MU-NLPC/Calc-aqua_rat huggingface dataset:
Which of the following triples of numbers have the same standard deviation as the numbers x, y and z?
I. x-2, y-2, z-2
II. 0,x-y, z-y
III.x-4, y+5, z-1	Pick one:  A) I only  B) II only  C) I and III only  D) II and I only  E) I, II, and III

Solution: If we add or subtract a constant to each term in a set the standard deviation will not change.   Set {x-2, y-2, z-2} is obtained by subtracting 2 from each term of {x, y, z}.   Set {0, x-y, z-y} is obtained by subtracting s from each term of {x, y, z}.   Set {x-4, y+5, z-1} is totally different from {x, y, z}.   Thus the answer is I and II only.   Answer: II and I only.
Answer: D
The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:  Pick one:
A) 3500
B) 4000
C) 4050
D) 5000
E) 5500

Solution: Explanation:   Let P, Q and R represent their respective monthly incomes. Then, we have:   P + Q = (5050 x 2) = 10100 .... (i)   Q + R = (6250 x 2) = 12500 .... (ii)   P + R = (5200 x 2) = 10400 .... (iii)   Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)   Subtracting (ii) from (iv), we get P = 4000.   P's monthly income = Rs. 4000.   ANSWER IS 4000
Answer: B
A man swims downstream 96 km and upstream 64 km taking 4 hours each time; what is the speed of the current?	Choose the correct choice from the following choices
A) 6
B) 4
C) 2
D) 8
E) 5

Solution: 96 --- 4 DS = 24   ? ---- 1   64 ---- 4 US = 16   ? ---- 1 S = ?   S = (24 - 16)/2= 
(24 - 16)/2 = 4
4   Answer: 4
Answer: B
Five gallons of a solution of vinegar and water with 8% vinegar is to be diluted with water to make a 4% vinegar mixture. How many gallons of water should be added?
Choices.
A) 10  B) 5  C) 4  D) 2  E) 1

Solution: In these types of mixture questions, if the answers are numbers, then it's likely that you can TEST THE ANSWERS to quickly get to the solution. Here's how:   First, we need to know about the original mixture of vinegar and water. We're told that a 5 gallon mixture is 8% vinegar....   (5 gallons)(.08) = 0.4 gallons vinegar   The rest = 4.6 gallons water   We're told to ADD WATER until the mixture goes from 8% vinegar to 4% vinegar.   Since the answer choices are numbers, we know that one of them will lead us to a 4% mix when added to the current mix. Changing 8% to 4% means that we have to add a significant amount of water (relative to what we started with), so I would TEST one of the bigger numbers first.   Let's TEST B   If 5 gallons of water were added, then we'd have....   0.4 gallons vinegar   9.6 gallons of water   0.4/10 = 4% vinegar. This is EXACTLY what we're looking for, so B MUST be the answer.   Final Answer:   5
Answer: B
A company has a job to prepare certain number of cans and there are three machines A, B and C for this job. A can complete the job in 2 days, B can complete the job in 8 days and C can complete the job in 10 days. How many days the company will it take to complete the job if all the machines are used simultaneously?
Choose one.
A) 4/27 days  B) 40/29 days  C) 3/4 days  D) 1/2 days  E) 1/4 days

Solution: Let the total number of cans to be prepared be 40.   The number of cans prepared by A in 1 day = 20.   The number of cans prepared by B in 1 day = 5.   The number of cans prepared by C in 1 day = 4.   Thus, the total number of cans that can be prepared by all the machines working simultaneously in a single day = 29.   Therefore, the number of days taken to complete the whole work = 40/29 days.   ANSWER:40/29 days
Answer: B
Three hoses work to fill a tub at at different rate. Hose E and B, working together, can fill the tub in 6/5 of an hour. Hoses E and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub?
Edited for accurate solution	Choose the correct option:
A) 3/10 B) 2/5 C) 1/2 D) 1 E) 6/5

