MU-NLPC/Calc-aqua_rat huggingface dataset:
A sum of $800 amounts to $920 in 3 years at simple interest. If the interest rate is increased by 3% it would amount to how much ? Select:
A) $506
B) $774
C) $992
D) $854
E) $1021

Solution: S.I = 920-800= 
920-800 = 120
120   P= $800   T = 3 years   R = 100*120 / 800*3 = 5%   New rate = 5+3= 
5+3 = 8
8%   New S.I.= 800*8*3/100= 
800*8*3/100 = 192
$192   New amount= 800+192= 
800+192 = 992
$992   Answer is $992
Answer: C
The ratio, by weight, of coffee to sugar to water in a pot of coffee is 5:2:20. The ratio is then altered so that the ratio of coffee to sugar is halved while the ratio of coffee to water is tripled. If the altered pot of coffee contains 8 grams of sugar, how many grams of water does it contain after alteration? Choose one:
A) 12
B) 12.5
C) 13
D) 13.5
E) 14

Solution: The new ratio of coffee to sugar is 2.5:2   The new ratio of coffee to water is 15:20.   The new ratio of coffee to sugar to water is 15:12:20.   If there are 8 grams of sugar, then there are  (21/12)*8= 
 (21/12)*8 = 14
14 grams of water.   The answer is 14.
Answer: E
Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.
Year	Item of Expenditure
Salary	Fuel and Transport	Bonus	Interest on Loans	Taxes
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98
Total expenditure on all these items in 1998 was approximately what percent of the total expenditure in 2002?
Select.
A) 62%
B) 69.45%
C) 70%
D) 71%
E) 72%

Solution: Required percentage   =	[	(288 + 98 + 3.00 + 23.4 + 83)	x 100	]	%   (420 + 142 + 3.96 + 49.4 + 98)   =	[	495.4	x 100	]	%   713.36   ~= 69.45%.   69.45%)
Answer: B
The area of sector of a circle whose radius is 12 metro and whose angle at the center is 54Â° is?  Select the correct option
A) 52.6  B) 52.9  C) 67.9  D) 52.1  E) 52.2

Solution: 54/360 * 22/7 * 12 * 12 = 67.9 m2   Answer: 67.9
Answer: C
What is 1! + 2! + ... + 10! ?	Pick one:
A) 4,037,910	B) 4,037,913	C) 4,037,915	D) 4,037,916	E) 4,037,918

Solution: All options have different Unit digit so calculating unit digit of the sum above will suffice   Unit digit of (1! + 2! + 3! + 4! + 5! + 6!+... + 10!) = 1 + 2+ 6 + 4 + 0 + 0 + 0 + 0+ 0 + 0 = Unit digit 3, Hence   every Factorial of an integer greater than 4 will have Unit digit 0 as it will be a multiple of 10   Answer: option 4,037,913
Answer: B
Apples are bought at 11 for a $ and an equal number more at 9 a $. If these are sold at 10 for a $, find the loss or gain percent?  Choose the correct choice from the following:	A) 5% loss	B) 7% loss	C) 3% loss	D) 2% loss	E) 1% loss

Solution: 1% loss   1% loss
Answer: E
There are two groups of students in the sixth grade. There are 20 students in group A, and 80 students in group B. If, on a particular day, 20% of the students in group A forget their homework, and 15% of the students in group B forget their homework, then what percentage of the sixth graders forgot their homework?	Choose the correct option:
A) 13%	B) 14%	C) 15%	D) 16%	E) 17%

Solution: Number of students in group A = 20   students who forget homework in group A = 20 % of 20 = 4 students   Number of students in group B = 80   students who forget homework in group B = 15 % of 80 = 12 students   Total number of students = 20 + 80= 
20 + 80 = 100
100   students who forgot homework= 4 + 12= 
4 + 12 = 16
16 students   percentage of students who forget homework= 16/100 * 100= 
16/100 * 100 = 16
16%   Answer: 16%
Answer: D
What is the value of (44444445*88888885*44444442+44444438)/44444444^2	Select the correct option:
A) 88888883  B) 88888827  C) 16992677  D) 88888237  E) 88888182

