MU-NLPC/Calc-aqua_rat huggingface dataset:
Find the number of ways of arranging a pen and 6 pencils at a circular table so that the pen always sits in a particular place? Select
A) 3!  B) 6!  C) 11!  D) 12!  E) 14!

Solution: Ans.(B)   Sol. Total number of persons = 7. The pen can sit in a particular place in one way. Now, remaining positions are defined relative to the pen. Hence, the remaining can sit in 6 places => 6! Ways ... The number of required arrangements = 6! x 1= 6! = 6! ways
Answer: B
What decimal of an hour is a second ? Select:
A) .0025  B) .0256  C) .00027  D) .00016  E) .000126

Solution: Required decimal =	1/(60x60)   =	1/3600   = .00027   answer :.00027
Answer: C
How many of the following numbers are divisible by 3 but not by 9?
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
Choose the correct choice from the following options
A) 5  B) 6  C) 7  D) 8  E) None of these

Solution: Taking the sum of the digits, we have:   S1=9, S2=12, S3=18, S4= 9, S5=21, S6= 12, S7=18, S8=21, S9=15, S10=24.   Clearly S2, S5, S6, S8, S9, S10 are all divisible by 3 but not by 9. So, the number of required numbers= 6.   Answer:6
Answer: B
Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg
Pick:
A) 2:0
B) 2:3
C) 2:1
D) 2:2
E) 2:8

Solution: 2:3y the rule of alligation:   Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind   Required ratio = 60 : 90 = 2 : 3   Answer: 2:3
Answer: B
if price of t.v set is reduced by 25%, then its sale increases by 75%, find net effect on sale value  Choose the correct choice from the following choices
A) 31	B) 32	C) 46	D) 47	E) 48

Solution: - a + b + ((-a)(b)/100)   = -25+75+(-25*75)/100   = -25+75-19= 
-25+75-19 = 31
31   31NSWER:31
Answer: A
5000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?	Choose the correct option:
A) 10600 B) 11600 C) 12600 D) 10680 E) 20600

Solution: (x*3*1)/100 + [(5000 - x)*5*1]/100 = 144   3x/100 +( 25000 – 5x)/100 = 144   => x = 10600   10600NSWER:10600
Answer: A
If a person walks at 12 km/hr instead of 8 km/hr, he would have walked 20 km more. The actual distance traveled by him is?	Choose the correct answer.
A) 50 km
B) 58 km
C) 60 km
D) 40 km
E) 65 km

Solution: Let the actual distance traveled be x km. Then,   x/8 = (x + 20)/12   3x - 2x = 40 =>x = 40 km.   Answer :40 km
Answer: D
Find the least number must be added to 433124 so that remaining no.is divisible by 17?  Choose the most appropriate option:
A) 3	B) 2	C) 5	D) 6	E) 1

Solution: On dividing 433124 by 17 we get the remainder 15, so 2 should be added   2
Answer: B
Tom planted vegetables in a rectangular garden that was 22 feet long and 15 feet wide. He used
1/3 of the area for corn and 1/5 of it for peas. How many square feet are left for other vegetables?
Choose one:
A) 154 sq. ft.  B) 156 sq. ft.  C) 157 sq. ft.  D) 158 sq. ft.  E) 159 sq. ft.

Solution: area of garden is 22 x 15 = 330 sq. ft.   1/3 x 330 = 110 sq. ft. for corn   1/5 x 330 = 66 sq. ft. for peas   110 + 66= 
110 + 66 = 176
176 sq. ft. used     330 - 176= 
  330 - 176 = 154
154 sq. ft. left over   correct answer 154 sq. ft.
Answer: A
Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms did Mary pick?	Choose the correct choice from the following choices.
A) 12 B) 24 C) 48 D) 52 E) 37

