MU-NLPC/Calc-aqua_rat huggingface dataset:
A company has 15 managers and 75 associates. The 15 managers have an average salary of $210,000. The 75 associates have an average salary of $30,000. What is the average salary for the company?  Choose the correct choice from the following answers
A) $35,000 B) $45,000 C) $55,000 D) $60,000 E) $75,000

Solution: Another method is to get ratios   Say 30000=a and   We know the # of people are in 1:5 ratio   Average=(7a*1+a*5)/6= 12a/6=2a12 /6= 
12 /6 = 2
2a=60000   Answer is D. $60,000
Answer: D
If 10 gallons of grape juice are added to 40 gallons of a mixture, which contains 10 percent grape juice then what percent of the resulting mixture is grape juice? Choose the most appropriate option:
A) 14%	B) 25%	C) 28%	D) 34%	E) 50%

Solution: Mixture contains 4 gallons of grape juice out of 40 gallons   After addition: 14 gallons of grape juice out of 50 gallons ==> 28%   Answer 28%
Answer: C
What will be the compound interest on Rs. 45000 after 3 years at the rate of 12 % per annum  Select the correct option:
A) Rs 18221.76
B) Rs 18123.30
C) Rs 18123.40
D) Rs 18123.50
E) None of these

Solution: Explanation:   (45000×(1+12/100)3)   =>45000×28/25×28/25×28/25   =>63221.76   So Compound interest will be   63221.76 - 45000= 
  63221.76 - 45000 = 18_221.76
Rs 18221.76   Option Rs 18221.76
Answer: A
A certain auto manufacturer sold 3% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.6 million vehicles in 2006, how many vehicles, to the nearest 1,000, did the manufacturer sell in 2007?	Select
A) 63,000  B) 2,000,000  C) 2,030,000  D) 2,040,000  E) 2,300,000

Solution: Let's assume in 2006 he has sold X. Therefore in 2007 he should have sold 97/100×X.   97/100×2100=2037   -->2,037,000 sold in 2007. When rounded to the nearest 10,000 :   63,000   63,000
Answer: A
If xy = 5 and x^2 + y^2 = 14, then x/y + y/x =	Select:
A) 2 4/5	B) 3 1/7	C) 5 1/3	D) 7	E) 60

Solution: x/y+y/x=(x^2+y^2)/xy =substitute given we get 14/5=2 4/5   answer 2 4/5
Answer: A
Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:	Choose the correct choice from the following answers
A) 9	B) 11	C) 13	D) 15	E) 12

Solution: Let the three integers be x, x + 2 and x + 4.   Then, 3x = 2(x + 4) + 3 x = 11.   Third integer = x + 4 = 15.   Answer: 15
Answer: D
Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?
Pick one:
A) 10	B) 99	C) 88	D) 77	E) 66

Solution: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.   x + y = 7 --- (1) ; 2x = 4 --- (2)   solving both the equations, we get y = 5   So, time taken to cover both ways by cycle = 2y hours = 10 hours.   10nswer: 10
Answer: A
The area of a rectangle is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the rectangular field?	Select the correct option.
A) 20	B) 27	C) 26	D) 188	E) 11

Solution: Explanation:   Let breadth=x meters.   Then,Length = meters   Given that,   => x = 20   Breadth = 20   20nswer: 20) 20 m
Answer: A
A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is?
Choose the correct choice from the following answers.
A) 10	B) 20	C) 50	D) 30	E) 40

Solution: Man's speed with the current = 15 km/hr   => speed of the man + speed of the current = 15 km/hr   speed of the current is 2.5 km/hr   Hence, speed of the man = 15 - 2.5= 
15 - 2.5 = 12.5
12.5 km/hr   man's speed against the current= speed of the man - speed of the current   = 12.5 - 2.5= 
12.5 - 2.5 = 10
10 km/hr   10nswer is 10.
Answer: A
A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A? Answers:  A) 7219  B) 3000  C) 2799  D) 2797  E) 2788

