MU-NLPC/Calc-aqua_rat huggingface dataset:
In the city of San Durango, 60 people own cats, dogs, or rabbits. If 32 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?
Choose the correct choice.
A) 5	B) 4	C) 8	D) 12	E) 32

Solution: Total = C + D + R - (CD + DR + CR) - 2CDR   60 = 32 + 40 + 10 - (12) - 2x   x = 5   So, answer will be 5
Answer: A
Ratio of two numbers x and y is 1:2. If x is increased by 20% and y is increased by 4 then the new ratio becomes 1:5. What is the ratio 2y:x Pick: A) 1:3 B) 3:1 C) 2:3 D) 4:1 E) 1:4

Solution: Let:   x = 1n   y = 2n   1.2n/(2n+4) = 1/5   6n = 2n+4   n = 1   So, x =1; y=2   2y/x = 4/1= 
4/1 = 4
4:1   Answer= 4:1
Answer: D
Marco rode his dirt bike at 30 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride?  Choose the correct choice from the following choices
A) 14 mph
B) 20 mph
C) 70/3 mph
D) 80/3 mph
E) 30 mph

Solution: Average speed for first two hours, S1 = 30 mph   Distance travelled in these two hours, D1 = 60 miles   Average speed for the entire 5 hour ride, S = 30 mph   Total Distance traveller in the entire 5 hour ride, D = 30 x 5 = 150 miles.   Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 150 - 60= 
150 - 60 = 90
90   Average speed for the latter 3 hour period S2= D2/3 = 90/3= 
90/3 = 30
30   Hence, the correct answer is 30 mph
Answer: E
In a diving competition, each diver has a 30% chance of a perfect dive. The first perfect dive of the competition, but no subsequent dives, will receive a perfect score. If Janet is the third diver to dive, what is her chance of receiving a perfect score? (Assume that each diver can perform only one dive per turn.) Choose the correct choice from the following choices:
A) 1/5	B) 1/15	C) 4/25	D) 16/125	E) 71/483

Solution: Probability = Favourable Outcomes / Total Outcomes = 1 - (Unfavourable Outcomes / Total Outcomes)   Given:Probability of Perfect dive = 0.3 = 30/100 = 2/7   i.e. Probability of Non-Perfect dive = 0.7 = 70/100 = 2/3   The probability of Janet to dive and get a perfect score depends on that other other previous two dives must be Imperfect   Method-1:   i.e. Probability of First two being Imperfect and Third being Perfect dive = (2/3)*(2/3)*(2/7) = 71/483   71/483
Answer: E
In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes?	Choose the correct choice.
A) 6  B) 7  C) 8  D) 9  E) 10

Solution: If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥60. The smallest n which fulfills this condition is n = 8.   Answer 8
Answer: C
A warning notice is to be prepared for a building demolition in which the 'warning' is written in 8 differnent languages, including english, french and german. The authority requires you to put french after english and german after french. In how many different order of languages can you prepare the notice?	Choose the correct choice from the following answers
A) 4!
B) 5!
C) 6!
D) 7!
E) 8!

Solution: The problem requires you to find the total number of arrangements in which 8 object can be arranged paying attention to the given constraints. The constrain is that English, French and German mus follow the order E>F>G. Since there is only one way to arrange E,F and G, we can consider EFG as one object. Therefore 6 object is to be arranged and we can do this in 6! Ways. So the correct option is C. 6!.
Answer: C
Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many E hours does it currently take Anne to clean the house on her own?
Choose the correct choice from the following answers
A) 6
B) 7
C) 8
D) 12
E) 14

Solution: Lets suppose Anne and Bruce take A and B hrs working separately   So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours)   After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to 1/3 (As the work is completed in E=3 hours)   Solving these 2 equations we can find B as 12   So, 12
Answer: D
How many cubes of 10 Cm edge can be put in a cubic box of 1 m edge?
Pick:
A) 4000 B) 2000 C) 3000 D) 5000 E) 1000