Solution: Let x be the amount Peter picked. Then Mary and Lucy picked 2x and x+2x, respectively. So   x+2x+x+2=26   4x=24   x=6   so 2x=2*6= 
2*6 = 12
12   correct answer is 12) 12
Answer: A
A corporation paid $10 million in federal taxes on its first $50 million of gross profits and then $30 million in federal taxes on the next $150 million in gross profits. By approximately what percent did the ratio of federal taxes to gross profits increase from the first $50 million in profits to the next $150 million in profits?  Choose the correct choice from the following:
A) 0% B) 14% C) 20% D) 23% E) 43%

Solution: Difference in Ratios = (30/150) - (10/50)= 
(30/150) - (10/50) = 0
0   % Change= 0%   0%nswer - 0%
Answer: A
Reema took a loan of Rs 1800 with simple interest for as many years as the rate of interest. If she paid Rs. 632 as interest at the end of the loan period, what was the rate of interest. Choose the most appropriate option.
A) 5.925%	B) 5.253%	C) 7%	D) 6.52%	E) 5.200%

Solution: Explanation:   Let rate = R% then Time = R years.   =>1800∗R∗R /100=632   =>R2=35.11   =>R=5.925%   Option 5.925%
Answer: A
The measure of the side of a square is tripled. If x represents the perimeter of the original square, what is the value of the new perimeter?
Select the correct option: A) 3x B) 4x C) 9x D) 12x E) 27x

Solution: Original perimeter = x   Hence original side = x/4   New side = 3x/4   New perimeter = 4*3x/4 = 3x   Correct Option: 3x4*3 /4= 
4*3 /4 = 3
3x   Correct Option: 3x
Answer: A
Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio Q of men to women?
Choose the correct option.
A) 5:2 B) 5:1 C) 4:3 D) 4:1 E) 3:1

Solution: (5:2) Q=184 x 5 + 170 x 2 = 1260.5:2
Answer: A
If [M] denotes the least integer greater than or equal to M and [M] = 0, which of the following statements must be true?
Answers
A) M = 0	B) 0 <= M < 1	C) -1 < M <= 0	D) -1 <= M < 0	E) 0 < M <= 1

Solution: The answer for this is0 < = M< = 1   However it is not available in the options. The match to the above is-1 <M <= 0   Answer = -1 < M <= 0
Answer: C
A photograph measuring 8.5 by 7.5 cm is to be enlarged. If the enlargement of the longer side is 13.6 cm, what is the length of the smaller side? Answers:
A) 12 cm
B) 10 cm
C) 13 cm
D) 15 cm
E) 19 cm

Solution: 12 cm   12 cm   = (13.6 ÷ 8.5) × 7.5   = 12 cm.
Answer: A
A man can row with a speed of 10 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Answers:
A) A)63kmph
B) B)63kmph
C) C)15kmph
D) D)62kmph
E) E)74kmph

Solution: Explanation:   M = 10   S = 5   DS = 10 + 5= 
10 + 5 = 15
15   Answer: Option 15kmph
Answer: C
I have a huge bed-sheet of 1 meter long.
I want to cuts this role into pieces of 20 centimeter long cloth.
How long will it take me to cut the bed sheet if each 20 centimeter cut took me 5 minutes ? Select: A) 150 Min B) 245 Min C) 185 Min D) 300 Min E) 205 Min

Solution: B   It will take 49 cuts not 50.   so 49*5= 
49*5 = 245
> 245 minutes
Answer: B
The diameters of two spheres are in the ratio 1:2 what is the ratio of their surface area?
Choices.
A) 1:0 B) 1:4 C) 1:6 D) 1:2 E) 1:1

Solution: 1:4   Answer:1:4
Answer: B
What will be 40 percent of a number whose 200 percent is 90 ? Select.
A) 144
B) 72
C) 18
D) None of these
E) Cannot be determined

Solution: Answer   ∵ 200% of N = 90   ⇒ N = (90 x 100) / 200 = 45   ∴ 40% of N = (40 x 45) / 100 = 18   18orrect Option: 18
Answer: C
Icarus and three of his friends want to donate money to a family which has 9 members so that they can get $12.00 to buy Chanukkah gifts this year.
Icarus has $35.00, his second friend has $37.00. The third friend has $30.00
How much more money do they need so they can give $12.00 to each of the 9 family members.
Choose the correct choice from the following answers
A) $6
B) $9
C) $7
D) $10
E) $5

