MU-NLPC/Calc-aqua_rat huggingface dataset:
A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters. Answers:
A) 20,000 square meters B) 10,000 square meters C) 30,000 square meters D) 40,000 square meters E) 50,000 square meters

Solution: Let us first find the distance d jogged   distance = rate * time = (12 km / hr)* 30 minutes   = (12 km/hr)* 0.5 hr = 6 km   The distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to   6 km / 10 = 0.6 km = 0.6* 1000= 
0.6* 1000 = 600
600 meters   Let L and W be the length and width of the field. The length is twice the width. Hence   L= 2 W   The perimeter is 600 meters and is given by   2 (L + W) = 600   Substitute L by 2 W   2 (2 W + W) = 600   Simplify and solve for W   4 W + 2 W = 600   6 W = 600   W = 100   Find L   L = 2 W = 200   Find the area 20,000 square meters of the rectangle   20,000 square meters = L * W = 200 * 100 = 20,000 square meters correct answer 20,000 square meters
Answer: A
Integer X represents the product of all integers between 1 to 26 (inclusive). The smallest prime factor of (x+1) must be	Pick
A) Between 1 to 10 B) Between 11 to 15 C) Between 15 to 20 D) Between 20 to 26 E) Greater than 26

Solution: Answer = E = Greater than 26   This problem is asking smallest prime factor of (26!+1)   25! already have there prime factors 2,3,5,7,11,13.......... so on upto 23 (1 cannot be considered prime factor)   Just adding 1 to 26! will remove all the factors stated above;   so the smallest possible prime factor has to be greater than 26   Answer = Greater than 26
Answer: E
If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before? Select
A) 27 2/23 %	B) 33 1/3 %	C) 30%	D) 19%	E) 18%

Solution: Explanation:   100   150   ------   150-------50   100-------? => 331/3%   ANSWER IS 33 1/3 %
Answer: B
A car travels first half distance between two places with a speed of 40 km/hr and rest of the half distance with a speed of 60 km/hr. The average speed of the car is: Choose the correct choice from the following answers:
A) 48 km/hr
B) 42km/hr
C) 40 km/hr
D) 35 km/hr
E) None of these

Solution: Explanation :   Let the total distance covered be S km.   The total time taken is:-   =>S/(2×40)+S/(2×60)=5S/240.   Hence, the average speed = S×240/5S.   =>48 km/hr.   48 km/hrnswer : 48 km/hr
Answer: A
If the time is currently 1:30 pm, what time will it be in exactly 645 hours? Pick:  A) 9:30 am  B) 10:30 am  C) 11:30 am  D) 12:30 pm  E) 1:30 pm

Solution: 645 = 26(24) + 21/24   The time will be 21 hours later than 1:30 pm which is 10:30 am.   The answer is 10:30 am.
Answer: B
Which of the following is satisfied with |x-4|+|x-3|<6?	Choose the most appropriate option
A) 1<x<5 B) 2<x<5 C) 0.5<x<6.5 D) 0.5<x<4 E) 3<x<4

Solution: --> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<6 -> |x-4+x-3|<6 -> |2x-7|<6, -6<2x-7<6, 1<2x<13, 1/2<x<13 -="" 2="">0.5<x<6.5   Therefore, the answer is 0.5<x<6.5.</x<13>
Answer: C
A person spends 40% of his salary on food, 25% on house rent, 15% on entertainment and 5% on conveyance. If his savings at the end of the month is Rs. 1200, then his salary per month in rupees is:	Choose the correct choice from the following:
A) 4000  B) 6000  C) 8000  D) 10000  E) None of these

Solution: Total expenditure = 40 + 25 + 15 + 5= 
40 + 25 + 15 + 5 = 85
85%   Saving= (100 - 85)= 
(100 - 85) = 15
15%   15/100 × Salary= 1200, Salary = 8000 Rs.   Answer:8000.
Answer: C
The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum?
Answers.
A) Rs.17029 B) Rs.17028 C) Rs.17000 D) Rs.17008 E) Rs.17067