Solution: 88888883ns: 88888883   Let x = 44444444   (x+1)×(2x−3)×(x−2)+(x−6)x2(x+1)×(2x−3)×(x−2)+(x−6)x2   (x2−x−2)×(2x−3)+(x−6)x2(x2−x−2)×(2x−3)+(x−6)x2   2x3−2x2−4x−3x2+3x+6+x−6x22x3−2x2−4x−3x2+3x+6+x−6x2   2x3−5x2x2=2x−52x3−5x2x2=2x−5   Substituting the value of x in 2x - 5, we get 88888883   88888883nswer:88888883
Answer: A
Find average speed if a man travels at speed of 20km/hr up and 26km/hr dawn at an altitude of 240m. Choose one:
A) 25.8
B) 26.8
C) 22.6
D) 28.8
E) 29.8

Solution: avg speed=2*x*y/(x+y)   =2*20*26/(20+26)=22.6   ANSWER:22.6
Answer: C
Find the remainder Y when 12^190 is divided by 1729 ?
Choose the correct choice from the following:  A) 12  B) 1  C) 1728  D) 1717  E) 4

Solution: 12^(190) can be written as. ((12^3)^63)* 12. 12^3 when divided by 1729 gives a remainder Y -1. so in the numerator we have -12. Now acccording to remainder theorm the answer will be 1729-12=1717.1717
Answer: D
What is the perimeter of a square with area 9p^2/36 ?
Choose the correct choice from the following choices.
A) 3p/4
B) 3p^2/4
C) 2p
D) 3p^2
E) 4p/3

Solution: Area of square, (side)^2 = (3p/6)^2   Therefore side of the square = 3p/6   Perimeter of square = 4*side = 4* (3p/6) = 2p   Answer is 2p.4* (3 /6)= 
4* (3 /6) = 2
2p   Answer is 2p.
Answer: C
Find the simple interest on Rs.500 for 9 months at 6 paisa per month? Pick:  A) 238  B) 270  C) 987  D) 167  E) 121

Solution: I = (500*9*6)/100= 
(500*9*6)/100 = 270
270   Answer:270
Answer: B
A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
Choices
A) 600	B) 267	C) 132	D) 277	E) 161

Solution: Cost price = Rs.500   profit = 20% of 500 = Rs.100   Selling price = Cost price + Profit   = 500 + 100= 
500 + 100 = 600
600   600nswer:600
Answer: A
Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel C containing spirit and water in the ration 8 : 5?  Pick one:  A) 4 : 3  B) 3 : 4  C) 5 : 6  D) 7 : 9  E) None

Solution: Let the C.P. of spirit be Re. 1 litre.   Spirit in 1 litre mix. of A = 5/7 litre, C.P. of 1 litre mix. in A = Re. 5/7   Spirit in 1 litre mix. of B = 7/13 litre, C.P. of 1 litre mix. in B = Re. 7/13   Spirit in 1 litre mix. of C = 8/13 litre, Mean price = Re. 8/13.   By the rule of alligation, we have:   Required ratio = 1/13 : 9/91 = 7 : 9.   Answer 7 : 9
Answer: D
Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 240. Their H.C.F. is: Pick one.
A) 30	B) 20	C) 40	D) 60	E) 70

Solution: Explanation:   Let the number be 2x, 3x and 4x   LCM of 2x, 3x and 4x = 12x   12x = 240   => x = 240/12= 
240/12 = 20
20   HCF of 2x, 3x and 4x= x = 20   Answer: Option 20
Answer: B
A box contains 40 balls, numbered from 1 to 40. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd? Pick:
A) 1/4
B) 3/8
C) 1/2
D) 5/8
E) 3/4

Solution: I don't think order matters in this case, because 2 + 2 + 1 = 2 + 1 + 2   My answer is: 1/4   1/4
Answer: A
How many even prime numbers are there less than 50?	Select the correct option.
A) 15	B) 1	C) 2	D) 16	E) 17

Solution: 2 is the only even prime number   Answer is 1
Answer: B
The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 4th year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year?  Options:
A) 36	B) 41	C) 38	D) 40	E) 42

