MU-NLPC/Calc-aqua_rat huggingface dataset:
X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?	Answers
A) 6 days	B) 10 days	C) 15 days	D) 16 days	E) 20 days

Solution: Work done by X in 4 days =(1/20)*4=1/5   Remaining work =1 -1/5=4/5	.   (X + Y)'s 1 day's work =1/20+1/12 =	8/60	=	2/15	.   Now,	2/15	work is done by X and Y in 1 day.   So,	4/5	work will be done by X and Y in	(15/2x4/5)= 6 days.   Hence, total time taken = (6 + 4)= 
(6 + 4) = 10
10 days.   Option 10 days
Answer: B
A toy store sells small, medium, and large toy trucks in each of the colors red, blue, black, green, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?
Select the correct option
A) 2/5  B) 7/15  C) 11/15  D) 7/20  E) 11/30

Solution: Probability of NOT selecting medium out of 3 sizes = 2/3   Probability of NOT selecting red out of 5 colours = 4/5   Total probability of NOT selecting red and medium = (2/3)*(4/5) = 8/15   Required probability = 1 - 8/15 (this will select at least one of red and medium)   = 7/15   The answer is 7/15.
Answer: B
A student scored an average of 60 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?	Pick.
A) 86
B) 160
C) 76
D) 140
E) 26

Solution: Given M + P + C = 60 * 3= 
60 * 3 = 180
180 --- (1)   M + P= 90 * 2= 
90 * 2 = 180
180 --- (2)   P + C= 70 * 2= 
70 * 2 = 140
140 --- (3)   Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.   P= (2) + (3) - (1) = 180 + 140 - 180= 
180 + 140 - 180 = 140
140   Answer:140
Answer: D
Find the ratio between whole surfaces of a sphere and a hemisphere?  Choose the correct choice from the following choices.
A) 4:8	B) 4:3	C) 4:2	D) 4:1	E) 4:6

Solution: 4 πr2 : 3 πr2 => 4:3   Answer: 4:3
Answer: B
What least value should be replaced by * in 483*4312 so the number become divisible by 6
Choose the correct choice from the following options.
A) 3
B) 4
C) 5
D) 2
E) 7

Solution: Explanation:   Trick: Number is divisible by 6, if sum of all digits is divisible by 3 and 2,   Last digit is 2 so it is dividable by 2   so (4+8+3+*+4+3+1+2) = 25+* should be divisible by 6,   15+ will be divisible by ,   so that least number is 2.   Answer: Option 2
Answer: D
Marginal cost is the cost of increasing the quantity produced (or purchased) by one unit. If the fixed cost for n products is $10,000 and the marginal cost is $80, and the total cost is $16,000, what is the value of n?
Choose the most appropriate option.
A) 30  B) 50  C) 60  D) 75  E) 100

Solution: Total cost for n products = fixed cost for n products + n*marginal cost --> $16,000 = $10,000 + n * $80 --> n = 75.   Answer: 75.
Answer: D
How many odd numbers are possible between 1 to 10000? find out the number of odd number of digits?	Choose the correct choice from the following choices:
A) 2999	B) 3500	C) 4000	D) 4599	E) 4999

Solution: There are always one odd and one even no. And the question is odd no. Between 1 to 10000   So we have to find no. Between 1 to 10000 so we should not includes 1   10000/2 -1= 
10000/2 -1 = 4_999
4999   ANSW4999R:4999
Answer: E
If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true?
I. x > z
II. 4x+ 4y > 4z
III. yz > xz
IV. xy > y + z	Answers:
A) I only B) II only C) II and III only D) II and IV only E) III and IV only