Solution: (110×100×100)/10×10×10 = 1000   Answer is 1000.
Answer: E
If 45-[28-{37-(15-*)}]= 56, then * is equal to:	Pick one:
A) -29  B) -19  C) 17  D) 29  E) 39

Solution: 45-[28-{37-(15-*)}]= 56 => 45-[28-{37-15+*}]=56   45-[28-37+15-*]=56 => 45[43-37-*]=56   45-[6-*]=56 => 45-6+*=56   39+*=56 => *=56-39= 
56-39 = 17
17   ANSWER:17
Answer: C
If a trader bought 9 balls per rupee and sells at the rate of 8 balls per rupee, what is the percentage profit or loss? Choices.
A) 12.5 % B) 11.5 % C) 23.5 % D) 23.5 %x E) 14.5 %

Solution: Let he total number of oranges bought by the shopkeeper be 12.   If he buys 9 a rupee, his CP = 8   He selling at 8 a rupee, his SP = 9   Profit = SP - CP = 9 - 8= 
9 - 8 = 1
1   Profit Percent= 1/8 * 100= 
1/8 * 100 = 25/2 = around 12.5
12.5 %   12.5 %nswer: 12.5 %
Answer: A
A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 15 days respectively. They worked together for five days and then C completed the remaining work all alone. If $900 was the net sum to be paid for the entire work, what was the average daily wage of B?
Choices.
A) $144	B) $90	C) $60	D) $54	E) $48

Solution: The correct answer is $60.
Answer: C
In how many ways can the letters of the word ABEIX be arranged in a row so that the vowels appear in alphabetic order?	Choose the correct answer
A) 20  B) 30  C) 40  D) 50  E) 60

Solution: three letters can be arranged in 3! ways.   only one combination AEI is required.   5 letters can be arranged in 5! ways.   thus 5!/ 3! * 1 = 20.   20
Answer: A
A circle has 29 points arranged in a clock wise manner from o to 28. A bug moves clockwise manner from 0 to 28. A bug moves clockwise on the circle according to following rule. If it is at a point i on the circle, it moves clockwise in 1 sec by (1 + r) places, where r is the remainder (possibly 0) when i is divided by 11. If it starts in 23rd position, at what position will it be after 2012 sec. Options.
A) 10th
B) 15th
C) 20th
D) 25th
E) 28th

Solution: After 1st second, it moves 1 + (23/11)r = 1 + 1= 
1 + 1 = 2
2, So 25th position   After 2nd second, it moves 1 + 25/11= 1 + 3= 
1 + 3 = 4
4, So 29th position= 0   After 3rd second, it moves  1 + 0/11= 
 1 + 0/11 = 1
1 + 0= 
1 + 0 = 1
1, So 1st position   After 4th second, it moves 1 + 1= 3rd position   after 5th, 1 + 3/11 = 4 So 7th   After 6th, 1 + 7/11 = 8 so 15th   After 7th, 1 + 15/11 = 5 so 20th   After 8th, 1 + 20/11 = 10th, So 30th = 1st   So it is on 1st after every 3 + 5n seconds. So it is on 1st position after 2008 seconds (3 + 5 x 401) So on 20th after 2012 position.   ANSWER:20th
Answer: C
For how many unique pairs of nonnegative integers {a, b} is the equation a^2 - b^2 = 235 true?
Choose the correct choice from the following choices: A) 1 B) 2 C) 5 D) 7 E) 9

Solution: Answer 2   (a+b)(a-b)=235   2cases For (a+b), (a-b)   235, 1   47, 5   Answer 2
Answer: B
A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make? Options.
A) 22 B) 27 C) 40 D) 26 E) 11