Solution: 60*5:36*6:75*3   100: 72: 75   100/247 * 7410= 
100/247 * 7410 = 3_000
3000   Answer: 3000
Answer: B
S1 = 3 S2 = 6 ... Sn = 3n + 4 For the sequence above, in which any term n is defined as 3n + 4, what is the value of n for the first term in the sequence to exceed 50?	Select:
A) 13
B) 16
C) 12
D) 9
E) 8

Solution: term 16 = 3*16+4= 
3*16+4 = 52
52   Answer : 16
Answer: B
The smallest 3 digit prime number is? Choose the correct choice from the following options
A) 101	B) 102	C) 110	D) 112	E) 113

Solution: The smallest 3-digit number is 100, which is divisible by 2.   100 is not a prime number.   101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.   101 is a prime number.   Hence 101 is the smallest 3-digit prime number.   101)
Answer: A
If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is? Select the correct option.
A) 4/16 B) 4/10 C) 4/11 D) 4/13 E) 4/12

Solution: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.   P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13   Answer: 4/13
Answer: D
Four of the five parts numbered (a), (b), (c), (d) and (e) in the following equation are exactly equal. Which part is not equal to the other four? The number of that part is the answer	Choose the correct option:
A) x(x + y)2 – 2x2y B) x(x + y)2 + 2x2y C) x(x2 – y2) D) x[(x + y)2 – 2xy] E) x[(x + y)2 – 2xy2]

Solution: Others are x3 + xy2   Answer x[(x + y)2 – 2xy2]
Answer: E
The average of 17 numbers is 10.9. If the average of first nine numbers is 10.5 and that of the last nine numbers is 11.4, the middle number is  Pick one
A) 11.8	B) 11.4	C) 10.9	D) 11.7	E) 11.9

Solution: Sum of first nine numbers (N1 to N9) + Sum of last nine numbers (N9 to N17) = 10.5 x 9 + 11.4 x 9 = 21.9 x 9 = 197.1   Hence, the middle number   = 197.1 - 17 x 10.9   = 197.1 - 185.3= 
197.1 - 185.3 = 11.8
11.8   11.8NSWER:11.8
Answer: A
Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.60?  Answers:
A) 426
B) 430
C) 443
D) 470
E) 486

Solution: I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money:   -the 100 pack costs 1.5$, meaning 0.015$ per envelope   -the 50 pack costs 1$, meaning 0.02$ per envelope   -the single envelope costs 0.03$ per envelope   Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones.   Having 7.6$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 1.6 $ left. so we buy 1 pack of 50 for 1$. We now have 0.6$ left, so we buy 20 individual envelopes. If we add up the numbers, we get   400+50+20= 
  400+50+20 = 470
470 envelopes. Answer 470
Answer: D
If 3a + 1 < 2a < 9 - a, which of the following must be true?
I. -1 < a < 3
II. a < -1
III. a < 3
Options.
A) II only B) III only C) I and II only D) II and III only E) I, II and III

Solution: Just try plugging a in a number like 0 or 1, and you'll quickly find that the inequality doesn't hold.   So you can immediately cross out any answers with I or III, leaving just (II only) II only.
Answer: A
In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (4,3) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.
Select the correct option.
A) (-2,6)
B) (0,4)
C) (2,-6)
D) (2,6)
E) (4,0)

Solution: Area.pngSince A is equidistant from points O and B, then it must be somewhere on the green line (perpendicular bisector of OB).   (2,-6) and (2,6) are not on that line. If A is at (0,4) or (3,0), then the area is 1/2*4*3= 
1/2*4*3 = 6
6. Thus A must be at (2,-6).   Answer: (2,-6).
Answer: C
A firm has 5 senior partners and 4 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different) Choose the correct option
A) 70  B) 75  C) 80  D) 85  E) 90

Solution: The total number of ways to form a group of 3 is 9803 = 84   The number of groups without a senior partner is 4803 = 4   The number of groups which include a senior partner is  84-4= 
 84-4 = 80
80   The answer is 80.
Answer: C
A car is running at a speed of 110kmph. What distance will it cover in 9sec? Choose the correct choice from the following answers
A) 100m  B) 279m  C) 180m  D) 200m  E) 250m