Solution: Convert the given time to rate and you will be able to add it up.   Total Rate of E and B = Rate of E + Rate of B = 1/(6/5) = 5/6   Total Rate of E and C = Rate of E + Rate of C = 1/(3/2) = 2/3   Total Rate of B and C = Rate of B + Rate of C = 1/2   Adding all three,   2(Rate of E + Rate of B + Rate of C) = 5/6 + 2/3 + 1/2= 
5/6 + 2/3 + 1/2 = 2
2   Rate of E + Rate of B + Rate of C= 1 tub/hour   Time taken by all three together to fill up the tub is 1 hour=1
Answer: D
A team won 50 percent of its first 60 games in a particular season, and 80 percent of its remaining games. If the team won a total of 60 percent of its games that season, what was the total number of games that the team played?
Choose the correct choice from the following options
A) 180	B) 120	C) 90	D) 85	E) 30

Solution: Won 50 % of the first 60 games means it won 30 games.   Let the number of remaining games played be x. Hence the number of remaining games won is 0.8x.   So the equation for winning can be written as:   30+0.8x= 0.6(60+x)   x=30   Total games played= 60+30= 
60+30 = 90
90   Option 90.
Answer: C
If the price of an item is decreased by 30% and then increased by 30%, the net effect on the price of the item is	Answers:
A) A decrease of 99%
B) No change
C) A decrease of 1%
D) A decrease of 9%
E) none

Solution: initially assume 100 rupees   30% discount in 100 gives price of 70 rupees   then 30% raise in 70 is only 21 rupees.   therefore total price =91 rupees.   hence 9% is the loss   ANSWER:A decrease of 9%
Answer: D
In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?	Choose the correct choice from the following answers.
A) 11  B) 66  C) 19  D) 10  E) 77

Solution: Convert kmph to mps. 36 kmph = 36 * 5/18= 
36 * 5/18 = 10
10 mps.   The distance to be covered is equal to the length of the train.   Required time t= d/s = 100/10= 
100/10 = 10
10 sec.Answer: 10
Answer: D
Let Q represent a set of two distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be? Choose the correct option:
A) 1
B) 5
C) 3
D) 2
E) 7

Solution: Q = p1+p2= even (and all primes are distinct)   if the least prime is 2 then we have sum of Q =even.   Ans. D. 2
Answer: D
Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A ?  Answers:
A) Rs. 13, Rs. 19 B) Rs. 13, Rs. 17 C) Rs. 13, Rs. 12 D) Rs. 13, Rs. 11 E) Rs. 13, Rs. 13

Solution: Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A.   Then, 2x + 3y = 77 ...(i) and   3x + 2y = 73 ...(ii)   Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y = 85 or y = 17.   Answer: Rs. 13, Rs. 17
Answer: B
A can run 128 metre in 28 seconds and B in 32 seconds. By what distance A beat B?	Options:
A) 38 metre	B) 28 metre	C) 23 metre	D) 16 metre	E) 28 metre

Solution: Clearly, A beats B by 4 seconds   Now find out how much B will run in these 4 seconds   Speed of B = 16 metreistance/Time taken by B=128/32= 
128/32 = 4
4 m/s   16 metreistance covered by B in 4 seconds= Speed Ã— time =4Ã—4=16 metre   i.e., A beat B by 16 metre   Answer is 16 metre
Answer: D
A sum of Rs. 2769 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?	Select the correct option
A) 1642	B) 1640	C) 1632	D) 2789	E) 1704

Solution: (x*8*3)/100 = ((2769 - x)*3*5)/100   24x/100 = 41535/100 - 15x/100   39x = 41535 => x = 1065   Second sum = 2769 – 1065   =1704   Answer:1704
Answer: E
The length of a rectangle is twice its breadth if its length is decreased by 5cm and breadth is increased by 5cm, the area of the rectangle is increased by 75 sq cm. Find the length of the rectangle.	Choose the correct choice: A) 22 B) 40 C) 38 D) 278 E) 29