Solution: 1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer))   2ndyear : 1-2 (age), we take age = 1   3rd year : 2-3 (age), we take age = 2   4th year : 3-4 (age), we take age = 3   5th year : 4-5 (age), we take age = 4   6th year : 5-6 (age), we take age = 5   Thus for the 4th year = 50,   5th year = 50 -4= 
50 -4 = 46
46   6th year= 46-5= 
46-5 = 41
41   The correct answer is 41.
Answer: B
The number of singles that a baseball player hit increased 18 percent from her first season to her second season, and the number of doubles that she hit in the same time period decreased by 6 percent. If the total number of singles and doubles that she hit increased 3 percent from her first season to her second season, what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season? Choose the correct choice:
A) 1:3	B) 4:5	C) 1:5	D) 2:5	E) 3:5

Solution: Soln:-   1.18S + 0.94D = 1.03[S + d]   0.15S = 0.09D   S/D = 3/5   ANSW3:5R:3:5
Answer: E
Jill, who lives in City C, plans to visit 3 different cities, M, L, and S. She plans to visit each city exactly once and return to City C after the 3 visits. She can visit the cities in any order. In how many different orders can she visit the 3 cities?
Choices
A) 3 B) 6 C) 8 D) 9 E) 12

Solution: 3! = 6   M	L	S	C   M	S	L	C   L	M	S	C   L	S	M	C   S	M	L	C   S	L	M	C   She can visit the cities in any order. Number of ways of arranging the three cities is 3! = 6 ways. Hence 6.
Answer: B
What approximate value should come in place of the question mark (?) in the following equation?
39.05 × 14.95 – 27.99 × 10.12 = (36 + ?) × 5	Pick:
A) 22	B) 29	C) 34	D) 32	E) 25

Solution: Solve using approximation   Answer 25
Answer: E
If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of Rs. 372, C will receive
Choose one:
A) 60
B) 51
C) 900
D) 72
E) 271

Solution: Explanation:   Let 4A = 6B = 1OC = k. Then, A = k/4, B = k/6, and C =k/10 .   A : B :C = k/4 : k/6 : k/10 = 15 : 10 : 6.   Hence, C's share (372 * 6/31) = Rs, 72.   Answer: 72) Rs.72
Answer: D
If y exceeds x by 25%, then x is less than y by?
Choose the correct choice from the following:
A) 22% B) 67% C) 20% D) 16% E) 11%

Solution: X=100	y=125   125--------25   100--------? => 20%   Answer: 20%
Answer: C
In a 500 member association consisting of men and women, exactly 20% of men and exactly 50 % women are homeowners. What is the least number of members who are homeowners? Choose the correct choice from the following options
A) 149
B) 147
C) 101
D) 143
E) 141

Solution: Solution simple   Out of 500 20% are male i.e 100 and 50% are female i.e 250 , so total homeowner is 350.   Now min number homeowner is 100 and max is 250 so question ask us to find least and 101 has least value among all option.   So ans is 101.   Ans: 101
Answer: C
7/9 of 3/5 of a number is greater than 2/9 of 5/6 of the same number by 152. What is half of that number? Choose the correct choice from the following choices:	A) 165	B) 195	C) 240	D) 270	E) 315

Solution: Let no. be x   7/9*3/5*x - 2/9*5/6*x =152   by further solving   21x/45- 10x/54=152   114x/405=152   x=540   we have to find x/2   =540/2= 
540/2 = 270
270   ANSWER:270
Answer: D
In a class of 120 students, 25 did not opt for math. 10 did not opt for science and 2 did not opt for either. How many students of the class opted for both math and science?  Choose the correct choice from the following answers: A) 63 B) 95 C) 77 D) 87 E) 48

Solution: 120 students total   25 did not opt for math   10 did not opt for science   2 did not opt for either   Total of 95 students in math and 8 did not opt for sci but did for math    95-8= 
 95-8 = 87
87   87 students of the class opted for both math and science   Answer:   D. 87
Answer: D
The number N is 6,2X4, where X represents the ten's digit. If N is divisible by 9, what is the value of X? Options: A) 1 B) 3 C) 5 D) 7 E) 6

Solution: Integer is divisible by 9 - Sum of digits is divisible by 9   Answer: 6
Answer: E
A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is:
Pick one.
A) 8%
B) 6%
C) 9%
D) 10%
E) 11%

