MU-NLPC/Calc-aqua_rat huggingface dataset:
The perimeter of a square is equal to the perimeter of a rectangle of length 17 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
Pick one: A) 23.57 B) 23.54 C) 23.5 D) 24.35 E) 24.51

Solution: Let the side of the square be a cm.   Perimeter of the rectangle = 2(17 + 14) = 62 cm   Perimeter of the square = 62 cm   i.e. 4a = 62   A = 15.5   24.35iameter of the semicircle = 15.5 cm   Circumference of the semicircle   = 1/2(∏)(15.5)   = 1/2(22/7)(15.5) = 24.35 cm to two decimal places   Answer: 24.35
Answer: D
If r and s are positive integers and r-s=6, which of the following has the greatest value K?
Choose the correct option:
A) 2r B) 2s C) r +s D) 2r-s E) 2s-r

Solution: You can answer this question by using Number Properties and logic or by TESTing VALUES.   We're told that R and S are POSITIVE INTEGERS and that R-S = 6. We're asked which of the 5 answers has the GREATEST value.   IF....   R = 8   S = 2   2rnswer 2r: 2R = 2(8) = 16   2rnswer B: 2S = 2(2) = 4   2rnswer C: R+S = 8+2= 
8+2 = 10
10   2rnswer D: 2R-S= 2(8) - 2 = 14   2rnswer E: 2S-R = 2(2) - 8 = -4   Final 2rnswer:   2r
Answer: A
Felix earned 30% more per month than Oscar. If Felix’s salary is decreased 10% and Oscar’s salary is increased by 10%, then Felix would be earning what percent more than Oscar?  Choose the correct choice from the following answers:
A) 10%	B) 9.09%	C) 7%	D) 6.36%	E) It cannot be determined from the information given.

Solution: the very first step requires taking some numbers for each..   ONE should be 100...   it is easy to take 70 and 100 here..   but the BASE is 100 here, so the salary can be 100 and 130..   100 increases 10% =110..   130 decreases 10%=117..   so the increase is 7..   again the BASE is 110, so answer 7/110 * 100= 6.36% D   without calculations,   answer cannot be equal to or greater than 7, as 7 is on 110..   so 6.36% is the only one left   ANSWER:6.36%
Answer: D
1/5 of a number is equal to 5/8 of the second number. If 35 is added to the first number then it becomes 4 times of second number. What is the second number ?	Choose the correct choice from the following:
A) 125  B) 70  C) 40  D) 25  E) 27

Solution: Answer   Let first and second numbers are p & q.   p/5 = 5q/8   ∴ p/q = 25/8 ...(i)   p + 35 = 4q   or 25q/8 + 35= 4q   ∴ q = 40   40orrect Option: 40
Answer: C
A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed?  Options:
A) 3 days
B) 6 days
C) 7 days
D) 2 days
E) 8 days

Solution: B   6 days   Work done by A and B in the first two hours, working alternately = First hour A + Second hour B = 1/4 + 1/12 = 1/3.   Total time required to complete the work = 2 * 3= 
2 * 3 = 6
6 days.
Answer: B
The difference of the squares of two consecutive even integers is divisible by which of the following integers ? Choices:
A) 3
B) 4
C) 6
D) 7
E) 9

Solution: Let the two consecutive even integers be 2n and (2n + 2). Then,   (2n + 2)2 = (2n + 2 + 2n)(2n + 2 - 2n)   = 2(4n + 2)   = 4(2n + 1), which is divisible by 4.   ANSWER 4
Answer: B
There are two numbers. If 60% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
Choose the most appropriate option:
A) A)3/7  B) B)5/8  C) C)6  D) D)6/7  E) E)5/12

Solution: Let the two numbers be x and y.   60/100 * x + y = 5/4y   => 3/5 x = 1/4 y => x/y = 5/12   5/12)
Answer: E
In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 250 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
Choices.
A) 140 B) 146 C) 152 D) 162 E) 183

Solution: The probability of survival for each of the first 3 months of life is 1-1/10=9/10, so of 250 newborn 250*9/10*9/10*9/10=~183 is expected to survive.   Answer: 183.
Answer: E
Two MBA admissions committees are to be formed randomly from 6 second year MBAs with 3 members each. What is the probability E that Jane will be on the same committee as Albert?  Select the correct option:	A) 12%	B) 20%	C) 33%	D) 40%	E) 50%