Solution: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150   Profit(%) = (31150 - 22250)/22250 * 100= 
(31150 - 22250)/22250 * 100 = 40
40%.Answer:40
Answer: C
Three pipes of same capacity can fill a tank in 12 hours. If there are only two pipes of same capacity, the tank can be filled in?
Choose the correct choice from the following:
A) 18 B) 8 C) 12 D) 6 E) 4

Solution: The part of the tank filled by three pipes in one hour   = 1/12   => The part of the tank filled by two pipes in 1 hour   = 2/3 * 1/12 = 1/18.   The tank can be filled in 18 hours.   18nswer:18
Answer: A
A certain jeans in a shop was marked down 30% the first week and another 20% the next week. What percent of the regular price was the final cost of the jeans after the two markdowns?
Choose one
A) 30%  B) 36%  C) 40%  D) 56%  E) 60%

Solution: If the price of the jeans is 100, and it is marked down by 30% and 20% respectively or charged 70% of the price first and 80% of the price of reduced price, the final price is :-   100*70*80/10000= 
100*70*80/10000 = 56
56   56% is the final price of old price.   56% is the answer
Answer: D
The average (arithmetic mean) of 20, 40, and 60 is 5 more than the average of 20, 60, and what number? Select:
A) 25	B) 30	C) 35	D) 40	E) 45

Solution: a1 = 120/3= 
120/3 = 40
40   a2= a1 -5 = 35   sum of second list = 35*3= 
35*3 = 105
105   therefore the number= 105 -80= 
105 -80 = 25
25   25
Answer: A
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? Choose the correct choice from the following answers.
A) 12 days
B) 15 days
C) 16 days
D) 18 days
E) 22 days

Solution: A's 2 day's work = (1/20 × 2) = 1/10	.   (A + B + C)'s 1 day's work = (1/20 + 1/30 + 1/60) = 1/10.   Work done in 3 days = (1/10 + 1/10) = 1/5.   Now,	1/5	work is done in 3 days.   Therefore, Whole work will be done in (3 x 5) = 15 days.   CORRECT ANSWER: "15 days".
Answer: B
The number of sequences in which 8 players can throw a ball, so that the youngest player may not be the last is ?  Choose one.
A) 43280  B) 43280  C) 35280  D) 32786  E) 36124

Solution: x Not younger   The last ball can be thrown by any of the remaining 8 players. The first 6 players can throw the ball in 7P7 ways.   The required number of ways = 7(7!)   = 35280   Answer:35280
Answer: C
A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200. If a store employee applied the 10 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder?  Choose the correct choice from the following choices.
A) $198  B) $216  C) $220  D) $230  E) $240

Solution: Wholesale cost of video recorder = 200 $   Video recorder was priced at 20 percent above 200 = 240 $   % discount given by store employee = 10   Employee paid = .9 * 240= 
.9 * 240 = 216
216 $   Answer $216
Answer: B
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 37, the how old is B?	Choose the correct answer:
A) 7 B) 9 C) 8 D) 14 E) 10

Solution: Explanation:   Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.   (2x + 2) + 2x + x = 37   ⇒ 5x = 35   ⇒ x = 7.   Hence, B's age = 2x = 14 years.   Answer: 14
Answer: D
The mean of 40 observations was 100. It was found later that an observation 50 was wrongly taken as 75 The corrected new mean is  Choices
A) 125.8
B) 102.8
C) 99.375
D) 100.52
E) 122

Solution: Explanation:   Correct Sum = (100 * 40 + 50 - 75)= 
(100 * 40 + 50 - 75) = 3_975
3975.   99.375orrect mean= = 3975/40= 
3975/40 = 795/8 = around 99.375
99.375   Answer: 99.375
Answer: C
A and B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 4000 as profit, what is their total profit?  Choose the most appropriate option
A) 27000	B) 25000	C) 29000	D) 28000	E) 26000