Solution: Rs 1552 income = Rs 128   By investing Rs 97 income = 128/1552*97= 
128/1552*97 = 8
Rs 8   Divdend= 8%   8%NSWER 8%
Answer: A
A Scooter is sold for Rs. 65000, a shop keeper gains 25%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?	Choices:
A) 25%
B) 12.5%
C) 22.5%
D) 15%
E) 36%

Solution: Explanation:   Marked price = Rs. 65000   C.P. = 100/125 * 65000 = Rs. 52000   Sale price = 90% of Rs. 65000 = Rs. 58500   Required gain % = 650/52000 * 100 = 12.5%.   Answer: 12.5%
Answer: B
How many 6 digit number can be formed from the digits 1, 2, 3, 4, 5, 6 which are divisible by 4 and digits are not repeated?	Pick:
A) 192	B) 122	C) 140	D) 242	E) None

Solution: Solution   For the number to be divisible by 4, the last two digits must be any of 12, 24, 16, 64, 32, 36, 56 and 52. The last two digit places can be filled in 8 ways. Remaining 3 places in 4P3 ways.   Hence no. of 5 digit nos. which are divisible by 4 are 24 × 8 = 192   192nswer 192
Answer: A
The current birth rate per thousand is 50, where as corresponding death rate is 10 per thousand. The net growth rate in terms of population increase in percent is given by?  Pick:  A) 2%  B) 3%  C) 4%  D) 6%  E) 8%

Solution: Net growth on 1000 = 50-10= 
50-10 = 40
40   Net growth on 100= 40*100/1000= 
40*100/1000 = 4
4%   Answer is 4%
Answer: C
A machine puts c caps on bottles in m hours. How many hours will it take to put caps on b bottles?	Options.
A) 60bm/c B) bm/60c C) bc/60m D) bm/c E) b/60cm

Solution: A machine puts c caps on bottles in m minutes.   So, the machine puts 1 cap in m/c minutes   To put caps on b bottles, the machine will take bm/c hours   Answer : bm/c
Answer: D
If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 320, the cost of the article is Choose the correct choice from the following choices:
A) 289
B) 231
C) 200
D) 288
E) 600

Solution: Explanation:   Let C.P. be Rs. x.   Then, 5% of x = 350 - 320= 
350 - 320 = 30
30   x/20= 30 => x = 600   Answer: 600
Answer: E
How many of the positive factors of 24 are not factors of 26 Answers:
A) 2
B) 3
C) 4
D) 1
E) 6

Solution: factors of 24 - 1, 2, 3, 4, 6, 8, 12,24   factors of 26 -1, 2, 13, 26   Comparing both, we have 6 factors of 24 which are not factors of 26- 3, 4, 6, 8, 12,24   Answer: 6
Answer: E
A certain cube floating in a bucket of water has between 80 and 90 percent of its volume below the surface of the water. If between 6 and 13 cubic centimeters of the cube's volume is above the surface of the water, then the length of a side of the cube is approximately
Choose the correct choice from the following:
A) 4 B) 5 C) 7 D) 8 E) 9

Solution: If sides are 7, vol=7^3=343   80%= 274.4, 90%=308.7   so vol above water, between 68.6 and 34.3 -->too big   If side are 4, vol = 64   80%=51.2, 90%=57.6   vol above water between 12.8 and 6.4   So 4 should be the answer.   Check option C,   If sides are 5, vol = 125   80%= 100, .90%=112.5   vol above water between 12.5-25   (Sides are 4 cubic centimeters)   4
Answer: A
the radius of the circle is reduced from 5cm to 4cm then the % change of area .	Select the correct option:
A) 36%  B) 37%  C) 35%  D) 38%  E) 39%

Solution: for 5cm -> pi*r^2 --> 3.14 * 5 ^ 2 -> 78.539   for 4cm -> pi*r^2 --> 3.14 * 4 ^ 2 -> 50.265   %change -> (1- 50.265/78.539)*100= 36   ie 36%   36%NSWER:36%
Answer: A
Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?
Select the correct option:	A) 20	B) 22	C) 25	D) 27	E) 29

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131   a + b + c = √400 = 20   20
Answer: A
Balls of equal size are arranged in rows to form an equilateral triangle. the top most row consists of one ball, the 2nd row of two balls and so on. If 1104 balls are added, then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did. How many balls made up the triangle?
Choose the correct choice from the following answers:
A) 2145
B) 2209
C) 2878
D) 1210
E) 1560