Solution: The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year   So rate of the interest = (100 * 1530)/ (5100 * 1)= 
(100 * 1530)/ (5100 * 1) = 30
30% p.a.   So P= (100 * 10200)/ (30 * 2)   = Rs.17000   Answer:Rs.17000
Answer: C
How many different ways can you select a pilot and a co pilot if you have 40 people to choose from?  Options
A) 199 B) 200 C) 398 D) 4950 E) 1560

Solution: You are not just choosing two from 40. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.   So the answer is in a sense (40C2) x 2 = 1560=1560
Answer: E
In a garden, there are 10 rows and 16 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is Choose the correct choice from the following answers:
A) 32 m	B) 22 m	C) 24 m	D) 26 m	E) 28 m

Solution: Explanation:   Each row contains 16 plants.   There are 15 gapes between the two corner trees (15 x 2) metres and 1 metre on each side is left.   Therefore Length = (30 + 2)= 
(30 + 2) = 32
32 m.   32 mnswer: 32 m
Answer: A
Goldenrod and No Hope are in a horse race with 6 contestants. How many different Y arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?	Pick one.
A) 720 B) 360 C) 120 D) 24 E) 21

Solution: no hope finishing before goldenrod= 1/2 of the times   therefore the different Y arrangements are 1/2* 6! = 360 = 360
Answer: B
P and Q started a business investing Rs. 85,000 and Rs. 25,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively? Answers.
A) 17:6	B) 17:0	C) 17:4	D) 17:2	E) 17:5

Solution: P:Q = 85000 : 25000   = 17:5.   Answer: 17:5
Answer: E
Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second year, Alice and Bob each earned a 10 percent profit, Carol lost 60 percent, Dave earned 25 percent in profit, and Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains? Choose one.
A) 93%	B) 97%	C) 100%	D) 107%	E) 120%

Solution: 93%ssume 93%rthur had $100 and gave each of his children $20, then two years   93%=20(1+0.5)(1+0.1)=33   B=20(1+0.5)(1+0.1)=33   C=20(1+0.5)(1-0.6)=12   D=20(1-0.4)(1+0.25)=33   E=0   93%rthur's current money=93%+B+C+D+E=93   93%NSWER:93%
Answer: A
A cube of edge 15 cm is imersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20 cm * 15 cm, find the rise in waer level.
Select the correct option:
A) 11.25 cm.
B) 12.25 cm
C) 13.25 cm
D) 14.25 cm
E) None of these

Solution: Sol. Increase in volume = Volume of the cube = (15 * 15 * 15) cm³.   ∴ Rise in water level = [Volume/Area] = [15 * 15 * 15/20 * 15] cm = 11.25 cm.   11.25 cm.nswer 11.25 cm.
Answer: A
A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 63 km/hr. What is the length of the platform?	Choose the correct choice from the following options:
A) 240 B) 288 C) 277 D) 226 E) 280

Solution: Speed = 63 * 5/18= 
63 * 5/18 = 35/2 = around 17.5
17.5 m/sec.   Length of the train= 17.5 * 20= 
17.5 * 20 = 350
350 m.   Let the length of the platform be x m . Then,   (x + 350)/36= 17.5 => x = 280 m.   Answer: 280
Answer: E
An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 9 o'clock in the morning?	Choose the correct choice from the following answers
A) 120°
B) 60°
C) 30°
D) 90°
E) 150°

Solution: The angle traced by the hour hand in 12 hours is 360°, which is 30° per hour.   In 1 hour, the angle traced by the hour hand is 30°   The answer is 30°.
Answer: C
A train moves past a post and a platform 264 metre long in 8 seconds and 20 seconds respectively. What is the speed of the train?	Choose the correct option:
A) 79.2 km/hr
B) 69 km/hr
C) 74 km/hr
D) 61 km/hr
E) 55 km/hr