Solution: Suppose B's investment =x.   Then A's investment =3x   Suppose B's period of investment =y   then A's period of investment =2y   A : B =3x×2y:xy=6:1   Total profit ×1/7=4000   => Total profit =4000×7   =28000   Answer is 28000.
Answer: D
The area of a rectangular plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot?
Choose the correct answer:
A) 18m
B) 19m
C) 17m
D) 16m
E) 20m

Solution: length =115% of breadth.   length×breadth =460 m2   ⇒ 115% of breadth×breadth =460 m2   ⇒ 115100× breadth×breadth =460 m2   ⇒ breadth×breadth =400 m2   ⇒ breadth =20 m   Answer is 20m.
Answer: E
Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q and R are to be integers that satisfy the inequalities -4<=x<=5 and 6<=y<=16. How many different triangles with these properties could be constructed?  Choose the correct choice from the following options
A) 110  B) 1100  C) 9900  D) 10000  E) 12100

Solution: We know that P,Q, R can only lie on a grid 10x11   Let's start by fixing P' x-coordinate: we have 10 possible places for it   Then we choose x-coordinate for R: since PR || x-axis, R's x-coordinate can not coincide with P's x-coord, so we have only 9 possible choices left.   Then, we fix P's (and R's too) y-coordinate: 11 possible choices.   Finally, after we fixed P and R, Q's x-coordinate must be the same as P's (because P is the right angle and PR || x-axis), so the only choice is for y-coordinate, and we have 10 possible choices left.   So, total number of different triangles: 10*9*11*10=9,900   ANSWER:9900
Answer: C
A person's present age is two-fifth of the age of his father. After 8years, he will be one - half of the age of his father. How old is the father at present ?	Answers:
A) A)40  B) B)48  C) C)32  D) D)45  E) E)28

Solution: Let the father's present age be x years   Then the person's present age = 2x/5   (2x/5)+8 = 1/2(x+8)   2(2x+40) = 5 (x+8)   x = 40   40nswer is 40
Answer: A
Each of eight different locks has a matching key. The keys are randomly reassigned to the locks. What is the probability that exactly two of the keys fit the locks to which they are reassigned?  Choose the correct choice from the following choices.
A) 1/8 B) 1/6 C) 1/64 D) 3/8 E) 1/2

Solution: I was just going over probability questions.   can some one explain me what's wrong in my approach here.   Probability of choosing one right key out of 8 is 1/8.   Probability of choosing another right key is 1/8.   since the question is asking for 2 right keys , probability is multiplication of both = 1/8 * 1/8 = 1/64.   Ans 1/64
Answer: C
A person purchased a TV set for Rs. 17000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
Choose one:
A) 16.97%
B) 87.97%
C) 33.97%
D) 17.97%
E) 18.97%

Solution: The total CP = Rs. 17000 + Rs. 6250 = Rs. 23250 and SP   = Rs. 31150   Profit(%) = (31150 - 23250)/23250 * 100   = 33.97%   Answer:33.97%
Answer: C
If each edge of a cube is doubled, then its volume :	Choose the correct answer:
A) Becomes 8 times  B) Becomes 9 times  C) is double  D) Becomes 6 times  E) None

Solution: Sol.   Let original edge = a. Then, volume = a³   New edge = 2a. So, new volume = (2a)³ = 8a³   ∴ Volume becomes 8 times   Becomes 8 timesnswer Becomes 8 times
Answer: A
The current birth rate per thousand is 42, where as corresponding death rate is 22 per thousand. The net growth rate in terms of population increase in percent is given by?	Choose the correct choice from the following answers
A) 2.0%
B) 3.2%
C) 3.9%
D) 4%
E) 5.1%

Solution: Net growth on 1000 = 42-22= 
42-22 = 20
20   Net growth on 100= 20*100/1000= 
20*100/1000 = 2
2.0%   2.0%nswer is 2.0%
Answer: A
John have a 630ml mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3? Choose the correct choice from the following answers:
A) 40 ml  B) 60 ml  C) 70 ml  D) 80 ml  E) 90 ml