Solution: Total number of ways to choose 3 member committee - 6C3=(6!/3!3!)=20   No. of ways Albert n Jane are in same committee:- (4C1 * 2)= 8   Probability E= (8/20) *100= 
(8/20) *100 = 40
40%.   +1 for me.. :40%
Answer: D
A man can row 8 Kmph in still water. If the velocity of the current is 2 Kmph and it takes him 2 hours to row to a place and come back. How far is the place? Choose the correct option:	A) 5.5	B) 8.5	C) 6.5	D) 9.5	E) 7.5

Solution: Man's rate down stream = 8 + 2= 
8 + 2 = 10
10 kmph   Man's rate upstream= 8 - 2= 
8 - 2 = 6
6 kmph   Let the required distance be X km   Then X/10 + X/6= 2   3X + 5X = 60   8X = 60   X = 7.5 km   Answer is 7.5.
Answer: E
Rajiv can do a piece of work in 10 days , Venky in 12 days and Ravi in 15 days. They all start the work together, but Rajiv leaves after 2 days and Venky leaves 3 days before the work is completed. In how many days is the work completed ?  Choose the correct choice from the following answers.
A) 7	B) 8	C) 98	D) 6	E) 5

Solution: Explanation: Let the work be 60 units. If venky leave 3 days before the work, Last 3 days must be worked by Ravi. So the remaining days of work be x days, total days to complete the work be x + 3 days.   Now Capacities of Rajiv is 60/10= 
60/10 = 6
6, Venky is 5, Ravi is 4.   (6 + 5 + 4) 2 + (5 + 4) (x – 3) + 4 x 3= 60.   30 + 9x – 27 + 12 = 60   9x – 15 =30   9x = 45   x = 5   So total days to complete the work = 2 + 5= 
2 + 5 = 7
7 days.   7nswer:7
Answer: A
In a flower shop there were 4 flowers in each bouquet. If the seller has doubled the number of flowers in each bouquet then the new average of flowers in each bouque is	Choose the most appropriate option.
A) 12	B) 3	C) 8	D) 9	E) None of these

Solution: Answer   Now required average   = old average x Multiplicand   = 4 x 2 = 8   8orrect Option: 8
Answer: C
The 100-milliliter solution of sugar and water is 12% sugar. How much water (in milliliters) must be added to make a solution that is 8% sugar? Choose the correct choice from the following answers
A) 30	B) 40	C) 50	D) 60	E) 70

Solution: In the original solution the amount of sugar is 0.12*100= 
0.12*100 = 12
12 ml.   Let the volume of the new solution be V.   0.08V=12 ml.   V=150 ml.   The amount of water we need to add is   150 - 100= 
  150 - 100 = 50
50 ml.   The answer is 50.
Answer: C
Use distributive property to solve the problem below:
Maria bought 18 notebooks and 8 pens costing 2 dollars each.How much did Maria pay?  Answers.
A) 30 dollars
B) 40 dollars
C) 50 dollars
D) 60 dollars
E) 52 dollars

Solution: Solution   2 × (18 + 8) = 2 × 18 + 2 × 8 = 36 + 16= 
36 + 16 = 52
52 dollars   Answer 52 dollars
Answer: E
It takes John 25 minutes to walk to the car park and 45 to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.? Choose the most appropriate option
A) 6am	B) 7:30am	C) 8am	D) 5:45am	E) 7:50am

Solution: The time it takes John to get to work: time to walk to car park + time to drive     25 + 45= 
  25 + 45 = 70
70 minutes= 1 hour and 10 minutes   John needs to get out of the house 1 hour and 10 minutes before 9:00 am at   9:00 - 1:10 = 7:50 a.m.   Answer- 7:50am
Answer: E
How many Single-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?  Select
A) None	B) One	C) Two	D) Three	E) Four

Solution: The possible number N can be written as follow:   N = Multiple of LCM(6,10) + 1st such number   N = 30x + 1   Possible values = 1   Answer : One
Answer: B
A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?	Select:
A) 10 liters	B) 11 liters	C) 18 liters	D) 19 liters	E) 12 liters