Solution: Answer= A   Icarus and his 2 friends have a total of $102.00 ($35 +$37 +$30).   Each of the family members need $12.00.   $12 x 9 = $108   $108 - $102 = $6   $6nswer 108 -  102= 
 108 -  102 = 6
$6   $6nswer= $6
Answer: A
The equation (M )/84 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?	Select the correct option:
A) (P-7)*6	B) (P-7)*5	C) (P-7)*2	D) (P-7)*3	E) (P-7)*4

Solution: M/84 =(P-7)/21   M = (P-7)*84/21   =(P-7)*4   (P-7)*4
Answer: E
A shipment of 8 television sets contains 2 black-and-white sets and 7 color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set? Select the correct option:
A) 1/7 B) 1/4 C) 5/14 D) 11/28 E) 13/28

Solution: I get 1/4, which is not in the answer choices.   the probability of getting at least one b/w TV is 1-(the probability of getting 2 color TVs)   1-C(7,2)/C(8/2)=7/28=1/4   1/4
Answer: B
In a class, 20% of the members own only two cars each, 40% of the remaining own three cars each and the remaining members own only one car each. Which of the following statements is definitely true from the given statements ?
Choose the correct choice from the following options:
A) Only 20% of the total members own three cars each.
B) 48% of the total members own only one car each.
C) 60% of the total members own at least two cars each.
D) 80% of the total members own at least one car
E) None of these

Solution: Explanation:   Let total number of members be 100,   Then, number of members owning only 2 cars = 20.   Number of members owning 3 cars = 40% of 80 = 32.   Number of members owning only 1 car = 100 - (20 + 32)= 
100 - (20 + 32) = 48
48.   Thus, 48% of the total members own one car each.   Answer: Option 48% of the total members own only one car each.
Answer: B
In Solution P, the proportion of water to alcohol is 5:1. In Solution Q, the proportion of water to alcohol is 2:1. If the two solutions are combined, what is the concentration of alcohol in the new solution if the original solutions were mixed in equal amounts?	Choose the correct answer:
A) 21%
B) 23%
C) 25%
D) 27%
E) 29%

Solution: Let V be the total volume of the new solution.   The amount of alcohol added from Solution P is (1/6)*V/2=(1/12)*V   The amount of alcohol added from Solution Q is (1/3)*V/2=(1/6)*V   The total amount of alcohol in the new solution is (1/12+1/6)*V=(1/4)*V   The alcohol concentration is 1/4=25%   The answer is 25%.
Answer: C
There are 134 employees in Company X. If the number of employees who birth in June is the greatest, what is the least possible number of the employees in the company who birth in June? Choose the correct choice from the following: A) 10 B) 11 C) 12 D) 13 E) 14

Solution: IMO 14   Take each answer choice and substract it from 134 and the divided this with 11. 14
Answer: E
P is three times as old as Q. In 12 years, P will be twice as old as Q. How old was P three years ago?
Choose the correct choice from the following:
A) 21	B) 24	C) 27	D) 30	E) 33

Solution: P = 3Q so Q = P/3   P+12 = 2(Q+12) = 2(P/3+12)   P/3 = 12   P = 36   Three years ago, P was 33.   The answer is 33.
Answer: E
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/8 hours to fill the tank. The leak can drain all the water of the tank in?
Answers.
A) 17 hr  B) 19 hr  C) 10 hr  D) 34 hr  E) 36 hr

Solution: Work done by the tank in 1 hour   = (1/2 -2 1/8)   = 1/34 Leak will empty the tank in 34 hrs.   Answer:34 hr
Answer: D
. A boy has five trousers and 10 shirts. In how many different ways can he select a trouser and a shirt? Choices
A) 30
B) 40
C) 50
D) 60
E) 70