Solution: Explanation:   let length = 2x and breadth = x then   (2x-5) (x+5) = (2x * x)+75   5x-25 = 75 => x=20   length of the rectangle = 40 cm   Answer: 40) 40
Answer: B
An investor receives a total combined return of 7% on his two different investments. On his $20,000 investment he receives a return of 6%. What is the return on his $20,000 investment?	Choose the correct choice from the following options.
A) 7.25%  B) 4.9%  C) 8%  D) 8.5%  E) 9%

Solution: 0.06 * 20000 + 20000x = 0.07(40000)   solving for x give x = 8%   option 8%
Answer: C
In Company B, the total monthly payroll for the 20 factory workers is $36,000 and the total monthly payroll for the 50 office workers is $110,000. By how much does the average (arithmetic mean) monthly salary of an office worker exceed that of a factory worker in this company?  Answers
A) $400	B) $450	C) $500	D) $550	E) $600

Solution: The average monthly salary of a factory worker is: $36,000 / 20 = $1800.   The average monthly salary of an office worker is: $110,000 / 50 = $2200.   The difference in average salary is: $2200 - $1800 = $400.   The answer is $400.  2200 -  1800= 
  2200 -  1800 = 400
$400.   The answer is $400.
Answer: A
An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2500, what will be the difference between Q and R's share?	Choose the correct choice from the following answers:
A) 2225
B) 2325
C) 2425
D) 2625
E) 2525

Solution: 4 --- 2100   5 --- ? => 2625   ANSWER:2625
Answer: D
Find the invalid no.from the following series 13, 18, 25, 30, 37, 40 Pick one:
A) 13  B) 18  C) 40  D) 37  E) 40

Solution: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.   40
Answer: C
A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 17 months? Choose the correct choice from the following answers.
A) 17:11  B) 18:15  C) 18:19  D) 18:121  E) 18:112

Solution: A invests Rs.8000 for 17 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.   17:11 : B   8000*17 : (8000*4) + (4000*14)   136000 : 88000   17:11:B = 17:11.17:11nswer:17:11
Answer: A
A boatman goes 3 km against the current of the stream in 3 hour and goes 1 km along the current in 30 minutes. How long will it take to go 3 km in stationary water? Choices:
A) 5 hours
B) 4 hours
C) 3 hours
D) 2 hours
E) 1 hours

Solution: Explanation:   Speed upstream = 3/3= 
3/3 = 1
1 km/hr   Speed downstream= 1/(30/60)= 
1/(30/60) = 2
2 km/hr   Speed in still water= 1/2(2+1)= 3/2 km/hr   Time taken to travel 3 km in still water = 3/(3/2) = 6/3= 
6/3 = 2
2 hours   Answer: Option 2 hours
Answer: D
What is the ratio between perimeters of two squares one having 5 times the diagonal then the other?  Choices:
A) 3: 8  B) 3: 6  C) 3: 7  D) 5: 1  E) 3: 3

Solution: d = 5d d = d   a√2 = 5d a√2 = d   a = 5d/√2 a = d/√2 => 5: 1   Answer:5: 1
Answer: D
What is the rate percent when the simple interest on Rs.600 amount to Rs.160 in 4 Years? Choose the correct choice from the following answers
A) 6.66%  B) 7.66%  C) 6.06%  D) 6.16%  E) 8.66%

Solution: 160 = (600*4*R)/100   R = 6.66%   6.66%NSWER:6.66%
Answer: A
A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 30% of the original number. What percent of the red candies remain? Select the correct option: A) 22.5% B) 31.5% C) 37.5% D) 42.5% E) 46.5%

Solution: Let x be the original number of each color so there are a total of 5x candies.   Kaz eats all of the green candies and half of the orange ones.   There are 0 green candies and 0.5x orange candies remaining.   He eats half of the remaining pieces of each color.   There are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies.   He eats red and yellow candies in equal proportions.   orange+blue+red+yellow = 0.75x + red + yellow = 1.5x   red + yellow = 0.75x   red = 0.375x, since red = yellow.   The answer is 37.5%.
Answer: C
Consider two postmen A and B respectively. A is young and can deliver 20 parcels in 3 hours while B is older than A and can deliver only 15 parcels in 4 hours. If the total number of parcels to deliver is 60, how long they will take working together.	Options
A) 144/22	B) 144/25	C) 144/21	D) 144/221	E) 144/219