Solution: Number of liters of water in 125 liters of the mixture = 20% of 150 = 1/5 of 150 = 30 liters   Let us Assume that another 'P' liters of water are added to the mixture to make water 25% of the new mixture. So, the total amount of water becomes (30 + P) and the total volume of the mixture becomes (150 + P)   Thus, (30 + P) = 25% of (150 + P)   Solving, we get P = 10 liters   10 litersnswer: 10 liters
Answer: A
There are 4 prime numbers in ascending order. The multiplication of 1st 3 is 385 and that of last 3is 1001. what is the last no. is? Choose the correct choice.
A) 8
B) 10
C) 11
D) 13
E) 15

Solution: abcbcd=3851001=>ad=513   abcbcd=3851001=>ad=513   So d = 13   13
Answer: D
In an election between two candidates, 10% of votes are were declares invalid. First candidate got 7200 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was:
Choose the correct choice from the following answers.
A) 9000	B) 98000	C) 40000	D) 11000	E) 12000

Solution: 100 % - 10 % = 90 %   54%-36%=18%   18% ------> 7200 ( 18 × 400   54 -36= 
  54 -36 = 18
18%   18% ------> 7200 ( 18 × 400= 7200)   100% -------> 40000 votes (100 × 400 = 40000)   40000
Answer: C
What is the smallest positive integer nn such that 6,480∗n√6,480∗n is a perfect cube?  Pick:
A) 5 B) 5^2 C) 30 D) 30^2 E) 30^4

Solution: Sol: Let's factorize 6480 and we get 6480= 3^4*2^4*5   Now we need to see for what minimum value of n√n*6480= a^3 where a is an Integer   So from 6480 we already have 2^4*3^4*5*n√n = (2^2)^3* (3^2)^3*(5)^3 why cause a is an integer which will need to be have the same factors which are in LHS   solving for n√n = (2^6*3^6*5^3)/ 2^4*3^4*5 and we get   n√n= 2^2*3^2*5^2   Or n = 2^4*3^4*5^4 or 30^4   Ans is 30^4
Answer: E
One side of a rectangular field is 16 m and one of its diagonal is 17 m. Find the area of the field. Choose the correct choice from the following choices: A) 100 B) 120 C) 91.2 D) 180 E) None

Solution: Solution   Other side = √(17)2 - (16)2   = √289 - 256= 
289 - 256 = 33
√33= 5.7 m.   ∴ Area = (16 x 5.7)m2 = 91.2 m2.   Answer 91.2
Answer: C
Robert is travelling on his cycle and has calculated to reach the point A at 2 pm .if he travells at 10kmph;he will reach there at 12 noon if he travels at 15 kmph . at what speed he must travel to reach A at 1p.m	Choose the correct choice from the following
A) 65km
B) 85km
C) 36km
D) 12km
E) 369km

Solution: let the distance travelled be x km   Then x/10-x/15=2   3x-2x=60   x=60km   time taken to travel 60km at 10km/hr=(60/10)hrs=60hrs   so robert stared 6hrs before 2p.m ie 8 A.m   therefore the required speed =(60/5)= 
(60/5) = 12
12kmph   answer is (12km)
Answer: D
Which fraction should be added to:
1/(2 Ã— 3) + 1/(3 Ã— 4) + 1/(4 Ã— 5) + ....... + 1/(25 Ã— 26)
so that the result is equal to 1?  Choose the correct answer.
A) 5/13  B) 6/13  C) 7/13  D) 8/13  E) 9/13

Solution: The given expression   = 1/(2 Ã— 3) + 1/(3 Ã— 4) + 1/(4 Ã— 5) + ...... + 1/(25 Ã— 26)   = (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + .......... + (1/25 - 1/26)   = 1/2 - 1/26 = 12/26   Thus, the fraction we should add = 1 - 12/26 = 7/13   The answer is 7/13.
Answer: C
The total age of A and B is 14 years more than the total age of B and C. C is how many year younger than A  Pick one: A) 11 B) 12 C) 13 D) 14 E) 15

