MU-NLPC/Calc-aqua_rat huggingface dataset:
In Kiran's opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Kiran and he thinks that Kiran's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Kiran?  Choices.
A) 70 kg  B) 69 kg  C) 61 kg  D) 67 kg  E) 65 kg

Solution: Explanation:   Let Kiran's weight = x. Then   According to Kiran, 65 < x < 72 ----(equation 1)   According to brother, 60 < x < 70 ----(equation 2)   According to mother, x ≤≤ 68 ----(equation 3)   Given that equation 1,equation 2 and equation 3 are correct. By combining these equations, we can write as   65<x≤68   i.e., x = 66 or 67 or 68   Average of different probable weights of Kiran = 66+67+683=67   Answer: Option 67 kg
Answer: D
The average of six numbers is 3.75. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?
Pick one.
A) 4.7
B) 4.6
C) 4.0
D) 4.1
E) 4.9

Solution: Explanation:   Sum of the remaining two numbers = (3.75 * 6) - [(3.4 * 2) + (3.85 * 2)]   = 22.50 - (6.8 + 7.7) = 22.50 - 14.5= 
22.50 - 14.5 = 8
8.   Required average= (8 / 2) = .   Answer: 4.0) 4.0
Answer: C
A committee of 5 persons is to be formed from 3 company secretaries, 4 economists and 1 chartered accountant. What is the probability that each of the three professions is represented in the committee?
Choose the correct choice from the following options:
A) 1/28
B) 3/28
C) 60/14
D) 4/28
E) 3/14

Solution: 3/8*4/7*1/6*5! = 3/14. We are multiplying by 5! because we can choose secretary,economist, and accountant is several way:   Answer: 60/14.
Answer: C
A batsman scored 100 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets? Answers.
A) 45(4/11) % B) 40 % C) 45(5/11) % D) 44(5/11) % E) None of these

Solution: Explanation :   Total runs scored = 100   Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60   Total runs scored by running between the wickets = 100 - 60= 
100 - 60 = 40
40   Required %= (40/100) × 100 = 40%   Answer : Option 40 %
Answer: B
A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start at same point at 10:30 am. They shall first cross each other at ?	Options:
A) 7:15 am
B) 7:30 am
C) 10: 42 am
D) 7:50 am
E) 7:60 am

Solution: Explanation:   Relative speed between two = 6-1= 
6-1 = 5
5 round per hour   They will cross when one round will complete with relative speed,   which is 1/5 hour= 12 mins.   So 10:30 + 12 mins = 10:42   Option 10: 42 am
Answer: C
Maria bought 10 notebooks and 5 pens costing 2 dollars each.How much did Maria pay?  Pick.
A) $10 B) $20 C) $30 D) $40 E) $50

Solution: 2 × (10 + 5) = 2 × 10 + 2 × 5 = 20 + 10= 
20 + 10 = 30
30 dollars   correct answer is $30)$30
Answer: C
If x = 3d, where d is a prime number greater than 2, how many different positive even divisors does x have, including x?
Pick one
A) 0  B) 1  C) 2  D) 3  E) It cannot be determined from the information given

Solution: d is prime greater than 2 thus d is odd   3d is odd   Thus no even factors   0ns:0
Answer: A
Elizabeth can get a certain job done in 15 days, and Tony can finish only 75% of that job within the same time. Tony worked alone for several days and then Elizabeth joined him, so they finished the rest of the job in 6 days, working together.
For how many days have each of them worked and what percentage of the job have each of them completed? Choose the correct choice:
A) 5 days and 40%  B) 6 days and 30%  C) 6 days and 40%  D) 7 days and 40%  E) 7 days and 30%

Solution: First we will find the daily productivity of every worker. If we consider the whole job as unit (1), Elizabeth does 115 of the job per day and Tony does 75% of 115, i.e.   75100⋅115=120. Suppose that Tony worked alone for x days. Then he finished x20 of the total job alone. Working together for 6 days, the two workers finished 6⋅(115+120)=6⋅760=710 of the job.   The sum of x20 and 710 gives us the whole job, i.e. 1. So we get the equation:   x20+710=1   x20=310   x=6. Tony worked for   6 + 6= 
  6 + 6 = 12
12 days and Elizabeth worked for 6 days. The part of job done is 12⋅120=60100=60% for Tony, and 6⋅115=40100=40% for Elizabeth.   Answer is 6 days and 40%.
Answer: C
How many different positive integers are factors of 36 ?
Pick
A) 4 B) 6 C) 7 D) 9 E) 11