Solution: Explanation:   The boy can select one trouser in five ways.   The boy can select one shirt in 10 ways.   The number of ways in which he can select one trouser and one shirt is   5 * 10= 
  5 * 10 = 50
50 ways.   Answer: Option 50
Answer: C
Find the HCF of
22×32×72, 2×34×7	Choose the correct choice:
A) 128 B) 126 C) 146 D) 434 E) None of these

Solution: Explanation:   HCF is Highest common factor, so we need to get the common highest factors among given values. So   we got   2 * 3*3 * 7= 
2 * 3*3 * 7 = 126
126   Answer: Option 126
Answer: B
Abigail has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have?
Choose the correct option:
A) 32
B) 30
C) 29
D) 28
E) 27

Solution: 5g + 10h = 460   g > h   Pick an easy number to work with.   suppose g=30.   Then you have 150.   You need another 310 and that means you need h=31 which is greater than g.   Therefore, g > 30.   The only answer choice where g > 30 is if g = 32.   32 is the answer.
Answer: A
After striking the floor, a rubber ball rebounds to 4/5th of the height from which it has fallen. Find the total distance that it travels before coming to rest if it has been gently dropped from a height of 120 metres. Choose the correct choice.
A) 540 m B) 960 m C) 1080 m D) 1020 m E) 1120 m

Solution: Solution: The first drop is 120 metres. After this the ball will rise by 96 metres and fall by 96 metres. This process will continue in the form of infinite GP with common ratio 0.8 and first term 96. The required answer is given by the formula:   a/(1-r)   Now,   [{120/(1/5)}+{96/(1/5)}]   = 1080 m.   Answer 1080 m  120/(1/5) + 96/(1/5)= 
  120/(1/5) + 96/(1/5) = 1_080
1080 m.   Answer 1080 m
Answer: C
Rahim bought 40 books for Rs.600 from one shop and 20 books for Rs.240 from another. What is the average price he paid per book ? Pick:
A) s.14  B) s.18  C) s.12  D) s.11  E) s.10

Solution: s.14verage price per book   = (600 + 240) / (40 + 20) = 840/ 60   = Rs.14   s.14nswer:s.14
Answer: A
A boat goes 100 km downstream in 10 hours, and 45 km upstream in 15 hours. The speed of the stream is?  Choices.
A) 4km/h  B) 3km/h  C) 2km/h  D) 3.5 km/h  E) E)None

Solution: 100 --- 10 3.5 km/hS = 10   ? ---- 1   45 ---- 15 US =3   ? ----- 1 S = (10 - 3)/2= 
(10 - 3)/2 = 7/2 = around 3.5
3.5 kmph   ANSWER:3.5 km/h
Answer: D
A collection of 20 coins, each with a face value of either 10 cents or 35 cents, has a total face value of $2.5. How many of the coins have a face value of 10 cents?
Choose the correct choice from the following answers
A) 24
B) 18
C) 32
D) 16
E) 20

Solution: 0.10(x)+0.35(20-x)=2.5   0.10x+7-0.35x=2.5   so x=18   ans is 18
Answer: B
Find the average of the first 25 natural numbers? Choices:
A) 8 B) 9 C) 13 D) 11 E) 12

Solution: Average of the first 'n' natural numbers = (n + 1)/2   We get  (25 + 1)/2= 
 (25 + 1)/2 = 13
13   ANSWER:13
Answer: C
A group of tourists wants to visit only two of the four cities A, B, C, and D. How many travel itineraries can they make? All cities are connected to one another and please note that visiting the same cities in a different order counts as a different itinerary.
Options:
A) 12  B) 16  C) 24  D) 28  E) 32

Solution: The number of ways to choose two cities is 4C2=6.   The number of itineraries for each pair of 2 cities is 2!.   So the number of itineraries to two cities is  6*2= 
 6*2 = 12
12.   The answer is 12.
Answer: A
A beam 9 m long, 40 cm wide and 20 cm high is made up of iron which weighs 50 kg per cubic metre. The weight of the beam is Choose the correct choice from the following options.
A) 56 kg B) 36 kg C) 48 kg D) 27 kg E) None of these