Solution: Explanation:   Given that A+B = 14 + B + C   => A ? C = 14 + B ? B = 14   => C is younger than A by 14 years   Answer: Option 14
Answer: D
A furniture manufacturer has two machines, but only one can be used at a time. Machine P is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine P can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule? Choose the correct choice from the following answers:
A) 14	B) 13	C) 11	D) 9	E) 7

Solution: machine P finish the job in 2*12= 
2*12 = 24
24 shifts   machine B finish the job in   2*15= 
  2*15 = 30
30 shifts   Lets assume total work require 120 shifts   Therefore,   rate of P= 5 shifts/day   rate of B = 4 shifts/day   rate of (P+B) = 9 shifts/day   According to current schedule work complete in a day = 5+4+(9/2)= 
5+4+(9/2) = 27/2 = around 13.5
13.5 shifts/day   Therefore, Time required to finish 120 shifts= (120/13.5) = 8.88.. days ~ 9 days=9
Answer: D
Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 24 minutes. The waste pipe can empty the full cistern in?	Choose the correct choice from the following choices.
A) A)7	B) B)6	C) C)8	D) D)9	E) E)5

Solution: 1/10 + 1/15 - 1/x = 1/24   x = 8   Answer:8
Answer: C
Rates for having a manuscript typed at a certain typing service are $10 per page for the first time a page is typed and $5 per page each time a page is revised. If a certain manuscript has 100 pages, of which 20 were revised only once, 30 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed? Answers
A) $1200 B) $1500 C) $1400 D) $1250 E) $1350

Solution: 50 pages typed 1x   20 pages typed 2x (original + one revision)   30 pages typed 3x (original + two revisions)   50(10)+20(10+5)+30(10+5+5)=500+300+600= 
500+300+600 = 1_400
1400   Answer - $1400
Answer: C
If 1/(x+5)+1/(x-5)=1/(x-5), what is the value of x?	Choose the correct choice
A) -1 B) 3 C) 1 D) 2 E) 5

Solution: If we solve the question, we get x=5.   Option: 5
Answer: E
Five points lie on the circumference of a circle. What is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points? Select:
A) 4
B) 10
C) 6
D) 15
E) 5

Solution: Number of triangles can be formed out of 6 points= 5C3=10   Number of quadrilaterals can be formed out of 6 points= 5C4=5   10-5= 
10-5 = 5
5.   Answer=5
Answer: E
A sum of Rs. 4000 amounts to Rs. 4600 in 5 years at a certain rate of simple interest. What would be the amount, if the rate of interest is increased by 3 %.  Choose one:	A) Rs. 5202	B) Rs. 5200	C) Rs. 5228	D) Rs. 5212	E) Rs. 5182

Solution: Explanation:   Principal = Rs. 4000, Amount = Principal + SI = Rs. 4600   SI = Amount – Principal = 4600 – 4000 = Rs. 600   Given : Principal = Rs. 4000, Time = T = 5 years and SI = Rs. 600   SI =PRT/100   600 = 4000 *R * 5/100   600 = 200R   R = 3 % p.a.   Now the new interest rate is = 3% + 3% = 6 % p.a.   SI 3  + 3= 
3  + 3 = 6
6 % p.a.   SI= PRT/ 100 = 4000 * 6 * 5/ 100 = Rs. 1200   Amount = Principal + SI   = 4000 + 1200= 
4000 + 1200 = 5_200
5200   ANSWER:Rs. 5200
Answer: B
A man's speed with the current is 22 km/hr and the speed of the current is 5 km/hr. The man's speed against the current is	Answers
A) 9
B) 10
C) 11
D) 12
E) 13

Solution: Man's rate in still water = (22 - 5) km/hr = 17 km/hr.   Man's rate against the current = (17 - 5) km/hr = 12 km/hr.   Answer:12
Answer: D
The diagonal of a rhombus are 70 m and 160 m. Its area is:  Select the correct option:
A) 1940
B) 4800
C) 5600
D) 5200
E) 5000

Solution: Area of the rhombus = 1/2 d1d2 = ( 1/2 Ã— 70 Ã— 160) 5600m(power)2   = 70 Ã— 80 = 5600 5600m(power)2   Answer is 5600.
Answer: C
John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase? Pick
A) 16%  B) 16.66%  C) 17.9%  D) 18.12%  E) 18%