Solution: 6×6=3^2 × 2^2   So total factors = (2+1)(2+1) = 9   Answer: 9
Answer: D
What is the maximum number of pieces that a circular pizza can be cut into with 6 linear cuts?
Choose the correct choice from the following choices
A) 12
B) 13
C) 16
D) 20
E) 22

Solution: 1 cut makes 2 pieces   a second cut can make 4 pieces by cutting through 2 of the pieces   a third cut can make 7 pieces by cutting through 3 of the pieces   a fourth cut can make 11 pieces by cutting through 4 of the pieces   a fifth cut can make 16 pieces by cutting through 5 of the pieces   a sixth cut can make 22 pieces by cutting through 6 of the pieces   22
Answer: E
A departmental store charges the commission of 18 percent on the first sale of items worth $50,000 and then an additional 10 percent on any sale price that exceeds the initial $50,000. If the department store earned $24,000 in commissions for the sale of a series of diamonds, what was the sale price of the diamond set?	Choices:
A) $215,000  B) $365,000  C) $115,000  D) $200,000  E) $160,000

Solution: 24,000 = 0.18 *(50000) + 0.10 (x - 50000)   24000 - 9000 = 0.10 (x-50000)   150000 = x - 50000   x = 2,00,000   Answer : $200,000
Answer: D
Five times a number equals one hundred. The number is  Pick:
A) 50 B) 10 C) 15 D) 25 E) 20

Solution: Since five times the number equals one hundred, then the number equals one hundred divided   by five. Therefore the number is  100/ 5= 
 100/ 5 = 20
20.   correct answer 20
Answer: E
Fill in the missing number:
18 14 ? 11 10.5 10.25
Options.
A) 10.1	B) 12	C) 10.2	D) 10.5	E) 10.3

Solution: 12   Divide each number by 2 and then add 5 to it.   ANSWER 12
Answer: B
P, Q and R can do a piece of work in 20, 30 and 60 days respectively. In how many days can P do the work if he is assisted by Q and R on every third day? Choices:	A) 15 DAYS	B) 12 DAYS	C) 10 DAYS	D) 18 DAYS	E) 20 DAYS

Solution: P's 2 day's work =	1/20*2=1/10   P+Q+R)'S 1 D15 DAYSY'S WORK = 1/20+1/30+1/60 = 6/60 = 1/10   WORK IN D15 DAYSYS = 1/5   NOW 1/5 DONE IN 3 D15 DAYSYS   WHOLE WORK WILL BE DONE IN(3*5)= 
(3*5) = 15
15 D15 DAYSYS   15 DAYSNSWER 15 DAYS
Answer: A
The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 30. Which of the following integers is the higher of the remaining two integers?  Answers.
A) 32	B) 86	C) 44	D) 22	E) 87

Solution: Let the four integers be A, B, C and D where A > B > C > D.   (A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)   A = 93, D = 39 and B - C = 30   (1) => B + C = 276 - (A + D) = 276 - 132= 
276 - 132 = 144
144.   B + B -30= 144   B = (144 + 30)/2= 
(144 + 30)/2 = 87
87   Answer:Option 87
Answer: E
A train 300 m long passed a pole in 14 sec. How long will it take to pass a platform 540 m long?	Options:
A) 12 sec	B) 59 sec	C) 40 sec	D) 45 sec	E) 46 sec

Solution: Speed = 300/14   = 21 m/sec.   Required time = (300 + 540)/21= 
(300 + 540)/21 = 40
40 sec.   Answer: 40 sec
Answer: C
The least common multiple of positive integer q and 3-digit integer n is 690. If n is not divisible by 3 and q is not divisible by 2, what is the value of n?  Choose the correct choice from the following options.
A) 115
B) 230
C) 460
D) 575
E) 690

Solution: The LCM of n and q is 690 = 2*3*5*23.   q is not divisible by 2, thus 2 goes to n   n is not divisible by 3, thus 3 goes to q.   From above:   n must be divisible by 2 and not divisible by 3: n = 2*... In order n to be a 3-digit number it must take all other primes too: n = 2*5*23= 
2*5*23 = 230
230.   Answer: 230.
Answer: B
A rectangular rug with side lengths of 4 feet and 6 feet is placed on a square floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the floor, what fraction of the area of the floor is not covered by the rug?
Choose the correct choice from the following:
A) A.3/16
B) 1/4
C) C.1/2
D) 5/8
E) 7/8