Solution: Speed = 110kmph = 110*5/18 = 31 m/s   Distance covered in 9sec = 31*9= 
31*9 = 279
279m   Answer is 279m
Answer: B
If 34 men do a work in 40 days, in how many days will 20 men do it?  Choose the correct answer:
A) 65 B) 68 C) 61 D) 55 E) 74

Solution: 34 * 40 = 20 * x   x = 68 days   Answer: 68
Answer: B
A grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each soap box is 7 inches by 6 inches by 5 inches, then what is the maximum number of soap boxes that can be placed in each carton? Choose the correct choice from the following options.
A) 210
B) 252
C) 280
D) 300
E) 420

Solution: Maximum number of soap boxes that can be placed in each carton = Volume of each carton/ volume of each box   = (25*42*60)/(7*6*5)= 
(25*42*60)/(7*6*5) = 300
300   ANSWER:300
Answer: D
Vijay went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? Choose the correct choice from the following
A) 19.7  B) 20.1  C) 21.4  D) 21.7  E) 21.8

Solution: Total cost of the items he purchased = Rs.25   Given that out of this Rs.25, 30 Paise is given as tax   => Total tax incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (25−30/100−x)6/100 = 30/100   ⇒ 6(25 −0.3 −x) = 30   ⇒ (25 − 0.3 − x) = 5   ⇒ x = 25 − 0.3 − 5 = 19.7   19.7)
Answer: A
A pharmaceutical company made 3000 strips of tablets at a cost of Rs. 4800. The company gave away 1000 strips of tablets to doctors as free samples. A discount of 25% was allowed on the printed price. Find the ratio profit if the price is raised from Rs. 3.25 to Rs. 4.25 per strip and if at the latter price, samples to doctors were done away with. (New profit / Old profit).  Select the correct option.
A) 55.5
B) 63.5
C) 75
D) 99.25
E) 80

Solution: Solution: Total sales revenue (Old) = 2000*3.25*0.75= 
2000*3.25*0.75 = 4_875
4875[0.75 as 25% discount was allowed]   ProfitOld= Total sales revenue - 4800   = 4875-4800= 
4875-4800 = 75
75   Total sales revenue (New)= 3000*4.25*0.75= 
3000*4.25*0.75 = 9_562.5
9562.5[New price is calculated on doctors samples as well.]   ProfitNew= 9562.5 - 4800= 
9562.5 - 4800 = 4_762.5
4762.5   Ratio,   ProfitNew / ProfitOld= 4762.5/75 = 63.5.   Answer: Option 63.5
Answer: B
In shop contains 500 articles each of a cost of $10. He sold them at a price of $20. If the shop keeper has a order of 200 articles, how much profit he will get?
Choose the correct option: A) A)200 B) B)4000 C) C)1500 D) D)2000 E) E)600

Solution: Total money after selling articles = 200*20= 
200*20 = 4_000
4000   cost price= 200*10= 
200*10 = 2_000
2000   profit= 2000   correct option is 2000
Answer: D
7 points are marked on a straight line and another 8 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?	Choose one
A) 21  B) 91  C) 168  D) 196  E) 364

Solution: select 2 points from one line and one from another.   7C2 * 8C1 [ 2 points from the line containing 7 points and 1 from the line containing 8 points]   +   8C2 * 7C1 [ 2 points from the line containing 8 points and 1 from the line containing 7 points]   =364   ANSW364R: [364]
Answer: E
During a sale, the price of a pair of shoes is marked down 13% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?
Choices
A) 9%	B) 10%	C) 11%	D) 15%	E) 90%

Solution: Assume the price = 100   Price during sale = 87   Price after sale = 100   Percent increase = 13/87*100 = 15% approx.   Correct Option: 15%
Answer: D
Working alone, A can complete a certain kind of job in 3 hours. A and D, working together at their respective rates, can complete one of these jobs in 2 hours. In how many hours can D, working alone, complete one of these jobs? Pick:	A) 2	B) 4	C) 6	D) 8	E) 10