Solution: Work done by 1st in 1 hour = 20/3 parcels / hour , Work done by 2nd om 1 hour = 15/4 parcels / hour   Total work done by both together per hour = 20/3 + 15/4 = 125/12 parcels/hour   Time to do 60 unit work (ie, parcels)= 60 ÷ 125/12 = 60 × 12/125 = 144/25 hours.   Answer:144/25
Answer: B
In what time will a train 175 m long cross an electric pole, it its speed be 180 km/hr?	Choose the correct option:
A) 7.5 B) 6.5 C) 5.5 D) 4.5 E) 3.5

Solution: Speed = 180 * 5/18= 
180 * 5/18 = 50
50 m/sec   Time taken= 175/50= 
175/50 = 7/2 = around 3.5
3.5 sec.   Answer: 3.5
Answer: E
Twenty five percent of Country Y's yearly exports come from fruit exports. One-fifth of all fruit exports from Country Y are orange exports. If country Y generates $10 million from its orange exports, how much money does it generate from its yearly total of exports?
Choose the correct choice from the following choices
A) $2125m	B) $25m	C) $200m	D) $300m	E) $153m

Solution: 25/100*1/5*(total) = 10   1/20*(total) = 10   (total) = 10*20= 
10*20 = 200
200   Answer: $200m
Answer: C
On planet korba, a solar blast has melted the ice caps on its equator. 9 years after the ice melts, tiny planetoids called echina start growing on the rocks. Echina grows in the form of circle, and the relationship between the diameter of this circle and the age of echina is given by the formula d = 4*[sqrt(t-9)] for t>9, where d represents the diameter in mm and t the number of years since the solar blast. Jagan recorded the radius of some echina at a particular spot as 7mm. How many years back did the solar blast occur?
Choose the correct choice from the following answers:
A) 17	B) 21.25	C) 12.25	D) 14.05	E) 18

Solution: radius=7mm.   So dia= 14mm.   putting D=14 in equation we can easily calculate   t=21.25   ANSWER:21.25
Answer: B
Point (m,n) is on the circle represented by m^2+n^2=10, and m, n are integers. How many such points are possible?	Choose the correct choice
A) 0 B) 2 C) 4 D) 6 E) 8

Solution: m^2+n^2=10 and m, n are integers means that 10 is the sum of two perfect squares.   10 is the sum of only one pair of perfect squares 1 and 9.   So, there can be 8 such points, 4 in each quadrant:   (1, 3);   (1, -3);   (-1, 3);   (-1, -3);   (3, 1);   (3, -1);   (-3, 1);   (-3, -1).   Answer: 8.
Answer: E
In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is
Pick one.
A) 50 liters	B) 55 liters	C) 60 liters	D) 70 liters	E) 75 liters

Solution: Quantity of milk = 60 x 2 litres = 40 litres.   3   Quantity of water in it = (60- 40)= 
(60- 40) = 20
20 litres.   New ratio= 1 : 2   Let quantity of water to be added further be x litres.   Then, milk : water = 40 .   20 + x   Now, 40 = 1   20 + x 2   20 + x = 80   x = 60.   Quantity of water to be added = 60 liters.   60 liters
Answer: C
In a school 10% of the boys are same in number as 1/4th of the girls. what is the ratio of boys to the girls in the school?	Choose the correct option.
A) 5:2 B) 2:3 C) 1:4 D) 3:7 E) 2:5

Solution: 10% of B = 1/4 G   10B/100 = G/4   B = 5G/2   B/G = 5/2   B:G = 5:2   5:2nswer is 5:2
Answer: A
The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?  Choose the correct choice from the following:
A) 31 m
B) 32 m
C) 16 m
D) 20 m
E) 22 m