Solution: we do not know the values or the relative values but that the three are consecutive..   so the max difference in any two number is 2 and min 1..   lets see the choices..   I. x > z...   we do not know the values or the relative values... need not be true..   II. 4x+ 4y > 4z or x+ y > z   we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true   III. yz > xz   we do not know the values or the relative values between x and y..need not be true   IV. xy > y + z   xy-y>z or y(x-1)>z...   again lets take the worst scenario..   we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true   only ii is true   ans II only
Answer: B
A large delicatessen purchased p pounds of cheese for K dollars per pound. If d pounds of the cheese had to be discarded due to spoilage and the delicatessen sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the purchase? (gross profitequalssales revenueminusproduct cost)  Choose the correct option:
A) (p − d)(s − c)
B) s(p-d) - Kp
C) c(p − d) − ds
D) d(s − c) − pc
E) pc − ds

Solution: Total cost price = K*p ............... (1)   Wastage = d pounds   Quantity sold = p-d   Selling price per pound = s   Total selling price = s(p-d) ........... (2)   Profit = (2) - (1)   = s(p-d) - Kp   s(p-d) - Kp
Answer: B
A jogger running at 9 km/hr along side a railway track is 190 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?	Choices:
A) 88  B) 27  C) 36  D) 31  E) 12

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 190 + 120= 
190 + 120 = 310
310 m.   Time taken= 310/10= 
310/10 = 31
31 sec.   Answer: 31
Answer: D
A new basketball cost increased 5% last week. A basketball coach wanted to buy two dozen basketballs in bulk for his team. He was able to negotiate paying only 90% of the posted price for the bulk purchase. How much did the coach save by purchasing in bulk?
Options: A) 2.5% B) 3.5% C) 4.5% D) 5.5% E) 6.5%

Solution: Quantity X Rate = Price   1 X 1 = 1   0.9 X 1.05 = 0.945   5.5%ecrease in price = (0.055/1) Ã— 100 = 5.5%   Answer = Option 5.5%
Answer: D
The average age 12 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?  Pick one.
A) 24 years  B) 21 years  C) 18 years  D) 29 years  E) 30 years

Solution: 12 * 2= 
12 * 2 = 24
24 years   24 yearsnswer:24 years
Answer: A
29 persons can repair a road in 16 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? Choose the correct answer
A) 12.88
B) 3.88
C) 13.88
D) 15
E) 18.8

Solution: Let the required number of days be x   More persons, less days (indirect proportion)   More hours, less days (indirect proportion)   Hence we can write as   (persons)29:30   }::x:16   (hours)5:6   29*5*16=30*6*x   x=12.88   12.88NSWER:12.88
Answer: A
If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a black card or a king?  Choose one.
A) 6/13
B) 7/10
C) 4/11
D) 7/13
E) 5/26

Solution: There are 26 black cards and 2 red kings.   P(black card or king) = 28/52 = 7/13   The answer is 7/13.
Answer: D
Jack and Jill are marathon runners. Jack can finish a marathon (42 km) in 5 hours and Jill can run a marathon in 4.2 hours.What is the ratio of their average running speed? (Jack: Jill)	Choose one:
A) 14/15  B) 15/14  C) 4/5  D) 21/25  E) Cannot be determined

Solution: Average Speed of Jack =21/25istance/ Time   = 42 /5   Average Speed of Jill = 42/(4.2)= 
42/(4.2) = 10
10   Ratio of Average speed of Jack to Jill= (42/5)/10 =42/50 =21/25   Answer 21/25
Answer: D
The S.I. on a certain sum of money for 2 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?  Choose the correct answer:  A) 2197  B) 1267  C) 1750  D) 2267  E) 2625

Solution: Explanation:   C.I. = [4000 * (1 + 10/100)2 - 4000]   = (4000 * 11/10 * 11/10 - 4000) = Rs. 840.   Sum = (420 * 100)/(2 * 8) = Rs. 2625   Answer:2625
Answer: E
The dimensions of a room are 10m x 7m x 5m. There are 2 doors and 3 windows in the room. The dimensions of the doors are 1m x 3m. One window is of size 2m x 1.5m and the other 2 windows are of size 1m x 1.5m. The cost of painting the walls at Rs. 3 per sq m is
Choose the correct choice from the following:	A) 2488	B) 378	C) 739	D) 474	E) 291