Solution: Area of the rectangular rug = 4*6= 
4*6 = 24
24   Fraction not covered by the rug= (Total Area - Rug area) / Total Area   = (64 - 24)/64   = 5/8=5/8
Answer: D
There are 10 reading spots in a room. Each reading spot has a round table. Each round table has 4 chair. If different no of persons are sitting at each reading spot. And if there are 10 persons inside the room then how many reading spots donot have atleast a single reader. Choose the correct choice:
A) 5
B) 6
C) 8
D) 9
E) 7

Solution: 10 reading spots and 4 chairs each   total 10 persons   different no. of seating must   so   1st-1person   2nd-2person   3rd-3person   4th-4person   by above way 10 peoples are seated   so empty chairs = 10chairs - 4chairs = ans: 6chairs   ANSWER:6
Answer: B
A fruit seller sells 8 oranges at a cost price of 9. The profit percent is Choose the correct option:
A) 12 1⁄2	B) 11 1⁄9	C) 5 15⁄17	D) 8 2⁄3	E) None of these

Solution: Let C.P. of one orange = 1   Then C.P. of 8 oranges = 8   S.P of 8 oranges = 9   ∴ Gain % = 9−8/8×100=100/8=12 1/2%   12 1⁄2nswer 12 1⁄2
Answer: A
The average age of 36 students in a group is 14 years. When teacher's age is included to it, the average increases by one. Find out the teacher's age in years?  Choose the correct choice from the following answers.
A) 50
B) 49
C) 53
D) 54
E) 51

Solution: average age of 36 students in a group is 14   Sum of the ages of 36 students = 36 × 14   When teacher's age is included to it, the average increases by one   => average = 15   Sum of the ages of 36 students and the teacher = 37 × 15   Hence teachers age   = 37 × 15 - 36 × 14   = 37 × 15 - 14(37 - 1)   = 37 × 15 - 37 × 14 + 14   = 37(15 - 14) + 14   = 37 + 14= 
37 + 14 = 51
51   Answer is 51.
Answer: E
By selling an article at Rs.300, a profit of 25% is made. Find its cost price?	Select the correct option.
A) s.486
B) s.455
C) s.240
D) s.480
E) s.489

Solution: SP = 300   s.240P = (SP)*[100/(100+P)]   = 300* [100/(100+25)]   = 300* [100/125]   = Rs.240   Answer: s.240
Answer: C
A and B start a business with Rs.5000 and Rs.15000 respectively. How should they share their profits at the end of one year?
Choose the correct option:
A) 1:3 B) 3:4 C) 2:5 D) 3:7 E) 2:1

Solution: They should share the profits in the ratio of their investments.   The ratio of the investments made by 1:3 and B =   5000 : 15000 => 1:3   1:3NSWER:1:3
Answer: A
P , Q, R enter into a partnership & their share are in the ratio 1/2 : 1/3 : 1/4 , after two months , P withdraws half of the capitals & after 10 months , a profit of Rs 378 is divided among them . What is P's share? Choose the correct choice from the following answers: A) 114 B) 126 C) 134 D) 144 E) None of these

Solution: Explanation :   The ratio of their initial investment = 1/2 : 1/3 : 1/4   = 6 : 4: 3   Let's take the initial investment of P, Q and R as 6x, 4x and 3x respectively   A:B:C = (6x * 2 + 3x * 10) : 4x*12 : 3x*12   = (12+30) : 4*12 : 3*12   =(4+10) : 4*4 : 12   = 14 : 16 : 12   = 7 : 8 : 6   P's share = 378 * (7/21)= 
378 * (7/21) = 126
126. Answer : Option 126
Answer: B
Out of the total production of iron from hematite, an ore of Iron, 20% of the ore gets wasted, and out of the remaining iron, only 25% is pure iron. If the pure iron obtained in a year from a mine of hematite was 80,000 kg, then the quantity of hematite mined from that mine in the year is	Choices: A) 5,00,000 kg B) 4,00,000 kg C) 4,50,000 kg D) None of these E) Cannot be determined

