/5 * 100= 
 .375/5 * 100 = 7.5
7.5% of its weight in water.   Now, we just need to use weighted averages:   Wt/Ws= (7.5 - 10)/(10 - 13.75) = 2.5/3.75 = 2/3   Answer (2/3)
Answer: E
A and B together invested Rs. 10,000 in a business. At the end of the year, out of total profit is Rs. 2,000 B's share was Rs. 800. A's investment was  Select
A) s. 4,000  B) s. 6,000  C) s. 10,500  D) s. 11,250  E) s. 12,250

Solution: A+s. 6,000=10000   total profit=2000   2000-800= 
2000-800 = 1_200
1200   1200;800=3:2   then   3*10000/5= 
  3*10000/5 = 6_000
6000   ANSWER:s. 6,000
Answer: B
Mrs. Peter got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.  Choose the correct choice.
A) $145  B) $231  C) $112  D) $214  E) $321

Solution: A   $145   Let the 1st paycheck be x (integer).   Mrs. Peter got a weekly raise of $ 145.   So after completing the 1st week she will get $ (x+145).   Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.   = $ (x + 145 + 145)   = $ (x + 290)   So in this way end of every week her salary will increase by $ 145.
Answer: A
In a box there are 5 red balls and 6 blue balls. What is the probability of drawing at least one red ball when drawing 3 consecutive balls randomly?
Choose the correct option
A) 201/202 B) 164/165 C) 256/259 D) 98/103 E) 115/217

Solution: P(at least one red) = 1 - P(no red, so 3 blue) = 1- 3/11*2/10*1/9 = 164/165.   Answer is 164/165
Answer: B
if 28 is divided into two parts such that one fourth of the greater part is equal to one third of the lesser part,then the greater part is
Pick one
A) 16 B) 18 C) 20 D) 22 E) 24

Solution: 28 divided as (16 + 12).   one fourth of 16(greater part) = 4   one third of 12(lesser part) = 4   16NSWER:16
Answer: A
The sum of seven numbers is 235. The average of the first three is 23 and that of the last three is 42. The fourth number is  Choose the most appropriate option: A) 40 B) 126 C) 69 D) 195 E) None

Solution: Explanation:   Average of the first three is 23. Therefore their sum = 23 x 3   Average of the last three is 42. Therefore their sum = 42 x 3   Sum of all number = Sum of first three + Fourth number + Sum of last three   (23×3+a+42×3)=235⇒a=40   Correct Option: 40
Answer: A
How many multiples of 5 are there between 5 to 90?  Choose the correct option:
A) 9 B) 16 C) 17 D) none of these E) Cannot be determined

Solution: Explanation :   As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the units place).   So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85.   Answer : 16
Answer: B
A store has 10 bottles of juice, including 6 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 4 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought. Choose one.
A) 2/5
B) 3/5
C) 2/3
D) 1/2
E) 3/7

Solution: The total number of ways to sell 6 bottles from 10 is 10C6 = 210.   The number of ways to sell 4 bottles of apple juice is 6C4*4C2 = 15*6= 
15*6 = 90
90   P(selling 4 bottles of apple juice)= 90/210 = 9/21 = 3/7   The answer is 3/7.
Answer: E
At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 65 other employees of Company K, how many employees does Company K have? Choose one
A) 260 B) 180 C) 190 D) 200 E) 400

Solution: Let the total number of employees in the company be x   % of secretaries = 15%   % of salespeople = 60%   % of of employees other than secretaries and salespeople = 100 - 75= 
100 - 75 = 25
25%   But this number is given as 65   so 25% of x= 65   x = 260   Therefore there a total of 260 employees in the company K   Correct answer - 260
Answer: A
What is the minimum percentage increase in the mean of set G {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?	Choose the correct option: A) 25% B) 50% C) 75% D) 100% E) 200%

Solution: Mean of G is (-4-1+0+6+9)/5= 
(-4-1+0+6+9)/5 = 2
2;   In order the increase to be minimal we should replace two smallest elements of G, which are -4 and -1, with two smallest primes, which are 2 and 3. Hence our new set will be {2, 3, 0, 6, 9} --> new mean is   (2+3+0+6+9)/5= 
  (2+3+0+6+9)/5 = 4
4.   Percent increase=(4-2)/2*100= 
(4-2)/2*100 = 100
100%.   Answer: 100%.
Answer: D
Which of the following CANNOT be a product of two distinct positive integers a and b?  Choose the most appropriate option:
A) a B) b C) 3b + 2a D) b - a E) ba

Solution: we can eliminate answer choices A, B, and E right away. There is no reason to distinguish between aa and bb, so if aa cannot be a product, then bb cannot be either and since we cannot have two correct answers in PS problems, then neither A nor B can be correct. As for E it's clearly cannot be correct answer.   So, we are left with options C and D.   For C, can ab=3b+2aab=3b+2a? --> ab−2a=3bab−2a=3b --> a(b−2)=3ba(b−2)=3b --> a=3bb−2a=3bb−2. Now, if b=3b=3, then a=9a=9, so in this case ab=3b+2aab=3b+2a is possible.   Only option left is D.   Answer: b - a.
Answer: D
How many paying stones, each measuring 2 m * 1 m are required to pave a rectangular court yard 30 m long and 16 m board? Choose the correct choice from the following answers:  A) 240  B) 18  C) 26  D) 17  E) 12