Solution: A/8 = 8 * 8 => A = 8 * 8 * 8   x * 2x = 8 * 8 * 8   x = 16 => 2x = 32   ANSWER:32 m
Answer: B
Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 5 inches by 24 inches and Jordan's rectangle is 8 inches long, how wide is Jordan's rectangle, in inches? Pick one:  A) 25  B) 23  C) 22  D) 15  E) 18

Solution: Area of Carol's rectangle = 24*5= 
24*5 = 120
120   Let width of Jordan's rectangle= w   Since , the areas are equal   8w = 120   =>w = 15   Answer 15
Answer: D
At a meeting of the 3 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 3 Chiefs of Staff be seated around a circular table?	Choose the correct choice from the following answers
A) 120	B) 480	C) 960	D) 2520	E) 5040

Solution: Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer C (960), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect?960
Answer: C
If in a 20 over cricket match, there were no wide balls, no wides, no extras and no overthrows.
What is the maximum number of runs that a batsman can score in an ideal case scenario?
Choose the correct choice from the following choices: A) 663 B) 720 C) 625 D) 640 E) None

Solution: Solution:   663   Explanation:   For an ideal case, the batsman will hit a six on each ball. But if he hits six on the last ball of the over, the strike will change in the next over. Thus, the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over. Thus the total runs that he can score in each over:    6 * 5 + 3= 
 6 * 5 + 3 = 33
33   But this will have to go like it only till the 19th over. In the last over, he can hit a six in the last ball as well as that will be the last ball of the match.   Thus runs for the last over will be 6 * 6= 
6 * 6 = 36
36.   Hence the maximum runs= 33 * 19 + 36= 
33 * 19 + 36 = 663
663   663nswer 663
Answer: A
Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is  Options:	A) 42	B) 36	C) 28	D) 20	E) 15

Solution: Explanation:   Distance covered = 120+120= 
120+120 = 240
240 m   Time= 12 s   Let the speed of each train = v. Then relative speed = v + v = 2v   2v = distance/time = 240/12= 
240/12 = 20
20 m/s   Speed of each train= v = 20/2= 
20/2 = 10
10 m/s= 10 × 36/10 km/hr = 36 km/hr.   Answer: 36
Answer: B
In a hostel of 12 boys and some girls, an average consumption of rice per month is 12 kg, while the Average consumption for boys is 16 kg per head and for girls 8 kg per head. The number of girls in The hostel? Choose the correct answer: A) 12 B) 13 C) 14 D) 15 E) 16

Solution: Explanation:   Number of girls — G   (12+G) × 12 = (12 × 16)+(8 × G)   144 + 12G = 192 + 8G   12G − 8G = 192 − 144   4G = 48   G = 12.   12nswer 12
Answer: A
The speed of a boat in still water is 12 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 18 minutes is  Choose the correct answer:
A) 1.6 km B) 2 km C) 3.6 km D) 4.8 km E) None of these

Solution: Explanation:   Speed downstreams	=(12 + 4)= 
(12 + 4) = 16
16 kmph.   4.8 kmistance travelled= (16 x 18/60)km   = 4.8km   Option 4.8 km
Answer: D
How many digits are in the number 50^8 × 8^3 × 11^2 x 10^6?
Pick one: A) 22 B) 20 C) 19 D) 18 E) 17

Solution: Whenever you are asked to find the number of digits, try to bring the number in multiples of 10. This way, we can wasily calculate the umber of 0's through the powers of 10   50^8 × 8^3 × 11^2 x 10^6 = (5^2*2)^8*2^9*11^2 x 10^6 = 5^16*2^17*11^2 x 10 ^6= 2*11^2*10^16 x 10^6= 242*10^22   Hence we would have 16 trailing 0's and the three digits from 242   Total digits = 3 + 22= 
3 + 22 = 25
25   Correct Option: 17
Answer: E
If dy > 0 and yz < 0, which of the following must be negative:	Choose the correct choice from the following answers:
A) dyz B) dy(z^2) C) d(y^2)z D) x(y^2)(z^2) E) (x^2)(y^2)(z^2)