Solution: lenghth and speed of the train x m and v m   train crosses the post in 8 sec   x=8v---1)   train crosses the platform in 20 sec   x+264=20v   (2)-(1)+>12v=264   v=264/12= 
264/12 = 22
22m/s   22 * 18/5 km/hr= 79.2km/hr   79.2 km/hrNSWER 79.2 km/hr
Answer: A
Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?  Choose the correct choice:
A) 270 m
B) 278 m
C) 290 m
D) 270 m
E) 220 m

Solution: Relative speed = (72 - 36) * 5/18 = 2 * 5= 
2 * 5 = 10
10 mps.   Distance covered in 27 sec= 27 * 10= 
27 * 10 = 270
270 m.   The length of the faster train= 270 m.270 mnswer: 270 m
Answer: A
In a certain match all the teams were to play with each other. If there are 10 teams, how many matches will have to be played?	Choose the correct choice.
A) 40
B) 45
C) 60
D) 90
E) None of the above

Solution: 10c2   =45   ANSWER:45
Answer: B
If x - 3 > 2 and x - 3 < 7, the value of x must be between which of the following pairs of numbers?
Choose the correct choice from the following options:
A) -3 and 10	B) -3 and 4	C) 2 and 7	D) 3 and 4	E) 5 and 10

Solution: Let’s isolate x in each inequality.   x - 3 > 2   x > 5   Next we simplify x – 3 < 7.   x – 3 < 7   x < 10   We know that x is greater than 5 and less than 10.   The answer is 5 and 10.
Answer: E
Two numbers N and 16 have LCM = 48 and GCF = 4. Find N. Choose the correct choice from the following choices:
A) 35  B) 56  C) 76  D) 87  E) 12

Solution: The product of two integers is equal to the product of their LCM and GCF. Hence.   16* N = 48 * 4   N = 48*4 / 16= 
48*4 / 16 = 12
12 correct answer 12
Answer: E
A man can row with a speed of 30 kmph in still water. If the stream flows at 10 kmph, then the speed in downstream is?
Pick:	A) 40	B) 27	C) 20	D) 99	E) 2

Solution: M = 30   S = 10   DS = 30 + 10= 
30 + 10 = 40
40   40nswer:40
Answer: A
A trader purchases several articles at the rate of 13 for Rs. 10 and sells them at the rate of 10 for Rs. 13. What is his gain/loss?	Choose the correct choice from the following answers.
A) 68 % B) 69 % C) 66 % D) 63 % E) 29 %

Solution: Explanation:   We have, C. P of 13 articles = Rs. 10   & S. P of 10 articles = Rs. 13   S. P of 13 articles = ?   = (13 * 13) / 10= 
(13 * 13) / 10 = 169/10 = around 16.9
16.9   Gain= [(16.9 – 10)/10] * 100 = 69 %   ANSWER: 69 %
Answer: B
Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 30 kg of fresh grapes? Choose the correct choice from the following answers:
A) 3.75 kg
B) 2.4 kg
C) 2.5 kg
D) 10 kg
E) none of these

Solution: The weight of non-water in 30 kg of fresh grapes (which is 100-90= 
100-90 = 10
10% of whole weight) will be the same as the weight of non-water in x kg of dried grapes (which is 100-20= 
100-20 = 80
80% of whole weight), so 30âˆ—0.1=xâˆ—0.8--> x=3.75   3.75 kgnswer: 3.75 kg
Answer: A
Mangoes sell for $3.25 for a piece that costs a total of $2.85 to source. Oranges sell $2.80 for a piece that costs $2.65 to get. If you sell 55,000 mangoes in a month, how many oranges you must sell to make at least as much in total gross profit as for mangoes ?	Options:  A) 7,858  B) 8,301  C) 14,667  D) 63,840  E) 146,667

Solution: Mangoes : Profit/piece = 3.25-2.85= 
3.25-2.85 = 0.4
0.4   : No of pieces= 55,000   : Gross Profit = 55,000*0.4 = 22,000   Oranges : Profit/piece = 0.15   : Gross Profit = 22,000   : No of pieces = 22,000/0.15 = 220,000/1.5 (only closes is 146,667)   Answer 146,667
Answer: E
A boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water? Choose the correct choice from the following:	A) 2.75	B) 5.95	C) 7.95	D) 3.25	E) 4.95