Solution: Let total time taken by D to complete the job = D   total time taken by A to complete the job = 3   Work done by A in an hour   1/A = 1/3   Working together A and D can complete the job in 2 hours   1/A + 1/D = 1/2   =>1/D = 1/2 - 1/A   = 1/2- 1/3   = 1/6   => D = 6 hours   Answer 6
Answer: C
There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability that the number of men is equal to that of women? Choices:
A) 18/35  B) 16/35  C) 14/35  D) 13/35  E) 12/35

Solution: men= women means 2 men 2 women   total such combinations = 4c2 * 4c2 = 4!/2!.2! * 4!/2!.2! = 6*6   total combinations = 8c4 = 8*7*6*5/4*3*2*1 = 70   so probability = 36/70 = 18/35   hence 18/35
Answer: A
The diagonals of a rhombus are 15 cm and 12 cm. Find its area? Choose the correct choice from the following answers.
A) 70  B) 90  C) 60  D) 80  E) 292

Solution: 1/2 * 15 * 12= 
1/2 * 15 * 12 = 90
90   Answer:90
Answer: B
The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
Choose the correct choice from the following:	A) 6	B) 8	C) 4	D) 9	E) 3

Solution: S = 1   M = x   DS = x + 1   US = x - 1   35/(x + 1) + 35/(x - 1) = 12   x = 6   6nswer: 6
Answer: A
If 45-[28-{37-(15-*)}]= 59, then * is equal to:	Choose the correct option.
A) -29
B) -19
C) 20
D) 29
E) 39

Solution: 45-[28-{37-(15-*)}]= 59 => 45-[28-{37-15+*}]=59   45-[28-37+15-*]=59 => 45[43-37-*]=59   45-[6-*]=59 => 45-6+*=59   39+*=59 => *=59-39= 
59-39 = 20
20   ANSWER:20
Answer: C
A sum of money lent out at S.I. amounts to Rs. 820 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is?  Choose the correct choice from the following answers:
A) Rs.440
B) Rs. 500
C) Rs. 540
D) Rs. 740
E) Rs. 840

Solution: S.I for 5 years = (1020 - 820) = Rs. 200.   S.I. for 2 years = 200/5 * 2 = Rs. 80.   Principal = (820 - 80) = Rs. 740.   ANSWER:Rs. 740
Answer: D
At a contest with 2000 participants, 1/2 of the people are aged 16 to 18. Next year, the number of people aged 16 to 18 will increase by 1/4. After this change, what percentage of the total 2000 people will the 16- to 18- year-olds represent?	Select
A) 62.50%	B) 60%	C) 70%	D) 65%	E) 66/3%

Solution: I just wanted to mention a couple of things here:   * this is a pure ratio question; the number 2000 is completely irrelevant, and you can ignore it if you like. When we increase something by 1/4, we are multiplying it by 1 + 1/4 = 5/4, so the answer here must be (1/2)*(5/4) = 5/8 = 62.50 %.   62.50%nswer : 62.50%
Answer: A
Four milkmen rented a pasture. A grazed 24 cows for 3 months, B 10 cows for 5 months, C 35 cows for 4 months and D 21 cows for 3 months. If A’s share of rent is Rs.720, find the total rent of the field.
Choose one:
A) Rs.3250	B) Rs.3350	C) Rs.3450	D) Rs.3550	E) Rs.3650

Solution: Ratio of shares of A, B, C, D = (24 * 3) : (10 * 5) : (35 * 4) : (21 * 3)   = 72 : 50 : 140 : 63   Let total rent be Rs.x. Then, A’s share = Rs. 72x/325.   Therefore, 72x/325 = 720 => x = 720 * 325/72= 
720 * 325/72 = 3_250
3250.   Hence, total rent of the field is Rs.3250.   Rs.3250NSWER:Rs.3250
Answer: A
Sandy purchased 20 dozen toys at the rate of $144 per dozen. Sandy sold each toy at the rate of $15. What was the percentage profit? Choices:
A) 15%	B) 25%	C) 35%	D) 45%	E) 55%