Solution: concentration of water in mixture1 =29 (since the ratio of milk and water = 7:2) ...(1)   concentration of water in pure water= 1 ...(2)   Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3   => concentration of water in mixture2 =310   By rule of alligation,   concentration of water in mixture1 (29)   concentration of water in pure water (1)   Mean concentration   (310)   1−310=710   310−29=790   => Quantity of mixture1 : Quantity of water   =710:790=110:190=1:19   Given that Quantity of mixture1 = 630 ml   => 630 : Quantity of water =1:19   => Quantity of water =630×19=70 ml   70 ml
Answer: C
Alan has split his savings equally into two accounts. The first one is a simple interest savings account with 22% annual interest and the other is a savings account with r% annual compound interest. If both accounts have the same balance after two years, what is the value of r? Choose the correct choice from the following answers.
A) 11
B) 14.25
C) 18.5
D) 20
E) Cannot be determined

Solution: Let the amounts deposited on both accounts be $100.   Then we'd have that 100+100∗0.22+100∗0.22=100(1+r)2100+100∗0.22+100∗0.22=100(1+r)2 --> 144=100(1+r)2144=100(1+r)2 --> (1+r)2=1.44(1+r)2=1.44 --> 1+r=1.21+r=1.2 --> r=0.2   Answer is 20
Answer: D
A bag contains 8 red and 4 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Choose one:
A) 4/7 B) 2/3 C) 5/8 D) 1/4 E) 5/7

Solution: Total number of balls = 8+4= 
8+4 = 12
12   number of white balls= 8   Probability = 8/12 = 2/3   Answer is 2/3
Answer: B
A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained? Choose one:	A) 2298	B) 1000	C) 2888	D) 2771	E) 9911

Solution: Along one edge, the number of small cubes that can be cut   = 100/10= 
100/10 = 10
10   Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut= 10 * 10 * 10= 
10 * 10 * 10 = 1_000
1000   Answer:1000
Answer: B
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 each of them pick? Choose the correct answer
A) 6	B) 7	C) 1	D) 8	E) 9

Solution: Let xx be the amount Peter picked. Then Mary and Lucy picked 2x2x and x+2x+2, respectively. So   x+2x+x+2=26x+2x+x+2=26   4x=244x=24   x=6x=6   Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively.   6nswer:6
Answer: A
How many three digit numbers W are divisible by 78 or 91? Select
A) 17 B) 19 C) 20 D) 21 E) 22

Solution: The answer will be 19.   Explanation:   78= 2*3*13 now multiples of 78, 156 ....780, now   1000-780= 
  1000-780 = 220
220 only two more muktiples of 78 can exists. So total number of 3 digit Multiples of 78 are   9+2= 
  9+2 = 11
11   91= 13*7--Total number of three digit multiples --9   No remember we have a common multiples as well-- 13*7*6=91*6= 
91*6 = 546
546   So total number of multiples W--11+9 -1= 
--11+9 -1 = 19
19.   Hence Answer is 19.19
Answer: B
A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:	Choose the correct choice from the following choices
A) 22	B) 24	C) 26	D) 23	E) 21

Solution: Let the number of hens be x and the number of cows be y.   Then, x + y = 48 .... (i)   and 2x + 4y = 140 x + 2y = 70 .... (ii)   Solving (i) and (ii) we get: x = 26, y = 22.   The required answer = 26.   Answer is 26.
Answer: C
When divided by 5, x has a remainder of 4 and y has a remainder of 2. Which of the following could be the remainder when x + y is divided by 10?  Choose the most appropriate option.
A) 6  B) 7  C) 8  D) 9  E) 0

Solution: x = 5k+4 and y = 5j+2   x+y = 5(j+k) + 6   When divided by 10, the remainder is either 6 or 1.   The answer is 6.
Answer: A
The difference between two numbers is 1356. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is
Choose the most appropriate option.
A) 240  B) 270  C) 295  D) 360  E) 340