Solution: Speed downstream =22/4= 
22/4 = 11/2 = around 5.5
5.5 kmph   Speed upstream=22/5= 
22/5 = 22/5 = around 4.4
4.4 kmph   Speed of the boat in still water=(5.5+4.4)/2= 
(5.5+4.4)/2 = 4.95
4.95 kmph   Answer: 4.95
Answer: E
The length of a rectangular floor is more than its breadth by 200%. If Rs. 640 is required to paint the floor at the rate of Rs. 5 per sq m, then what would be the length of the floor?	Select the correct option:  A) 19.6m.  B) 20.0m.  C) 19.3m.  D) 18.5m.  E) 18.9m.

Solution: Let the length and the breadth of the floor be l m and b m respectively.   l = b + 200% of b = l + 3= 
+ 3 = 3
3b   Area of the floor= 640/5= 
640/5 = 128
128 sq m   l b= 128 i.e., l * l/3 = 128   l2 = 384 => l = 19.6m.   19.6m.NSWER:19.6m.
Answer: A
If y exceeds x by 15%, then x is less than y by?  Choose the correct choice from the following:
A) 1/12% B) 1/17% C) 1/21% D) 1/22% E) 1/23%

Solution: X=100	y=115   115------15   100-------? => 13 1/23%   Answer:1/23%
Answer: E
A rectangular-shaped carpet that measures x feet by y feet is priced at $8. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
Choose the correct choice from the following answers:
A) 72/(xy)
B) 90xy
C) xy/90
D) xy/10
E) 10/(xy)

Solution: The area of the carpet in feet is xy.   The area in square yards is xy / 9.   The price per square yard is 8 / (xy/9) = 72/(xy).   The answer is 72/(xy).
Answer: A
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 26 years now, the son's age 3 years back was:  Pick:  A) 14 years  B) 19 years  C) 33 years  D) 38 years  E) 10 years

Solution: Let the son's present age be x years. Then, (26 - x) = x   2x = 26   x = 13   Son's age 5 years back (13 - 3)= 
(13 - 3) = 10
10 years.   Answer: 10 years
Answer: E
An aeroplane covers a certain distance at a speed of 240 kmph in 6 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:  Choose the correct choice.
A) 520
B) 620
C) 820
D) 740
E) 864

Solution: Distance = (240 x 6) = 1440 km.   Speed = Distance/Time   Speed = 1440 /(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]   Required speed = (1440x3/5) km/hr = 864 km/hr   Answer 864) 864 Km/hr
Answer: E
In a sample of National college students, 30 percent are third year students and 60 percent are not second-year students. What fraction of those students who are not third-year students are second-year students?	Select the correct option
A) 3/4  B) 2/3  C) 4/7  D) 1/2  E) 3/7

Solution: = 40/70. = 4/7   my answer is 4/7 too
Answer: C
In a class of 250 students, 130 study Spanish and 100 study French. If a student must study at least one of these two languages, what percent of the students study French but NOT Spanish?	Choose the correct choice:
A) 60%  B) 40%  C) 30%  D) 20%  E) 10%

Solution: No of students study french= 250- No of students study spanish = 250-130= 
250-130 = 120
120   % of the students study french but not spanish= (120/200)*100= 
(120/200)*100 = 60
60 %   60%nswer: 60%
Answer: A
Volume of a right circular cylinder is 6o L. If radius of cylinder is doubled, then what will be the increase in volume?  Choose the most appropriate option
A) 120 L B) 180 L C) 240 L D) 300 L E) 360 L

Solution: Pi∗r^2∗h=60   double the radius.....Pi∗(2r)^2∗h=Pi∗4∗r^2∗h=4∗60=240   IMPORTANT.. we are looking at the increase so   240-60= 
  240-60 = 180
180   ANSWER:180 L
Answer: B
A 1000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?
Choose the correct choice: A) 6 B) 12 C) 18 D) 24 E) 48