Solution: A dozen toys cost $144, so each toy cost $12.   selling price / cost price = 15 / 12= 
15 / 12 = 5/4 = around 1.25
1.25   The percentage profit is 25%.   The answer is 25%.
Answer: B
The total number of digits used in numbering the pages of a book having 366 pages is Choose the correct choice from the following: A) 732 B) 990 C) 1098 D) 1305 E) 1605

Solution: Explanation:   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 267) = (9 + 180 + 801)= 
(9 + 180 + 801) = 990
990.   Answer: 990
Answer: B
If x is odd and y is odd, then x + y is Choose the correct choice from the following options
A) Odd  B) Odd whenever xy is even  C) Even whenever xy is odd  D) Even  E) It cannot be determined

Solution: x is odd and y is odd, then x + y is   Let's take x=9 and y=5.   x+y=9+5= 
9+5 = 14
14.   x+y=14=even.   Option: Even
Answer: D
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?  Answers.
A) 2/27	B) 2/29	C) 2/21	D) 2/22	E) 2/27

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³2/21₂/¹⁵2/21₂ = (3 * 2)/(15 * 14) = 1/35   Probability that both are yellow = ²2/21₂/¹⁵2/21₂ = (2 * 1)/(15 * 14) = 1/105   Probability that one blue and other is yellow = (³2/21₁ * ²2/21₁)/¹⁵2/21₂ = (2 * 3 * 2)/(15 * 14) = 2/35   Required probability = 1/35 + 1/105 + 2/35   = 3/35 + 1/105 = 1/35(3 + 1/3)   = 10/(3 * 35) = 2/21   Answer:2/21
Answer: C
A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 55 hrs and a machine of type S does the same job in 22 hours. If the company used the same number of each type of machine to do the job in 5 hours, how many machines of type R were used?  Choose one:
A) 22/7 B) 28/7 C) 23/7 D) 25/7 E) 22/7

Solution: Rate of machine R =1/55   Rate of machine S =1/22   since same no of machines used for R and S to do the same work in 5 hrs   So collective rate needed to finish the work in 5 hrs= 1/5   Let the no of machine be x   So, x/55 +x/22 =1/5   7x=22   x=22/7   So no of machine R is 22/7   Answer 22/7
Answer: E
A highway is to be divided into four lanes. For this purpose, three yellow stripes are painted so that stripes divide the highway into four lanes. If 3 gallons of paint cover an area of 5P square feet of highway, how many gallons of paint are needed to paint two stripes x inches wide on a stretch of highway m miles long? (1 mile = 5280 feet and 1 feet = 12 inches)
Answers.
A) 792mx/P  B) 264mx/P  C) 792P/mx  D) 264P/mx  E) 880mx/P

Solution: 1 square foot needs 3/5P gallons of paint.   The width of each stripe is x/12 feet.   The length of each stripe is 5280m feet.   The area of each stripe is (5280m)(x/12) = 440mx square feet.   For three stripes, the total area is 1320mx square feet.   The number of gallons needed is (1320mx)*(3/5P) = 792mx/P gallons.   The answer is 792mx/P.  (1320  )*(3/5 )= 
  (1320  )*(3/5 ) = 792
792mx/P gallons.   The answer is 792mx/P.
Answer: A
In how many years, Rs. 75 will produce the same interest at 6% as Rs. 800 produce in 2 years at 4½% ? Choose the correct choice
A) 4 years B) 16 years C) 8 years D) 9 years E) 12 years

Solution: Explanation :   Let Simple Interest for Rs.75 at 6% for n years = Simple Interest for Rs.800 at 4½ % for 2 years   75×6×n/100=800×9/2×2/100   75×6×n=800×9/2×2   75×6×n=800×9   n=16 years   Answer : Option 16 years
Answer: B
Three 6 faced dice are thrown together. The probability that all the three show the same number on them is ? Choose the most appropriate option.
A) 1/38  B) 1/36  C) 1/39  D) 1/31  E) 1/29

Solution: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6= 
6 * 6 * 6 = 216
216 ways.   Hence the probability is 6/216= 1/36   Answer:1/36
Answer: B
If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is ? Choose the most appropriate option
A) 1/6
B) 1/2
C) 1/9
D) 1/1
E) 1/5