Solution: Explanation:   Area of 4 walls = 2(l+b)h   =2(10+7) x 5 = 170 sq m   Area of 2 doors and 3 windows = 2(1x3)+(2x1.5)+2(1x1.5) = 12 sq m   area to be planted = 170 -12= 
170 -12 = 158
158 sq m   Cost of painting= Rs. 158 x 3 = Rs. 474   Answer:474
Answer: D
In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?  Choices.
A) 50400	B) 50420	C) 50500	D) 50540	E) 50590

Solution: The word 'CORPORATION' has 11 letters. It has the vowels 'O','O','A','I','O' in it and these 5 vowels should always come together. Hence these 5 vowels can be grouped and considered as a single letter. that is, CRPRTN(OOAIO).   Hence we can assume total letters as 7. But in these 7 letters, 'R' occurs 2 times and rest of the letters are different.   Number of ways to arrange these letters   =   7   !   2   !   =   7   ×   6   ×   5   ×   4   ×   3   ×   2   ×   1   2   ×   1   =   2520   =7!2!=7×6×5×4×3×2×12×1=2520   In the 5 vowels (OOAIO), 'O' occurs 3 and rest of the vowels are different.   Number of ways to arrange these vowels among themselves   =   5   !   3   !   =   5   ×   4   ×   3   ×   2   ×   1   3   ×   2   ×   1   =   20   =5!3!=5×4×3×2×13×2×1=20   Hence, required number of ways   =   2520   ×   20   =   50400   =2520×20=50400   50400)
Answer: A
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 1/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos? Choices.
A) 7/17	B) 14/31	C) 7/15	D) 14/19	E) 1/2

Solution: # of basic stereos was 1/3 of total and # of deluxe stereos was 2/3 of total, let's assume total=15, then Basic=5 and Deluxe=10.   Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be  5*1= 
 5*1 = 5
5 and total time for Deluxe would be 10*7/5= 
10*7/5 = 14
14 --> total time for both of them would be 5+14= 
5+14 = 19
19--> deluxe/total=14/19.   Answer: 14/19.
Answer: D
A corporation that had $10 billion in profits for the year paid out $200 million in employee benefits. Approximately what percent of the profits were the employee benefits? (Note: 1 billion = 10^9)	Choose the correct choice from the following answers
A) 50%	B) 20%	C) 5%	D) 2%	E) 0.2%

Solution: required answer = [employee benefit/profit] *100   =[(200 million)/(10 billion)]*100   =[(200*10^6)/(10*10^9)]*100   =(20/1000)*100= 
(20/1000)*100 = 2
2%   So answer is (2%)
Answer: D
What will come in place of the x in the following Number series? 177147 ,59049 ,19683 ,6561, 2187 , x	Choose the correct choice from the following:	A) 727	B) 729	C) 726	D) 722	E) 723

Solution: Go on dividing by 3 to the next number   Answer : 729
Answer: B
The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:  Pick one.
A) 12	B) 16	C) 24	D) 48	E) None

Solution: EXPLANATION   Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.   So, the numbers 12 and 16.   L.C.M. of 12 and 16 = 48.   Answer 48
Answer: D
All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?  Choose the correct choice from the following:
A) 1726 liters
B) 1362 liters
C) 1280 liters
D) 1184 liters
E) 1173 liters