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Smaller number = 270   ANSWER:270
Answer: B
A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently eight spaces behind player B, what is the probability that player B will be frozen after player A rolls?  Pick.
A) 1/12 B) 5/36 C) 1/6 D) 1/3 E) 17/36

Solution: no. of possible outcomes = 6*6= 
6*6 = 36
36   no. of outcomes that result a total of 8 (as A is 8 spaces behind 5/36)= 5 ( (2,6), (3,5), (4,4), (5,3), (6,2) )   So, the probability = 5/36 (Option 5/36)
Answer: B
A single discount equivalent to the discount series of 20%, 10% and 5% is?  Choose the correct choice: A) 31.5 B) 31.8 C) 31.6 D) 31.3 E) 31.1

Solution: 100*(80/100)*(90/100)*(95/100)= 
100*(80/100)*(90/100)*(95/100) = 342/5 = around 68.4
68.4   100 - 68.4= 
100 - 68.4 = 31.6
31.6   Answer:31.6
Answer: C
A zoo has an average of 500 visitors on sundays and 200 on other days . The avearge number of visitors per day in a month of 30 days beginning with a monday is? Choices:
A) 120
B) 150
C) 200
D) 210
E) 240

Solution: Since the month begin with monday, so there will be 4 sundays in the month   Required average = (500*4 + 200*26)/30= 
(500*4 + 200*26)/30 = 240
240   Answer is 240
Answer: E
For four days of work, a clerk had daily earnings of $120, $110, $120, and $120 respectively. In which of the following intervals does the standard deviation of the daily earnings lie? Choose the correct choice from the following answers.
A) Between $50 and $100 B) Between $20 and $40 C) Between $20 and $60 D) Between $0 and $10 E) Between $70 and $100

Solution: The standard deviation is between 0 and 10.   The reason is that none of the numbers in the set is further away from the mean than 10(or rather Abs(110-(120*3+110)/4)). I am not fully sure how to calculate the standard deviation(I simply remember that there were some formula for calculating the average of the squared distances from the mean for all items in the set from statistics classes - variation), but I believe this will suffice for any GMAT question related to standard deviation.   Answer : Between $0 and $10
Answer: D
A sum of money lent out at S.I. amounts to Rs. 660 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is? Choose the correct answer
A) s.440 B) s. 500 C) s. 540 D) s. 740 E) s. 516

Solution: S.I for 5 years = (1020 - 660) = Rs. 360.   S.I. for 2 years = 360/5 * 2 = Rs. 144.   Principal = (660 - 144) = Rs. 516.   ANSWs. 516R:s. 516
Answer: E
In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 9720 votes were polled, then how many valid votes did B get? Choose the most appropriate option:  A) 1888  B) 2999  C) 3159  D) 2777  E) 2991

Solution: Let the total number of votes polled in the election be 100k.   Number of valid votes = 100k - 20% (100k) = 80k   Let the number of votes polled in favour of A and B be a and b respectively.   a - b = 15% (100k) => a = b + 15k   => a + b = b + 15k + b   Now, 2b + 15k = 80k and hence b = 32.5k   It is given that 100k = 9720   32.5k = 32.5k/100k * 9720 = 3159   The number of valid votes polled in favour of B is 3159.   Answer: 315932.5 /100  * 9720= 
32.5 /100  * 9720 = 3_159
3159   The number of valid votes polled in favour of B is 3159.   Answer: 3159
Answer: C
5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.180 only. Menâ€™s wages are?  Choose the most appropriate option: A) 6Rs B) 2Rs C) 4Rs D) 9Rs E) 12Rs

Solution: 5M = xW = 8B   5M + xW + 8B ----- 180 Rs.   5M + 5M + 5M ----- 180 Rs.   15M ------ 180 Rs. => 1M = 12Rs.   Answer: 12Rs
Answer: E