Solution: As expected, this question boils down to 2 equation,   Consider total number of Balls in Triangle = T and number of balls in last row = x.   1+2+3+...+x = T   x(x+1)/2 = T ----(a)   As mentioned in the question, side of a square will be (x-8) and total number of Balls in square will be (T+1104)   (x-8)^2 = T+1104 -----(b)   Now the hardest part of the question will be to solve these 2 equations and this looks like time consuming BUT the easy way will be plug and play. Also, we've to find a value of T (from 5 optiosn given below) which can make a square of a a number. One we know this, it will be a cake walk.   We can see that option A fits this criteria in eq (b). Add - 2145+1104 = 3249 = 57^2 = (x-8)^2 Hence, x = 65.   Cross check by putting in eq (a) = x(x+1)/2 = T = > 65*66/2= 
65*66/2 = 2_145
2145   Hence, answer is 2145.
Answer: A
Find the probability that a number selected from numbers 1, 2, 3,..., 30 is a prime number, when each of the given numbers is equally likely to be selected?	Select.
A) 10/30 B) 1/30 C) 8/30 D) 3/30 E) 7/30

Solution: Let X be the event of selecting a prime number.   X = {2, 3, 5, 7, 11, 13, 17, 19, 23,29}   n(X) = 10,   n(S) = 30   Hence, the required probability is 10/30.   ANSWER:8/30
Answer: C
The price of a car is marked at $10,000. If the car has successive discounts of 25%, 20% and 10%, then at what price does a customer buy the car?  Choose the correct choice from the following answers
A) $4600
B) $4800
C) $5000
D) $5200
E) $5400

Solution: 0.9*0.8*0.75*10000= 
0.9*0.8*0.75*10000 = 5_400
$5400   The answer is $5400.
Answer: E
Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If 2 of the slips are the drawn, without replacement, what is the probability that both have a even number written on it?
Answers
A) 1/12  B) 1/10  C) 1/8  D) 1/2  E) 2/9

Solution: Key is that there is no replacement, so each successive choice will become more skewed towards picking a neg (i.e. the pool of positives decreases, while the pool of negatives stay the same)   P(+ on 1st pick) = 5/10   P(+ on 2nd pick) = 4/9   5/10*4/9=2/9   2/9
Answer: E
How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 75 km/hr? Choose one:	A) 25	B) 30	C) 99	D) 88	E) 61

Solution: Speed of train relative to man = 75 - 3= 
75 - 3 = 72
72 km/hr.= 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Time taken to pass the man= 500 * 1/20= 
500 * 1/20 = 25
25 sec.   25nswer: 25
Answer: A
John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?	Choose the correct choice from the following options:
A) 8  B) 10  C) 12  D) 16  E) 18

Solution: Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j)   and Rupesh + 6 = | (Ravi + 6) ...(ii)   Solving both the equations we get,   John= 12 years.   12
Answer: C
the cyclist walking at a constant rate of 15 miles per hour is passed by a car traveling in the same direction along the same path at 60 miles per hour. the car stops to wait for the cyclist for 6 minutes after passing her, while the cyclist continues to go at her constant rate, how many minutes must the car wait until the cyclist catches up?  Choose the correct choice from the following options:
A) 9	B) 10	C) 12	D) 15	E) 18

Solution: For the 6 minutes the car continues to overtake the cyclist, she is going at 45 miles per hour faster than the cyclist.   Once the car stops, the cyclist is going at 15 miles per hour while the car is at rest   So the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds. 45/15 * 6 or 18 minutes   Answer is (18)
Answer: E
A dishonest dealer professes to sell goods at the cost price but uses a weight of 840 grams per kg, what is his percent?  Choices:
A) 19  B) 25  C) 77  D) 88  E) 11

Solution: 840 --- 160   100 --- ? => 19%   19nswer:19
Answer: A
The visitors of a modern art museum who watched a certain Picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it. According to the results of the survey, all 110 visitors who did not enjoy the painting also did not feel they had understood the painting, and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting. If 3/4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting, then how many visitors answered the questionnaire? Select the correct option:
A) 90
B) 120
C) 160
D) 360
E) 440