Solution: B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.   Quantity of water in B = 8k - 5k = 3k.   Quantity of water in container C 8  - 5= 
8  - 5 = 3
3k.   Quantity of water in container C= 8k - 3k = 5k   Container: A B C   Quantity of water: 8k 3k 5k   It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.   5k - 148 8  - 3= 
8  - 3 = 5
5k   Container: A B C   Quantity of water: 8k 3k 5k   It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.   5k - 148= 3k + 148 => 2k = 296 => k = 148   The initial quantity of water in A = 8k = 8 * 148= 
8 * 148 = 1_184
1184 liters.   Answer:1184 liters
Answer: D
The difference of two numbers is 8 and one-fourth of their sum is 6. Find the numbers.
Choose the correct choice from the following answers.
A) 16,8 B) 10,2 C) 17,6 D) 14,10 E) 12,4

Solution: Let numbers be x and y.   Equation (i): x - y = 8   Equation (ii): (x + y)/4 = 6   Solve system of equations: x=16, y=8   16,8 is the correct answer.
Answer: A
In the number 11,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 50, what is the greatest possible value of B × A?
Select the correct option
A) 0
B) 5
C) 20
D) 15
E) 25

Solution: You should notice that 50*2=110 so 11,000 is divisible by 55: 55*200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> B*A=0*0= 
0*0 = 0
0. Next number divisible by 55 is 11,000+55=11,055: B*A=5*4= 
5*4 = 20
20 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25).   Answer: C.   !   Please post PS questions in the PS subforum:gmat-problem-solving-ps-140/   Please post DS questions in the DS subforum:gmat-data-sufficiency-ds-141/   No posting of PS/DS questions is allowed in the mainMath forum.   20
Answer: C
If three sides of the triangle are 8 , 15 and G respectively then the how many values can G ? Options:
A) [A] 6
B) [B] 7
C) [C] 8
D) [D]9
E) [E] infinite number of values

Solution: Needed: How many Values can G take   Concept: Sum of any two sides of a triangle is greater then the third side.   Case 1: 8+5 > G => G<13   Case 2: 5+G > 8 => G >3   Case 3: 8+G > 5 => G > -3 (Always true since G is one side of a Triangle)   Finally, 3 < G < 13. So, we can have infinite number of sides between 3 and 13.   Answer = E   PS: If question said G can take only integer value, the G = 9. Answer choice [D]9.
Answer: D
How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?	Answers.
A) 22	B) 88	C) 55	D) 200	E) 21

Solution: T = (660 + 165)/54 * 18/5= 
(660 + 165)/54 * 18/5 = 55
55.Answer: 55
Answer: C
3x+4y=10
x^3+y^3=6
What is the minimum value of 3x+11y=?
Pick
A) 32 B) 34 C) 35 D) 36 E) 38

Solution: on subtracting 2 eqns we get y=4 and x=-2.   therefore 3x+11y=-6+44= 
-6+44 = 38
38.   ANSW38R:38
Answer: E
Dan has a membership at a local gym that also gives classes three nights a week. On any given class night, Dan has the option of taking yoga, weight training, or kickboxing classes. If Dan decides to go to either one or two classes per week, how many different combinations E of classes are available? Answers:  A) 3  B) 6  C) E=7  D) E=9  E) E=12

Solution: I think it should be E only.   No where it is given that he attends different classes on each day.   Experts please provide your views.   --- EDITED my Response. It was a typo. I meant 12 is the answer.   If only E=9ay 1 : 3 options   If E=9ay 1 and E=9ay 2 : 3*3= 
3*3 = 9
9 Options   So, Total= 3+9= 
3+9 = 12
12.
Answer: D
How many independent words can 'HEARTLESS' be divided into without changing the order of the letters and using each letter only once ? Choose the correct choice from the following options:
A) 1	B) 2	C) 5	D) 3	E) 4

Solution: Explanation:   The words are HE, ART and LESS.   Answer: 3) 3
Answer: D
A cylinder has a base with a circumference of 20pi meters and an equilateral triangle inscribed on the interior side of the base. A marker is dropped into the tank with an equal probability of landing on any point on the base. If the probability of the marker landing inside the triangle is (Sqrt 3)/4 , what is the length of a side of the triangle?  Select:
A) 3(sqrt 2pi) B) 3(sqrt 3pi) C) 10*sqrt (pi) D) 10(sqrt 3pi) E) 20 pi