Solution: Solution : weight = 18/25 *50= 
18/25 *50 = 36
36 kg Answer 36 kg
Answer: B
At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint. Mauve paint is made by mixing 3 parts of red paint with 6 parts blue paint. How many liters of blue paint must be added to 16 liters of Fuchsia to change it to Mauve paint?	Choose the correct choice.
A) 9  B) 12  C) 14  D) 16  E) 18

Solution: in 16 liters, Red = 5/8 * 16= 
5/8 * 16 = 10
10 and Blue= 6   so, 10/(6+x) = 3/6   or, x = 14 (Answer 14)
Answer: C
Two stations A and B are 155 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?	Choose the most appropriate option.
A) 9  B) 10  C) 11  D) 12  E) 8

Solution: Suppose they meet x hours after 7 a.m.   Distance covered by A in x hours = 20x km.   Distance covered by B in (x - 1) hours = 25(x - 1) km.   Therefore 20x + 25(x - 1) = 155   45x = 180   x = 4.   So, they meet at 11 a.m.   Answer: Option 11
Answer: C
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 18 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?	Choose the most appropriate option:
A) 565 B) 444 C) 676 D) 767 E) 408

Solution: 1h ----- 2   ? ------ 60   12 h   RS = 16 + 18= 
16 + 18 = 34
34   T= 12   D = 34 * 12= 
34 * 12 = 408
408   Answer: 408
Answer: E
A first grade teacher uses ten flash cards, each numbered from 1 to10, to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '2' and '3' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible?	Choose the correct answer:
A) 80
B) 40
C) 50
D) 60
E) 70

Solution: problem of combination 8C4 = 8!/4!*(8-4)! = 8*7*6*5*4!/4!*4! 8 /4 *(8-4)= 
8 /4 *(8-4) = 8
8*7*6*5*4!/4!*4!=70   70
Answer: E
On a certain transatlantic crossing, 35 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?	Options.
A) 33 1/3%  B) 87.5%  C) 50%  D) 60%  E) 66 2/3%

Solution: On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?   Solution: Let total number of passengers be 100   According to Q stem 40% of passengers who had round-trip tics have taken cars - let number of passengers with round trip be X then   40% of X = 35 => X= 87.5.   Answer 87.5%
Answer: B
A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 110 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?  Choices:
A) 2989	B) 2765	C) 5600	D) 2989	E) 9772

Solution: Total production of salt by the company in that year   = 5000 + 5110 + 5220 + .... + 6210 = 67370.   Average monthly production of salt for that year   = 67370/12   = 5614.   Answer:5600
Answer: C
What will come in place of the x in the following Number series? 18, 22, 30, x ,78, 142  Select.
A) 35 B) 56 C) 46 D) 87 E) 98

Solution: (46)   The pattern is +4, +8, +16, +32, +64   So the missing term is = 30 + 16= 
30 + 16 = 46
46 .
Answer: C
The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit? Choose the most appropriate option.
A) 2000 B) 3000 C) 4000 D) 3500 E) 4500

Solution: Capital be x   then 1920 - x/x*100 = 1280   1920-x=x-1280   2x=3200   x=1600   req = 125% of rs 1600 = rs(125/100*1600)= 
(125/100*1600) = 2_000
2000   2000NSWER 2000
Answer: A
x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 6 will be equal to:  Choose the correct answer.
A) 3  B) 6  C) 1/4  D) 1/3  E) 9

Solution: Explanation :   Solution: Given x = k/y^2, where k is constant. Now, y=3 and x =1 gives k = 9.   .'. x = 9/y^2   => x =9 /6^2 = 1/4   Answer : 1/4
Answer: C
Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 32 percent ryegrass, what percent of the weight of this mixture is X ?
Options:
A) 10%
B) 33.33 %
C) 46.66%
D) 50%
E) 66.66 %