Solution: In: we have: 1,000/2min = 500 litres per minute   Out: we have: 1,000/4 + 1,000/6   Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (500 by that net inflow to get the minutes) - 6 min. 6nswer 6.
Answer: A
10 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. The suspects are made to stand in a line and each person declares that the person next to him on his right is guilty. The rightmost person is not questioned. Which of the following possibilities are true?	Choose the correct choice from the following choices
A) A or V B) A or C C) A or B D) A or D E) A or J

Solution: There are only 2 cases. Either left one is guilty or one of the remaining 9 to his right is guilty.   So If the left most is guilty, All the statements including the guilty one are lies. A and C are correct.   Or If Any one except left most one is guilty, Then one of the statements given by the person should be true. In this case all the suspects are lying does not hold. So If B is correct, A is not correct. i.e., only A or B is correct. Option C is correct.   Answer:A or B
Answer: C
The diagonals of a rhombus are 13 cm and 20 cm. Find its area?	Choose the correct choice from the following answers:
A) 176  B) 130  C) 150  D) 179  E) 172

Solution: 1/2 * 13 * 20= 
1/2 * 13 * 20 = 130
130   Answer:130
Answer: B
30^10 / 240^5=?  Pick:
A) 6^5
B) (15/4)^5
C) 3^6
D) 6^3
E) 15^3

Solution: 30^10 / 240^5=?   A. 6^5   B. (15/4)^5   C. 3^6   D. 6^3   E. 15^3   -> 30^10 / 240^5=(30^10)/(8^5)(30^5)=(30^5)/(8^5)=(2^5)(15^5)/(2^5)(4^5)=(15/4)^5.   Thus, (15/4)^5 is the answer.
Answer: B
The school's basketball team scores for a five game series were 70, 75, 100, 70 and x. If their median score was 5 points lower than their average (arithmetic mean) score in the series, which of the following could be x?
Choose one:
A) 75
B) 80
C) 85
D) 90
E) 95

Solution: Look at the options available   Value of x seems to 75 < = x < = 95   A. 75   B. 80   C. 85   D. 90   E. 95   So position of x is fourth   70 , 70 , 75 , x , 100   Median = 75   Median score was 5 points lower than the average, so average = 80   70 + 70 + 75 + x + 100 = 400   x = 85 = Answer = 85
Answer: C
If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area? Options
A) 120
B) 77
C) 66
D) 211
E) 12

Solution: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.   120rea of the triangle = 1/2 * 24 * 10= 
1/2 * 24 * 10 = 120
120 cm2   120nswer: 120
Answer: A
Y is an even number and X is a positive odd number. Which of the following expressions cannot be even?
Options:  A) X^3  B) X*3Y*3  C) (XY)^Y  D) XY  E) Y^2

Solution: X^3 WILL BE ODD   X^3
Answer: A
A shop sells bicycles and tricycles. In total there are 8 cycles (cycles include both bicycles and tricycles) and 19 wheels. Determine how many of each there are, if a bicycle has two wheels and a tricycle has three wheels.	Choose one:
A) b=2,t=3  B) b=5,t=3  C) b=6,t=2  D) b=2,t=5  E) b=3,t=4

Solution: Let b be the number of bicycles and let t be the number of tricycles.   Set up the equations   b+t=8............(1)   2b+3t=19............(2)   Rearrange equation (1) and substitute into equation (2)   2b+24-3b=19   -b=-5   b=5   Calculate the number of tricycles t   t=8−b   =8−5   =3   There are 3 tricycles and 5 bicycles.   Answer is b=5,t=3.
Answer: B
How many seconds will a 150 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 63 km/hr?  Choose the correct option.
A) 12 sec  B) 30 sec  C) 86 sec  D) 15 sec  E) 18 sec

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 150 * 3/50   = 15 sec.   Answer: 15 sec
Answer: D
What is the greatest of 3 consecutive integers whose sum is 24 ?  Choose the correct choice from the following:	A) 3	B) 76	C) 8	D) 9	E) 10