Solution: Prob of marker landing in the triangle = area of triangle / area of base = sqrt(3)/4   10*sqrt (pi)ircumference of base = 20pi meters   => Radius of base = 10 meters   => Area of base = 100 pi sq m   Therefore area of the triangle = 100 pi * sqrt(3)/4   As the area of an equilateral triangle is sqrt(3)*(side^2)/4,   any side of the triangle = 10*sqrt(pi)   ANSWER:10*sqrt (pi)
Answer: C
Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 12 years more than the present age of Anand. Find the present age of Anand?  Choose the correct option
A) 22	B) 16	C) 82	D) 27	E) 15

Solution: Explanation:   Let the present ages of Anand and Bala be 'a' and 'b' respectively.   a - 10 = 1/3 (b - 10) --- (1)   b = a + 12   Substituting b = a + 12 in first equation,   a - 10 = 1/3 (a + 2) => 3a - 30 = a + 2= 
+ 2 = 2
> 2a= 32 => a = 16.   Answer: 16
Answer: B
Solve: 387 x 387 + 114 x 114 + 2 x 387 x 114	Pick one:  A) 251001  B) 251000  C) 251010  D) 250101  E) None of them

Solution: = (387)2+ (114)2+ (2 x 387x 114)   = a2 + b2 + 2ab, where a = 387,b=114   = (a+b)2 = (387 + 114 )2 = (501)2 = 251001.   251001nswer is 251001
Answer: A
There are d cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?  Choose the correct answer:
A) n(n-1)	B) n(n+1)	C) d(d-1)	D) n(n+1)/2	E) n2

Solution: First of all, the possible number of airlines is d. Then, the possible number of airlines departing from one city to another becomes (d-1). Hence, the answer is d(d-1), d(d-1)
Answer: C
For any integer n greater than 1, #n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers E are there between #6 +2 and #6 +6 , inclusive? Choose the correct choice from the following:
A) None
B) One
C) Two
D) Three
E) Four

Solution: None is the answer. A.   Because for every k 6! + k :: k, because 6! :: k, since k is between 2 and 6.None
Answer: A
A man cheats while buying as well as while selling. While buying he takes 10% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 12% below the cost price of the claimed weight. Choose the most appropriate option:
A) 19.81%  B) 21%  C) 37.5%  D) 25%  E) 37.5%

Solution: There is a one step calculation method too. It requires more thought but is faster.   The man takes 10% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 110 pounds for which he will take from the customer $110. Hence, in effect, there is a 10% mark up.   While selling, he sells 20% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 80 pounds and should have got only $80 for it. So this is again a mark up of $20 on $80 which is 25%.   21%ut he also sells at 12% less   (1 + m1%)(1 + m2%)(1 - d%) = (1 + p%)   11/10 * 5/4 * 22/25 = (1 + p%)   profit % = 21%   21%
Answer: B
For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 75, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement. Choose the correct choice from the following answers:
A) K+35
B) 2K+35
C) (75+K)/2
D) (70-K)/2
E) 2(70-K)

Solution: Say Sue was hired when she was already 75 years old (k=75), then she could retire right away, at the age of 75. Now, plug k=75 in the answer choices and see which yields 75. Only C fits.   Answer: (75+K)/2.
Answer: C
A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number N is
Answers:  A) 74  B) N=75  C) N=175  D) N=680  E) 690

Solution: I solved this question by plugging in numbers from the answer choices.   A.) 74   Starting with answer choice A, I immediately eliminated it because 74 is not even divisible by 5.   B.) 75   I divide 75/5 and get 15 as an answer. I divide 75/34 and get a remainder of 7.   15-7= 
15-7 = 8
8 so I know the correct answer isN=75
Answer: B
A jeep takes 9 hours to cover a distance of 480 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time? Select.
A) 48 Kmph
B) 52 Kmph
C) 35 Kmph
D) 63 Kmph
E) 65 Kmph