Solution: If we exclude those cases and take the question at face value, then it seems straightforward.   Group #1 = (didn't like, didn't understand) = 110   Group #2 = (like understood) = 3/4   (1/4)N = 110   N = 440   Answer =(440)
Answer: E
A person started from point A to point B and returned back to A with a speed of 60 kmh. If the distance between A and B is 120km, calculate the time he travelled  Select the correct option:
A) 4 hours B) 2 hours C) 3 hours D) 6 hours E) 5 hours

Solution: Time = Distance/Speed   Total distance = (from 4 hours->B and from B->4 hours) = 120+120= 
120+120 = 240
240 km   Speed= 60 kmh    240/60= 
 240/60 = 4
4   4 hoursnswer: 4 hours
Answer: A
If the sum of three consecutive even numbers is 44 more than the average of these numbers, then the largest of these numbers is? Pick one:
A) 24
B) 66
C) 9
D) 7
E) 01

Solution: ANSWER: 24   Explanation:   Let the smallest of these number be x. The other two numbers are (x + 2) and (x + 4).   x + (x + 2) + (x + 4) = (X + (X+2) + (x+4)) / 3 + 44   3x + 3*(x + 2) + 3*(x + 4) = x + (x + 2) + (x + 4) + 132   9x + 18 = 3x + 138   6x = 120   x = 20   Therefore, the largest number is 24.   24NSWER: 24
Answer: A
If a: b :: 3 : 7, then what is (5a+6b): (a-2b)?
Answers.
A) 57:11 B) -57:11 C) 11 : 10 D) -11 : 10 E) -1 : 10

Solution: a/b= 3/7   Dividing numerator & denominator of ' (5a+6b)/(a-2b) 'by b,   [5(a/b)+6]/[(a/b)-2]= [5*(3/7)+6]/[(3/7)-2]= -57/11   ANSWER:-57:11
Answer: B
A is twice as good a workman as B and they took 8 days together to do the work B alone can do it in. Pick:  A) 24 days  B) 12 days  C) 29 days  D) 25 days  E) 27 days

Solution: WC = 2:1   2x + x = 1/8   x = 1/24 => 24 days   24 daysNSWER:24 days
Answer: A
A can do a job in 16 days, B can do same job in 12 days. With the help of C they did the job in 4 days. C
alone can do the same job in how many days ?
Choices:  A) 612days  B) 712days  C) 835days  D) 935days  E) None of these

Solution: Explanation:   In this question we having, A's work, B's work and A+B+C work. We need to calculate C's work.   We can do it by,   (A+B+C)'s work - (A's work + B's work)   Let's solve it now:   C's 1 day work =   14−(116+112)=(14−748)=548   So C can alone finish the job in 48/5 days,   Which is =   935days   Answer: 935days
Answer: D
Bert and Rebecca were looking at the price of a condominium. The price of the condominium was 25% more than Bert had in savings, and separately, the same price was also 50% more than Rebecca had in savings. What is the ratio of what Bert has in savings to what Rebecca has in savings.	Choose the correct option:
A) 1:5 B) 2:5 C) 3:5 D) 4:5 E) 1:1

Solution: Suppose bert had 100 so price becomes 125 , this 125 = 1.5 times R's saving .. so R's saving becomes 250   So required ratio is 100:250=2:5   ANSWER:2:5
Answer: B
A cylindrical vessel of a certain height and radius can hold 30 liters of water in it when filled to the brim. All the water in the cylindrical vessel is transferred to a spherical vessel. If the height and radius of the cylindrical vessel is the same as the radius of the spherical vessel, what percentage of the capacity of the spherical vessel will remain empty after the transfer?	Select the correct option.
A) 0%	B) 16.67%	C) 25%	D) 33.33%	E) 50%

Solution: Let R and H be the radius and height of the cylinder.   Let r be the radius of the sphere.   Volume of cylinder = Vc = π∗R2∗Hπ∗R2∗H = 30---> As both radius and height of the cylinder are equal to the radius of the sphere ---> R=H=r --->π∗r3π∗r3 = 30   Additionally, volume of the sphere = Vs =4π∗r334π∗r33 = 4/3*30= 
4/3*30 = 40
40 l   Thus the % of sphere volume still empty= 10/40 = 25%. 25% is the correct answer
Answer: C