Solution: 30 * 16 = 2 * 1 * x => x   = 240   240nswer: 240
Answer: A
The length of a rectangular floor is more than its breadth by 200%. If Rs.150 is required to paint the floor at the rate of Rs. 2 per sq m, then what would be the length of the floor?	Choose the correct answer.
A) 65
B) 15
C) 18
D) 16
E) 14

Solution: Let the length and the breadth of the floor be l m and b m respectively.   l = b + 200% of b = l + 2b = 3b   Area of the floor = 150/2= 
150/2 = 75
75 sq m   l b= 75 i.e., l * l/3 = 75   l2 = 225 => l = 15   Answer:15
Answer: B
A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is: Options: A) 7 B) 9 C) 8 D) 65 E) 4

Solution: Explanation:   Let the required number of revolutions made by larger wheel be x.   Then, More cogs, Less revolutions (Indirect Proportion)   {\color{9lack} \therefore } 14 : 6 :: 21 : x {\color{9lack} \Rightarrow } 14 x x = 6 x 21   x={\color{9lack} \frac{6\times 21}{14} } {\color{9lack} \Rightarrow } x=9   Answer: 9
Answer: B
The successive discounts 20% and 15% are equal to a single discount of? Pick one:
A) 35% B) 38% C) 32% D) 29% E) None of these

Solution: Let the CP of an article be Rs. 100   Given that successive discounts are 20% and 15%.   SP = 85% of 80% of 100 = (85/100)(80/100)(100)   => SP = Rs. 68   Clearly, single discount is 32%.   ANSWER:32%
Answer: C
Of the employees in a company, 30 % are female who have a master degree. If 20 % of the female employees do not have a master degree, what percent of the employees in the company are female?  Choose the most appropriate option:
A) 25% B) 32.5% C) 30% D) 45% E) 37.5%

Solution: No. of female employees with Masters = 0.3 x E   No. of female employees without masters = 0.2 x F   Therefore No. of female employees with masters = F - 0.2 F = 0.8 F   The 2 expressions equal each other therefore 0.8F = 0.337.5%; F/37.5% = 0.3/0.8 = 37.5%   Answer: 37.5%
Answer: E
A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part?
Choose the correct choice from the following answers:
A) 5ft. 7 inches
B) 3ft. 7 inches
C) 4ft. 7 inches
D) 2ft. 7 inches
E) 1ft. 7 inches

Solution: Length of board=7ft. 9 inches=(7*12+9)= 
(7*12+9) = 93
93 inches.   Therefore, Length of each part= (93/3)= 
(93/3) = 31
31 inches= 2ft. 7 inches   Answer is 2ft. 7 inches.
Answer: D
Tickets numbered 1 to 50 are mixed and one ticket is drawn at random. Find the probability that the ticket drawn has a number which is a multiple of 4 or 7? Choose the correct answer.
A) 9/25  B) 9/29  C) 9/26  D) 9/24  E) 9/21

Solution: Explanation:   S = {1, 2, 3, … , 49, 50}   E = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 7, 14, 21, 35, 42, 49}   n(S) = 50   n(E) = 18   P(E) = n(E)/n(S) = 18/50   = 9/25   9/25NSWER: 9/25
Answer: A
The average mark of 10 students is 80%. Later it was found that for one student, instead of 60%, the recorded 90%, by mistake. Now the corrected new percentage?
Choose the correct option:	A) 55	B) 66	C) 77	D) 88	E) 99

Solution: lets assume the total marks in the exam per student is 100.   and given that avg mark of 10 student is 80%   so, total mark=80*10= 
80*10 = 800
800 ;   but instead of 60 mark they take wrong as 90 mark;   so,800-90 + 60=770   this is correct mark of 10 student   and then average of 10 student is =770/10= 
770/10 = 77
77   ANSWER:77
Answer: C
A box contains ELEVEN bulbs out of which 5 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good
Choose one:  A) 65/66  B) 67/66  C) 69/66  D) 64/66  E) 61/66

Solution: Required probability = 1-5C4/11C4 = 1 - 1/66 = 65/166.65/66nswer:65/66
Answer: A
In a renowned city, the average birth rate is 6 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day.  Choose the correct choice from the following options: A) 32,300 B) 172,800 C) 468,830 D) 338,200 E) 259,200

Solution: Every 2 seconds, 4 persons are added (6-2). Every second 2 persons are added.   In a day 24hrs = 24 * 60 Minutes = 24 * 60 * 60= 
24 * 60 * 60 = 86_400
86400 seconds.   86400 * 2= 
86400 * 2 = 172_800
172800   Option 172,800 is the answer.
Answer: B
If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 9600 ?	Choose the correct answer
A) 11
B) 13
C) 14
D) 18
E) 16