Solution: dy > 0 means that dy is positive.   yz < 0 means that yz is negative.   d(y^2)z = (dy)(yz) = positive*negative = negative. Thus option d(y^2)z is always negative.
Answer: C
If the cost price of 11 pens is equal to the selling price of 10 pens, the gain percent is:  Answers:
A) 10%  B) 26%  C) 50%  D) 80%  E) 34%

Solution: Solution :   Let cost price of the price be Rs.1   10 pens C.P. = 10   11 pens S.P. = 11   Gain = 1/10*100= 
1/10*100 = 10
10 %   10%nswer : 10%
Answer: A
By walking at 3/4th of his usual speed, a man reaches office 20 minutes later than usual. What is his usual time?
Choose the correct option
A) 40min	B) 50min	C) 65min	D) 60min	E) 70min

Solution: let T be the usual time.   time spent=4T/3   therefore, 4T/3=T+20   4T=3T+60...therefor T=60min   ANSWER:60min
Answer: D
Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?  Choices
A) 6400 B) 7300 C) 6438 D) 6439 E) 9473

Solution: Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x).   Then, x x 14 x 2	/100	+ (13900 - x) x 11 x 2	/100	= 3508   28x - 22x = 350800 - (13900 x 22)   6x = 45000   x = 7500.   So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.   6400nswer:6400
Answer: A
The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
Options:	A) 3.5	B) 3.9	C) 4.2	D) 4.3	E) 4.6

Solution: Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]   = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.   Required average = (9.2 / 2) = 4.6.   4.6
Answer: E
The mean daily profit made by a shopkeeper in a month of 30 days was Rs. 350. If the mean profit for the first fifteen days was Rs. 285, then the mean profit for the last 15 days would be
Choices:
A) Rs. 200  B) Rs. 350  C) Rs. 275  D) Rs. 415  E) None of these

Solution: Average would be : 350 = (285 + x)/2   On solving, x = 415.   Answer: Rs. 415
Answer: D
Rajeev,Lakshmi and Muthu enter into partnership. Rajeev invests some money at the beginning, Lakshmi invests double the amount after 6 months, and Muthu invests thrice the amount after 8 months. If the annual gain be Rs.4500. Lakshmi's share is?	Choose the correct choice from the following choices
A) 1000	B) 1500	C) 500	D) 750	E) 1250

Solution: x* 12 : 2x* 6: 3x* 4   1:1:1   1/3 * 4500= 
1/3 * 4500 = 1_500
1500   Answer: 1500
Answer: B
There are 20 girls inhostel whose average age is decreased by 2 months, when one girl 18 yrs is replaced by a new boy.Find the age of new girl.  Choose one
A) 1 year	B) 1 year 2 months	C) 2 year 5 months	D) 3 year	E) None

Solution: Total decrease = 20 * 2= 
20 * 2 = 40
40 month= 3 years 4 month   None)None
Answer: E
The contents of a bag of candy consist of 11 green pieces of candy and 20 blue pieces of candy. How many blue pieces of candy must be eaten so that 55% of the candies in the bag will be green?
Pick:
A) 8
B) 10
C) 11
D) 13
E) 15

Solution: This question is rooted in basic arithmetic. Since the question asks how many marbles need to be removed and the answers ARE numbers, we can TEST THE ANSWERS until we find the one thatfits.   To start, we have a bag of candy....   11 green   20 blue   31 total   We're asked to eat enough blue candies until the green candies make up 55% of the bag....   Right now, green marbles make up 11/31 which equals about 35% of the bag, we need to eat blue candy to achieve green candies making up for 55% of the bag. We can test our answers   Let's TEST B....   IF 10 blue candies were eaten, then we'd have...   11 green candies   10 blue candies   21 total   11/21 is about 52%.   Let's TEST E...   IF 11 blue candies were eaten, then we'd have...   11 green candies   9 blue candies   20 total   11/20 IS 55%, so this MUST be the answer!   Final Answer:   11
Answer: C