Solution: The number of exhaustive outcomes is 36.   Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2   P(E) = 1 - 1/2   = 1/2.   Answer: 1/2
Answer: B
If S is a positive integer, which of the following must be odd?	Choose the correct choice from the following answers.
A) S+1
B) S^2+S
C) S^2+S+1
D) x^2−1
E) 3x^2−3

Solution: A. S+1 = can be odd or even. Since O + O =E or E + O = O   B. S^2 + S = S(S+1). Since from the above derivation we already know the term S+1 can be Odd or Even, directly substitute here. S(ODD) = Even (When S is Even) or S(EVEN) = EVEN [When S is ODD]   C. Here's the answer. Since we know the term S^2 + S can always take a EVEN number, EVEN + 1 = ODD   Hence S^2+S+1.
Answer: C
Present birth rate is 32 per thousand while death rate is 11 per thousand. What will be the percentage increase in the rate of population? Choose the correct option
A) 0.21%	B) 21%	C) 0.021%	D) 2.1%	E) None of these

Solution: birth rate=32/1000= 
32/1000 = 4/125 = around 0.032
0.032   death rate=11/1000= 
11/1000 = 11/1_000 = around 0.011
0.011   increase in population=0.032-0.011= 
0.032-0.011 = 0.021
0.021=2.1%   ANSWER:2.1%
Answer: D
What will be the output of the following code statements?
Integer a = 13, b = 39, c = 10 print (a × b / c) – c	Pick:  A) 65  B) 26  C) 29  D) 26  E) 41

Solution: 41xplanation:   Apply BODMAS rule   13 × 39 = 507/10-10 =50.7 –10 =40.7   Answer:41
Answer: E
The instructions state that Cheryl needs 2/9 square yards of one type of material and 1/8 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 4/18 square yards left that she did not use. What is the total amount of square yards of material Cheryl used? Choose the correct choice:
A) 1/12
B) 1/9
C) 1/8
D) 1 1/9
E) 2 1/9

Solution: Total bought = 2/9+1/8   left part 4/18--->2/9   so used part 2/9+1/8-2/9=1/8   ANSWER:1/8
Answer: C
The concentration of spirit in three different vessels A, B and C are 30%, 30% and 25% respectively. If 4 litres from vessel A, 5 litres from vessel B and 6 litres from vessel C are mixed, find the concentration of spirit in the resultant solution. Choose the correct choice from the following answers.
A) 32%
B) 33%
C) 34%
D) 35%
E) 28%

Solution: Quantity of spirit in new solution=(4*30/100)+(5*30/100)+(6*25/100)=1.2+1.5+1.5= 
1.2+1.5+1.5 = 4.2
4.2 liters   So % concentration of spirit=100*4.2/(4+5+6)= 
100*4.2/(4+5+6) = 28
28%   ANSW28%R:28%
Answer: E
Arnold wanted to create a perfect shade of pink for his new canvas painting. He started out replacing 25% of a 100% red colored paint with white. He then further replaced 15% of this shade with white. Finally, he repeated the process by replacing 10% of the shade with white. What was the final percentage of red in Arnold's pink paint?
Choose the correct choice from the following.
A) 62.40%
B) 51%
C) 68.21%
D) 57.37%
E) 70%

Solution: Quick answer: 100x0.75x0.85x0.9   We begin with 100% red paint. 25% of this is replaced with white paint which leaves us with a mixture of 75% red paint (as 25% is white)   Next, 15% of this mixture is further mixed with white paint. That implies that 85% of the previous red paint remains. Hence, the new percentage is 75x0.85% = 63.75%   Finally, 10% of the new paint mixture is again mixed with white. This leaves us with 90% of the previous red quantity. So the final percentage of red is 63.75x0.9% = 57.37%   Answer: 57.37%
Answer: D
If an item costs Rs.3 in '99 and Rs.203 in '00.What is the % increase in price? Select:
A) 200/3 %	B) 200/6 %	C) 100%	D) 200%	E) none of these

Solution: increase is 203-3= 
203-3 = 200
200   %increase is 200*100/3=6666.667%   ANSWnone of theseR:none of these
Answer: E