Solution: Required difference = [3 ½ % of Rs.9600] – [3 1/3 % of Rs.9600]   = [(7/20-(10/3)]% of Rs.9600 =1/6 % of Rs.9600   = Rs. [(1/6)8(1/100)*9600] = Rs. 16.   Answer is 16.
Answer: E
The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?	Choose the correct choice from the following options
A) 198  B) 243  C) 270  D) 290  E) 292

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Smaller number = 270.   270
Answer: C
From the given equation find the value of x: xÂ²-18x+45 Choose one.
A) 5  B) -15  C) -3  D) 14  E) 15

Solution: (X - 15)X - 3   X = 15 or 3   Answer is 15
Answer: E
The equation x = 2y^2 + 5y - 19, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is Pick one
A) 3x + y + 15 = 0 B) y - 3x - 11 = 0 C) -3x + y - 20 = 0 D) -2x - y - 7 = 0 E) -3x + y + 13.5 = 0

Solution: The question is made to look difficult though it is pretty simple if you focus on just the line and use process of elimination. (Remember that GMAT does not focus on parabolas so basically, the question should be quite do-able even if someone doesn't know how to handle parabolas.)   We need equation of l. Its slope must be 3.   Slope in option A and D is not 3 so we are left with B, C and E   The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant).   In options B and E, if you put x = -5, you get -ve value for y co-ordinate. So ignore them.   Answer must be (-3x + y - 20 = 0)
Answer: C
An article is bought for Rs.600 and sold for Rs.900, find the gain percent?  Choices:  A) 50%  B) 63 1/3%  C) 33 1/3%  D) 93 1/3%  E) 33 1/3%

Solution: Explanation:   600 ---- 300   100 ---- ? => 50%   50%nswer:50%
Answer: A
How many integers between 50 and 100 can be evenly divided by neither 3 nor 5?  Choose the most appropriate option:
A) 24 B) 25 C) 26 D) 27 E) 28

Solution: divisible by 3 between 50 and 100 = 17 (51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99)   divisible by 5 between 50 and 100 = 9 (55,60,65,70,75,80,85,90,95)   26ommon divisible for 5 and 3 = 3 (60, 75, 90)   Total divisible by 5 and 3 between 50 and 100 = 17+9-3= 
17+9-3 = 23
> 23   There are 49 numbers between 50 to 100 i.e 51 to 99   so the integers that are not divisible by 3 and 5=> 49 - 23= 
49 - 23 = 26
> 26   ANSWER:26
Answer: C
A train 200 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform?
Choose the correct choice from the following answers
A) 443 m
B) 354 m
C) 450 m
D) 350 m
E) 300 m

Solution: 300 m   300   300 m = 72 * 5/18 = 25 = 500 â€“ 200 = 300
Answer: E
A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.900 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?	Choose the correct answer:  A) 10000  B) 12000  C) 12019  D) 12197  E) 12012

Solution: [900 + (X-4000) * (2.5/100)] - X * (5/100)   = 600   X = 10000   10000nswer: 10000
Answer: A
A vessel of capacity 90 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?  Choices
A) 72.7 litres B) 73.9 litres C) 63.0 litres D) 93.7 litres E) 23.8 litres

Solution: Let the initial quantity of milk in vessel be T litres.   Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.   Quantity of milk finally in the vessel is then given by [(T - y)/T]n * T   For the given problem, T = 90, y = 9 and n = 2.   Hence, quantity of milk finally in the vessel   = [(90 - 9)/90]2 (90) =72.9 litres.   Answer: 73.9 litres
Answer: B
The price of commodity X increases by 30 cents every year, while the price of commodity Y increases by 20 cents every year. If in 2001, the price of commodity X was $4.20 and the price of commodity Y was $4.40, in which year will commodity X cost 80 cents more than the commodity Y?	Choose the correct choice from the following answers:
A) 2010.	B) 2011.	C) 2012.	D) 2013.	E) 2014.

Solution: The cost of commodity X increases by 10 cents per year relative to commodity Y.   The price of X must gain 20 + 80 = $1.00 cents on commodity Y, which will take 10 years.   The answer is 2011..
Answer: B
Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/9 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?	Select:
A) 1/2
B) 3/5
C) 4/13
D) 8/29
E) 6/33

Solution: Now ultimately the speed of every machine is given with respect to Mach O.   So lets assume the speed of O, say 12 hrs to make x units (assuming 6 because we can see we will need to divide by 3 and 4   Mach O makes x units in 12 hrs   So, Mach N = 2/9 of O = 2/9*12 = 8/3 hrs to make x units   and Mach M = 3/4 of N = 3/4*8/3 = 6 hrs to make x units   No they are running simultaneously. Lets see how much each mach makes in 1 hr   Mach O = x/12 units   Mach N = 3x/8 units   Mach M = x/6 units   In 1 hr, together they make - x/12+3x/8+x/6 = 5x/8   So what ratio of this has Mach N made?   (3x/8) / (5x/8) =3/5   Ans:3/5=3/5
Answer: B