Solution: Solution: Let 100 kg of hematite be obtained then 20% of it get wasted that means 80 kg of ore remains.   Pure iron = 25% of remaining ore = 80*25/100= 
80*25/100 = 20
20 kg.   20 kg pure Iron is obtained from 100 of hematite.   1 kg pure Iron is obtained from= 100/20 hematite;   Then, 80000 kg pure Iron is obtained from = (100/20)*80000= 
(100/20)*80000 = 400_000
400000 kg hematite.   Answer: Option 4,00,000 kg
Answer: B
3 gentlemen and 3 gentlewomen are candidates for 2vacancies. A voter has to vote for 2candidates. In how many ways can one cast his vote?
Choices:
A) 11  B) 12  C) 15  D) 16  E) 17

Solution: There are 6 candidates and a voter has to vote for any two of them.   So, the required number of ways is,   = 6C2 = 6!/2!*4!   = 15.   15
Answer: C
If the largest three digit number is subtracted from the smallest five digit number, then the remainder is  Select the correct option:
A) 9000
B) 9001
C) 90001
D) 9009
E) NOne

Solution: Sol.   Required number = (10000 - 999)= 
(10000 - 999) = 9_001
9001.   Answer 9001
Answer: B
The average weight of a group of boys is 30 kg. After a boy of weight 39 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? Select:
A) 4
B) 8
C) 5
D) 2
E) 9

Solution: Let the number off boys in the group originally be x.   Total weight of the boys = 30x   After the boy weighing 39 kg joins the group, total weight of boys = 30x + 39   So 30x + 39 + 31(x + 1) = > x = 8.   Answer: 8
Answer: B
P is a prime number. If 6p is between 15 and 95, which of the following T can be a value of 7p + 2?
Select: A) T=15 B) T=79 C) 121 D) 65 E) 21

Solution: [3,5,7,11,13] are prime numbers that fits this equation 15< 6X <95. Afterwards subtract 2 from all the answer n see if it's divisible by 7. Therefore A and E are out. Leaves out with B C D.   B =11   C =17   D = 9   Only 11 is the set of prime numbers that fit between 15 and 95. Therefore 79 is the answer.T=79
Answer: B
The average (arithmetic mean) of four numbers is 5x + 6. If one of the numbers is 2x, what is the average of the other three numbers? Options:
A) x + 1
B) 3x + 3
C) 5x + 1
D) 5x + 4
E) 6x + 8

Solution: The sum of all four numbers is 4 * (5x + 6) = 20x + 24.   If one of the numbers is 2x, the sum of the other 3 numbers is 18x+24.   The average of the remaining three numbers is (18x+24)/3 = 6x+8.   The answer is 6x + 8.
Answer: E
A batsman makes a score of 87 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning? Choose the correct choice from the following:
A) 19	B) 29	C) 39	D) 49	E) 59

Solution: let the average after 17th inning =x   Then average after 16th inning=(x-3)   Therefore 16(x-3)+87=17x   Therefore x=39   ANSWER:39
Answer: C
Pat's watch gains an extra 10 seconds every 2 hours. Kim's watch loses 6 seconds every 3 hours. If both watches are set to correct time at 8 o'clock in the morning and run without interruption, after 48 hours, what will be the difference in time between Pat's watch and Kim's watch? Choose the correct choice from the following choices:
A) 3 min 36 sec
B) 4 min 36 sec
C) 5 min 36 sec
D) 6 min 36 sec
E) 5 min 36 sec

Solution: In 48 hours Pat's watch will gain an extra   48/2*10= 
  48/2*10 = 240
240 seconds.   In 48 hours Kim's watch will lose   48/3*6= 
  48/3*6 = 96
96 seconds.   Hence the difference will be   240 + 96= 
  240 + 96 = 336
336 seconds.   Answer: 5 min 36 sec.
Answer: E
A runs 25% faster than B and is able to allow B a lead of 7 meters to end a race in dead heat. What is the length of the race?  Select:
A) 10 meters B) 25 meters C) 45 meters D) 15 meters E) 35 meters

Solution: Answer   A runs 25% as fast as B.   i.e., if B runs 100 m in a given time, A will run 125 m in the same time.   In other words, if A runs 5 m in a given time, then B will run 4 m in the same time.   Therefore, if the length of a race is 5 m, then A can give B a start of 1 m (A can allow B to start 1 ahead of the starting point) so that they finish the race in a dead heat.   Ratio of length of start given : length of race :: 1 : 5   In this question, we know that the start given is 7 m.   Hence, the length of the race will be   7 * 5= 
  7 * 5 = 35
35 m.   Choice 35 meters
Answer: E
Nine men went to a hotel. 8 of them spent 3 each over their meals and the ninth spent 2 more than the average expenditure of all the nine. The total money spent by all of them was  Choose the correct option
A) 26 B) 40 C) 29.25 D) 27 E) None of the above