Solution: Increase = (10/60)*100 = (1/6)*100 = 16.66%.   16.66%
Answer: B
The jogging track in a sports complex is1100m in circumference. Prakash and his wife start from the same point and walk in opposite directions at 5.2 km/hr and 5.6 km/hr respectively. They will meet for the first time in?
Choices: A) 6.11 min B) 6.88 min C) 7.18 min D) 8.33 min E) 9.00 min

Solution: Clearly, the two will meet when they are 1100 m apart.   To be (5.2 + 5.6)= 
(5.2 + 5.6) = 10.8
10.8 km apart, they take 1 hour.That is 60 minutes.   To be1100 m apart, they take= (1100/1080 * 60) min   = 6.11 min.   6.11 minnswer: 6.11 min
Answer: A
In Sam's hanger there are 23 boxes, 16 out of the boxes are filled with toys and the rest are filled with electrical appliances. 8 boxes are for sale, 6 of them are filled with toys. How many boxes with electrical appliances are in Sam's hanger that is not for sale?	Choose the correct choice from the following options:	A) 1.	B) 2.	C) 3.	D) 4.	E) 5.

Solution: Total boxes = 23   Filled with toys = 16   Filled with appliance = 7   Total boxes for sale = 8   Toy boxes for sale = 6   Appliance boxes for sale = 2   Appliance boxes not for sale = 7 - 2= 
7 - 2 = 5
5   Correct Option: 5.
Answer: E
A box contains 10 tablets of medicine A and 13 tablets of medicine B. What is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted.  Choose the correct choice from the following:
A) 12  B) 15  C) 17  D) 19  E) 21

Solution: The worst case scenario will be if we remove all 13 tablets of medicine B first. The next 2 tablets we remove have to be of medicine A, so to guarantee that at least two tablets of each kind will be taken we should remove minimum of   13+2= 
  13+2 = 15
15 tablets.   Answer: 15.
Answer: B
A and B can do a piece of work in 8 days. B and C can do it in 12 days and A and C in 16 days. Working together they will complete the work in how many days? Choose the correct choice from the following answers:
A) 7.33 days  B) 7.678 days  C) 9.38 days  D) 7.38 days  E) 7.32 days

Solution: A + B = 1/8   B + C = 1/12   C + A = 1/16   -------------------------------   2(A + B +C) = 1/8 + 1/12 + 1/16 = 13/48   A + B +C = 13/96   96/13 = 7.38 days   Answer: 7.38 days
Answer: D
The perimeter of a triangle is 20cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle
Choose the correct choice from the following choices:	A) A)72	B) B)828	C) C)25	D) D)34	E) E)35

Solution: Explanation:   Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   Area of triangle = 2.5 * 20/2= 
2.5 * 20/2 = 25
25 cm2   Answer: Option 25
Answer: C
In Arun's opinion, his weight is greater than 64 kg but leas than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 67 kg. If all of them are correct in their estimation, what is the average of diferent probable weights of Arun ? Choose the correct choice from the following:  A) 86.5 kg  B) 66.5 kg  C) 46.5 kg  D) 65.5 kg  E) 16.5 kg

Solution: Let Arun's weight be X kg.   According to Arun, 64 < X < 72.   According to Arun's brother, 60 < X < 70.   According to Arun's mother, X < 67.   The values satisfying all the above conditions are 65 and 66.   Required average = (65 + 66) / 2= 
(65 + 66) / 2 = 131/2 = around 65.5
65.5 kg   Answer: 65.5 kg
Answer: D
In the exam the average was found to be p mark. After deducting typographical error the average marks of 90 student reduced from 75 to 60 . Due to this the average came down by 15 marks. What was the number of students who took the exam?	Choose the correct option:
A) 90  B) 100  C) 110  D) 130  E) 160

Solution: Explanation :   Number of student = (75-60) * 90/15= 
(75-60) * 90/15 = 90
90   90nswer : 90
Answer: A
Anil spends 40% of his income on rent, 30% of the remaining on medicines and 20% of the remaining on education. If he saves Rs. 840 every month, then find his monthly salary?	Choose one
A) 2502	B) 2528	C) 2573	D) 2500	E) 2503