Solution: Explanation:   The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3   If the sum is 24, we need to solve the equation 3n + 3 + (  + 1) + (  + 2)= 
+ (  + 1) + (  + 2) = 3
3n + 3   If the sum is 24, we need to solve the equation 3n + 3= 24;   => 3n = 21;   => n = 7   The greatest of the three numbers is therefore   7 + 2= 
  7 + 2 = 9
9   Answer: 9) 9
Answer: D
Tough and Tricky questions: Word Problems.
In a rare coin collection, one in six coins is gold, and all coins are either gold or silver. If 10 silver coins were to be subsequently traded for an additional 10 gold coins, the ratio of gold coins to silver coins would be 1 to 3. Based on this information, how many gold coins would there be in this collection after the proposed trade? Choose the correct choice from the following answers:  A) 50  B) 60  C) 180  D) 200  E) 300

Solution: The correct answer is 180.
Answer: C
An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second?	Choose the correct answer:
A) 18,000 degrees / second
B) 26,000 degrees / second
C) 32,000 degrees / second
D) 47,000 degrees / second
E) 55,000 degrees / second

Solution: 3000 revolutions / minute   = 3000*360 degrees / 60 seconds   = 18,000 degrees / second   correct answer 18,000 degrees / second
Answer: A
The ratio of flour to water to sugar in a recipe is 11:5:2. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 7.5 cups of water, how much sugar is required?	Select:
A) 8 B) 9 C) 10 D) 11 E) 12

Solution: The ratio of flour to water is 22:5.   The ratio of flour to sugar is 5.5:2=22:8.   The new ratio of flour to water to sugar is 22:5:8   If we need 7.5 cups of water, then we need 12 cups of sugar.   The answer is 12.
Answer: E
If a certain number X is divided by 62, the reminder is 7. what is the reminder when X+11 is divided by 31? Answers:
A) 3  B) 5  C) 18  D) 6  E) 8

Solution: X can be written as 62K + 7 or X = 7,69,131,etc.   X + 11 = 62K + 7+11= 62K +18 or X + 11 = 18,80,142 etc.   When divided by 31, we will get the remainder 18.   18
Answer: C
The population of a city increases by 4% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years?
Choose the correct choice from the following answers:  A) 9%  B) 9.27%  C) 27%  D) 12%  E) None of these

Solution: Actual increase in population=3%   Let, earlier population=100 then the population after 3 years   =100(1+3/100)^3=109.2727   ∴Required percentage=9.27%   ANSWER:9.27%
Answer: B
A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
Choices
A) 323
B) 144
C) 278
D) 279
E) 171

Solution: Given that SP = Rs. 102 and loss = 15%   CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.   To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144   Answer: 144
Answer: B
At the end of each year, the value of a certain antique watch is "c" percent more than its value one year earlier, where "c" has the same value each year. If the value of the watch was "k" dollars on January 1, 1992, and "m" dollars on January 1, 1994, then in terms of "m" and "k", what was the value of the watch, in dollars, on January 1, 1995?	Choose the correct option.
A) m+1/2(m-k)  B) m+1/2((m-k)/k)m  C) (m*sqrt(m))/sqrt(k)  D) m^2/2k;  E) km^2

Solution: m = k*(1+c)^2   m/k = (1+c)^2   (m/k)^(1/2) = 1+c   c= (m/k)^(1/2) - 1   the value of the watch in jan 1 1995 is:   m(1+c)   so m(1+(m/k)^(1/2) - 1)   = m(m/k)^(1/2))   ANSWER:(m*sqrt(m))/sqrt(k)
Answer: C
A digital wristwatch was set accurately at 8.30 a.m and then lost 2 seconds every 5 minutes. What time was indicated on the watch at 6.30 p.m of the same day if the watch operated continuously that time ? Choose the correct choice from the following answers.
A) 5.56	B) 5.58	C) 6.0	D) 6.23	E) 6.26

Solution: for every 5 min watch looses 2 secs, so for 60 ms it looses 24 sec,   i.e., for 1 hr it looses 24 secs   8.30amto6.30pm=10 hr it looses 240 secs i.e., 4 mins , hence d watch will show 6.26   ANSW6.26R:6.26
Answer: E