Solution: ---------------->Ryegrass   X-------------->	40%   Y-------------->	25%   M(mixture)---->32%   0.4X + (M-X)0.25 = 0.32M   0.15X = 0.07M   X = 0.4666M   X = 46.66% of M   46.66%
Answer: C
In the new budget the price of cheese rose by 25%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?  Choose the correct choice from the following choices:
A) 20%
B) 9.1%
C) 10.9%
D) 12.6%
E) 15%

Solution: Reduce in consumption = R/(100+R) *100% = 25/125 *100= 
25/125 *100 = 20
20%   20%nswer is 20%
Answer: A
Each month, after Jill pays for rent, utilities, food, and other necessary expenses, she has one fifth of her net monthly salary left as discretionary income. Of this discretionary income, she puts 30% into a vacation fund, 20% into savings, and spends 35% on eating out and socializing. This leaves her with $99 dollar, which she typically uses for gifts and charitable causes. What is Jill’s net monthly salary?  Answers
A) $2400  B) $3300  C) $6000  D) $6400  E) $9600

Solution: let x be the monthly salary   15%of 1/5*x=99   x=3300   answer $3300
Answer: B
On a purchase of $112, a store offered a payment plan consisting of a $12 down payment and 12 monthly payments of $10 each. What percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan?
Pick
A) 10.7%	B) 11.7%	C) 12.7%	D) 13.7%	E) 14.7%

Solution: 12*10 + 12= 
12*10 + 12 = 132
132   (12/112)* 100= 10.7   10.7%nswer : 10.7%
Answer: A
A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
Choose the correct choice from the following:
A) 440
B) 440 * sqrt (2)
C) 400 * sqrt (3)
D) 450 * sqrt (4)
E) 440 * sqrt (5)

Solution: let the constant be k   F1 = 440   F2 = 440k   F3 = 440 k * k = 440 * k^2   F13= 440 * k^12   we know F13 = 2 *F1 = 2 * 440 2 * 1= 
2 * 1 = 2
2 * 440= 
2 * 440 = 880
880   880/440= k^12   k = twelfth root of 2   for F7...   F7 = 440 * k^6 ( as we wrote for F2 and F3)   F7 = 440 * (twelfth root of 2) ^ 6   F7 = 440 * sqrt (2)   Answer 440 * sqrt (2)
Answer: B
Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 2800 envelopes.
Select:
A) 2	B) 3	C) 4	D) 6	E) 60/7

Solution: You can either take the amount of work done as the same as Karishma has done or take the work done by each in the same time. I will do the latter   1. Work done in 1 hr by A is 2000 envelopes   2. Work done in 1 hr by A and C is 3000 envelopes   3. So work done in 1 hr by C is 1000 envelopes   4. Work done in 1 hr by B and C is 2400 envelopes   5. So work done in 1 hr by B is 1400 envelopes   6. So to process 2800 envelopes B will take   2800/1400= 
  2800/1400 = 2
2 hrs   So the answer is choice 2
Answer: A
Two numbers are respectively 50% and 20% more than a third number. The percentage that is first of the second is?
Pick.
A) 125%	B) 97%	C) 118%	D) 52%	E) 83%

Solution: I II III   150 120 100   120----------150   100-----------? => 125%   125%nswer:125%
Answer: A
A carpenter is building a frame for a wall painting. The painting is in the shape of a rectangle. If the sides of the rectangle are in the ratio of 3:2 and the shorter side has a length of 16 inches, how many inches of framing material does the carpenter need to frame the painting? Select the correct option
A) 12 B) 22 1/2 C) 37 1/2 D) 88 E) 80

Solution: (16/2) ( 2+3) * 2 = 80=80
Answer: E
In What proportion must flour at $0.8 per pound be mixed with flour at $0.9 per pound so that the mixture costs $0.855 per pound?  Choices.
A) 1:3
B) 1:2
C) 1:1
D) 2:1
E) 4:5

Solution: Using weighted average method:   Let x be the proportion in which the $0.8 per pound flour is mixed with $0.9 per pound flour.   Thus 0.8*x + 0.9*(1-x) = 0.855   0.9 – 0.1x = 0.855   x = 0.45   Thus ratio of both flours is 4:5   4:5
Answer: E