Solution: Let the average expenditure of all the ninte be x   Then, 3 × 8 + x + 2 = 9x   ⇒ x = 3.25   ∴ Total money spent = 9x = 9 × 3.25 = 29.25   Answer 29.25
Answer: C
If x^2 + 1/x^2 = √20 what is the value of x^4 + 1/x^4 ?	Choose the correct choice:
A) 10
B) 12
C) 14
D) 16
E) 18

Solution: IMPORTANT: I notice that if we SQUAR18 x², we get x⁴, and if we SQUAR18 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = √20 andSQUAR18both sides:   (x² + 1/x²)²= 20   So, (x² + 1/x²)(x² + 1/x²) = 20   18xpand to get: x⁴ + 1 + 1 + 1/x⁴ = 20   Simplify: x⁴ + 1/x⁴ = 18   Answer: 18
Answer: E
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
Choose the correct choice from the following:
A) 2.86	B) 2.88	C) 2.89	D) 2.834	E) 2.81

Solution: M = 6   S = 1.2   DS = 6 + 1.2= 
6 + 1.2 = 7.2
7.2   US= 6 - 1.2= 
6 - 1.2 = 4.8
4.8   x/7.2 + x/4.8= 1   x = 2.88   Answer: 2.88
Answer: B
The population of a town is 45000; 5/9th of them are males and the rest females 40% of the males are married. What is the percentage of married females?  Choose the correct answer: A) 56% B) 50% C) 57% D) 10% E) 80%

Solution: Male = 45,000* 5/9 = 25,000   Female = 45,000* 4/9 = 20,000   Married Male = 25,000* 40/100 = 10,000   Married Female = 10,000   20,000 ------------ 10,000   100 ------------- ? => 50%   Answer: 50%
Answer: B
Halle, Julia and Drew have 5 donuts to share. If one of them can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed.
Pick.
A) 20  B) 21  C) 22  D) 23  E) 24

Solution: these are the no of ways:   0 2 3 - 3! ways   2 2 1 - 3!/2 ways   5 0 0 - 3!/2 ways   4 1 0 - 3! ways   1 1 3 - 3!/2 ways   So total no of ways = 21   ANS:21
Answer: B
If 21 WOMen and 12 men can finish the work in 42 days.How many men should accompany 42 women to that the work will be completed in ten and half days???  Select the correct option.
A) 40 B) 45 C) 50 D) 60 E) 15

Solution: 15 men using chain rule   ANSW15R:15
Answer: E
In expressing a length 810472 km as nearly as possible with three significant digits, find the percentage error. Select the correct option:	A) 0.034	B) 0.024	C) 0.352	D) 0.063	E) 0.026

Solution: Error = (81.5 – 81.472)km = 0.028.   Required percentage = [(0.028/81.472)*100]% = 0.034%.   0.034nswer 0.034.
Answer: A
If there are eight varieties of ice cream to be tasted and judged in a competition, what is the probability that black currant is tasted before Vanilla and Vanilla is tasted before chocolate, although not necessarily consecutively?	Options
A) 1/8!
B) 3!/8!
C) 5!/8!
D) 1/3!
E) 1/2!

Solution: 8 flavors are too much. Lets try out only 3 flavors --> Black Currant, Vanilla, Chocalate   We can get Black Currant before Vanilla and Vanilla before Chocolate in only 1 way.   Probability = Possible/Total = 1/3!   Now lets consider 4 flavors --> BC, Van, Choc and X   Possibilities --> 1) BC, X, Van, Choc   2) X, BC, Van, Choc   3) BC, Van, Choc, X   4) BC, Van, X, Choc   Probability = 4/24 = 1/3!   Since the probability remains the same for both the cases, the probability will mostly remain true for the 8 varieties too.   Answer: 1/3!
Answer: D
A picnic attracts 200 persons. There are 20 more men than women, and 20 more adults than children. How many men are at this picnic?  Answers.
A) 240  B) 65  C) 110  D) 130  E) 200

Solution: Adult + Children = 200   Let, Children = y   then, Adult = y+20   i.e. y+(y+20) = 200   i.e. y = 900   i.e. Adult = 90+20= 
90+20 = 110
110   Adults include only Men and Women   i.e. Men + Women= 110   Let women, W = x   then Men, M = x+20   i.e. x+(x+20) = 2x+20 = 110   i.e. x = 45   i.e. Men, M = 45+20= 
45+20 = 65
65   Answer: Option 65
Answer: B
How many four-digit numbers that do not contain the digits 2, 3, 4, or 6 are there?	Pick.
A) 1025 B) 1080 C) 2096 D) 3040 E) 4200