Solution: Time = 9   Distance = 480   3/2 of 9 hours = 9 * 3/2= 
9 * 3/2 = 27/2 = around 13.5
13.5 Hours   Required speed= 480/13.5 = 35 Kmph   35 Kmph)
Answer: C
The ratio of the volumes of two cubes is 1728 : 2197. What is the ratio of their total surface areas?  Choose the correct choice from the following answers:
A) 12:18
B) 144:169
C) 44:22
D) 28:144
E) 96:12

Solution: Ratio of the sides = Â³âˆš1728 : Â³âˆš2197   = 12 : 13   Ratio of surface areas =144:169   Answer: 144:169
Answer: B
Points A, B, and, C have xy-coordinates (2,0), (8,12), and (14,0), respectively. Points X, Y, and Z have xy-coordinates (6,0), (8,4), and (10,0), respectively. What fraction S of the area of triangle ABC is the area of triangle XYZ?	Choose the correct choice from the following choices.
A) 1/9	B) 1/8	C) 1/6	D) 1/5	E) 1/3

Solution: If you notice, both triangles ABC and XYZ have a side on X axis. we can take these sides as bases for each triangle, therefore   1/9rea of 1/9BC is 1/2*12*12 (Height of 1/9BC is the y coordinate of the third point (8,12))   similarly 1/9rea of XYZ is 1/2*4*4   dividing area of XYZ with that of 1/9BC gives S=1/9.1/9
Answer: A
a and b are two numbers selected randomly from 1,2,3.... 25 what is the probability of a and b are not equal.	Choose the correct choice from the following choices.
A) 1/25  B) 24/25  C) 13/25  D) 2/25  E) 3/25

Solution: No of events=625((1,1),(1,2).......(25,25))   Probability of getting a&b are equal=(25/625)[(1,1),(2,2),(3,3).....(25,25)]   Probability of a and b or not equal=1-(25/625)   =600/625   =24/25   ANSWER:24/25
Answer: B
A number is missing from the number series below.
Can you find it ?
84, 155, 258, 399 , 584, ?.
Pick:
A) 275	B) 350	C) 399	D) 421	E) 819

Solution: E   The missing number is 819.   84 = 4^3 + 3^2 + 4   155 = 5^3 + 5^2 + 5   258 = 6^3 + 6^2 + 6   399 = 7^3 + 7^2 + 7   584 = 8^3 + 8^2 + 8   Thus,   819 = 9^3 + 9^2 + 9
Answer: E
Effective annual rate of interest corresponding to nominal rate of 6% per annum compounded half
yearly will be
Answers.
A) 6.09%
B) 6.10%
C) 6.12%
D) 6.14%
E) None of these

Solution: Explanation:   Let the amount Rs 100 for 1 year when compounded half yearly, n = 2, Rate = 6/2= 
6/2 = 3
3%   6.09%mount=100(1+3100)2=106.09   Effective rate = (106.09 - 100)= 
(106.09 - 100) = 6.09
6.09%   6.09%nswer: 6.09%
Answer: A
In 165 litres of mixtures of milk and water, water is only 28%. The milkman sold 40 litres of this mixture and then he added 30 litres of pure milk and 13 litres of pure water in the remaining mixture. What is the percentage of water in the final mixture?  Select:
A) 29.35%
B) 28. 57%
C) 24. 57%
D) 27. 75%
E) 26. 57%

Solution: Initially, milk = 118.2 l, and water = 46.2 l.   40 liters is withdrawn in same ratio as it was initially, i.e., 72:28.   Remaining milk = 90 l, and water = 35 l.   Now add 30 l of milk and 13 liter of water.   Then milk = 120 l and water = 48 l.   Percentage of water = 48*100/168 = 28.57 %   ANSWER:28. 57%
Answer: B