Solution: Let's Anil's salary be Rs. 100.   Money spent on Rent = 40% of 100 = Rs. 40.   Money spent on medical grounds = 30% of (100 - 40) = 3/10 * 60 = Rs. 18.   Money spent on education = 20% of (60 - 18) = 1/5 * 42 = Rs. 8.40   Anil saves 100 - (40 + 18 + 8.40) i.e., Rs. 33.60   for 33.6 ---> 100 ; 840 ---> ?   Required salary = 840/33.6 * 100 = Rs. 2500   Answer:2500
Answer: D
The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 96 square centimeters, what is the length of the rectangle in centimeters?	Choose the correct choice from the following:
A) 11  B) 12  C) 13  D) 14  E) 15

Solution: Perimeter = 2(W+L) = 5W   3W = 2L   W = 2L/3   WL = 96   2L^2/3 = 96   L^2 = 144   L = 12 cm   The answer is 12.
Answer: B
A train passes a station platform in 42 sec and a man standing on the platform in 12 sec. If the speed of the train is 54 km/hr. What is the length of the platform?  Choose the correct option.
A) 227
B) 450
C) 460
D) 480
E) 171

Solution: Speed = 54* 5/18= 
54* 5/18 = 15
15 m/sec.   Length of the train= 15 * 12= 
15 * 12 = 180
180 m.   Let the length of the platform be x m . Then,   (x + 180)/42= 15 => x = 450 m.   Answer:450
Answer: B
A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 360-mile journey? Assume that the train makes no intermediate stops.  Choices.
A) 8	B) 8.5	C) 9	D) 9.5	E) 10

Solution: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 360-mile journey? Assume that the train makes no intermediate stops.   I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total)   Hour miles/hour Total miles   1 10 10   2 20 30   3 30 60   4 40 100   5 50 150   6 60 210   7 70 280   8 80 360   It takes a total of Eight hours to cover the 360 mile distance.   8NSWER: 8
Answer: A
The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 75 and n is not prime, what is the greatest possible value of f(n)?	Answers:
A) 72  B) 69  C) 65  D) 60  E) 58

Solution: Since we need the largest value of f (n), we will start with the largest option.   Option A: 2*2*2*2*2*2 = . This is not a product of distinct prime numbers. Hence incorrect   Option B: 69 = 3*23. This is a product of distinct prime numbers.   Rest all the options are smaller that 69.   Correct Option: 69
Answer: B
Village X has a population of 74000, which is decreasing at the rate of 1200 per year. Village Y has a population of 42000, which is increasing at the rate of 800 per year .in how many years will the population of the two villages be equal?  Answers
A) 15 B) 16 C) 11 D) 18 E) 13

Solution: Let the population of two villages be equal after p years   Then, 74000-1200p=42000+800p   2000p=32000   p=16   Answer is 16.
Answer: B
Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?
Choose one.
A) 5!
B) 8!
C) 9!
D) 10!
E) 11!

Solution: Ans.(B)   Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways
Answer: B
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:	Select
A) 30720	B) 153600	C) 15360	D) 307200	E) 153700

Solution: Perimeter = Distance covered in 8 min. =12000/60x 8	m = 1600 m.   Let length = 3x metres and breadth = 2x metres   Then, 2(3x + 2x) = 1600 or x = 160.   Length = 480 m and Breadth = 320 m.   Area = (480 x 320) m2 = 153600 m2   ANSWER:153600
Answer: B
If (1*x)y=y, which of the following must be true?
Choose the correct choice.
A) x=-1 or y=0 B) x=0 or y=0 C) x=1 or y=1 D) x=-1 or y=-1 E) x=0 or y=1

Solution: We have (1*x)y=y.   If x=1, y=1 True   If y=1, (1*x)*1=1True   So, x=1 or y=1will be the answer.
Answer: C
What is the sum of all the numbers which divides 100 ? Options:	A) 408	B) 102	C) 816	D) 916	E) 416

Solution: You first have to know all the divisor of 100. They are 2,4,5,10,20,25,50 and 100. If you add all these numbers together, you get 408.   Final 408nswer:   408
Answer: A