Solution: The 1st digit can be filled up by the numbers: {1,5,7,8,9} = 5 ways   The 2nd digit can be filled up by the numbers: {0,1,5,7,8,9} = 6 ways   The 3rd digit can be filled up by the numbers: {0,1,5,7,8,9} = 6 ways   The 4th digit can be filled up by the numbers: {0,1,5,7,8,9} = 6 ways   The total number of such four-digit numbers is 6*7*7*7 = 1080   The answer is 1080.
Answer: B
The owner of a furniture shop charges his customer 10% more than the cost price. If a customer paid Rs. 8800 for a computer table, then what was the cost price of the computer table? Select the correct option:
A) 2299	B) 2699	C) 2670	D) 6725	E) 8000

Solution: CP = SP * (100/(100 + profit%))   = 8800(100/110) = Rs. 8000   Answer:8000
Answer: E
John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?  Pick one: A) 3 1/5 Km B) 3 2/5 Km C) 3 3/5 Km D) 3 5/7 Km E) 4 1/5 Km

Solution: Formula = S1*S2/S2-S1 * T1+T2/60   = 4*6/2 * 16/6   = 24/2 * 16/60   = 8 * 2/5   = 16/5 = 3 1/5 Km   3 1/5 Km)
Answer: A
Calculate the average of first 16 even numbers is?  Choose the correct answer.
A) 16 B) 15 C) 12 D) 17 E) 11

Solution: Explanation:   Sum of 10 even numbers = 16 * 17= 
16 * 17 = 272
272   Average= 272/16= 
272/16 = 17
17   Answer: Option 17
Answer: D
A square and an equilateral triangle have the same perimeter. What is the ratio of the area of the circle circumscribing the square to the area of the circle inscribed in the triangle?  Choose the correct choice from the following options
A) 9:8  B) 15:8  C) 27:8  D) 8:9  E) 8:15

Solution: let x be side of square   perimeter of square=4x=perimeter of triangle=3*side of triangle   so side of eq. triangle=(4/3)*x   diameter of circle circumscribing the square=sqrt(2)*x   area of circle circumscribing the square=pi*(sqrt(2)*x)^2/4=(pi/2)*x^2 ----(1)   to find radius of the circle inscribed in the triangle   area of triangle=r*s=sqrt(3)/4 * (4x/3)^2   now s=(4/3)*x+(4/3)*x+(4/3)*x/2=2x   so sqrt(3)/4 * (4x/3)^2=r*2x gives   r={2/3*(3^1/2)}*x   area of the circle inscribed in the triangle=pi*[{2/3*(3^1/2)}*x]^2   =pi*(4/27)*x^2 -------(2)   so reqd ratio= eqn(1)/eqn(2)   =[(pi/2)*x^2]/[pi*(4/27)*x^2]=27/8   so reqd ratio=27:8   ANSWER:27:8
Answer: C
A train 660 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?	Choose the correct choice from the following choices.
A) 640  B) 277  C) 500  D) 297  E) 435

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (660 + x)/60 = 65/3   x = 640 m.   640nswer: 640
Answer: A
Arjun and Bhishma are running on a circular track of length 600m. Speed of Arjun is 30 m/s and that of Bhishma is 20 m/s .They start fro the same point at the same time in the same direction. When will they meet again for the first time?
Pick one.
A) 22	B) 60	C) 27	D) 21	E) 19

Solution: Actually Arjun has to make a lead of 600 m, because when Arjun will be 600m ahead of Bhishma, they will be together again as a person when completes the total length it starts retracing he same path and thus Arjun and Bhishma can be together again.   Since , they make a difference of 10 m in 1 second. so, he will create 600m difference in 60 second.   ANSWER=60
Answer: B
If ten persons sit in a row, then the probability that three particular persons are always together is?
Choose one: A) 1/5 B) 1/4 C) 1/9 D) 1/6 E) 1/15

Solution: Ten persons can be arranged in a row in 10! ways.   Treat the three persons to sit together as one unit then there eight persons and they can be arranged in 8! ways.   Again three persons can be arranged among them selves in 3! ways.   Favourable outcomes = 3!8!   Required probability = 3!8!/10! = 1/15   Answer:1/15
Answer: E