mathewhe/aqua_rat huggingface dataset:
Question: 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 ?
(A) 4.7
(B) 4.6
(C) 4.0
(D) 4.1
(E) 4.9
Rationale: 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 = 8.
Required average = (8 / 2) = .
Answer: C) 4.0
Answer: (C) 4.0
Question: 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?
(A) 1/28
(B) 3/28
(C) 60/14
(D) 4/28
(E) 3/14
Rationale: 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: C.
Answer: (C) 60/14
Question: 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?
(A) 45(4/11) %
(B) 40 %
(C) 45(5/11) %
(D) 44(5/11) %
(E) None of these
Rationale: 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 = 40
Required % = (40/100) × 100 = 40%
Answer : Option B
Answer: (B) 40 %
Question: 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 ?
(A) 7:15 am
(B) 7:30 am
(C) 10: 42 am
(D) 7:50 am
(E) 7:60 am
Rationale: Explanation:
Relative speed between two = 6-1 = 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 C
Answer: (C) 10: 42 am
Question: Maria bought 10 notebooks and 5 pens costing 2 dollars each.How much did Maria pay?
(A) $10
(B) $20
(C) $30
(D) $40
(E) $50
Rationale: 2 × (10 + 5) = 2 × 10 + 2 × 5 = 20 + 10 = 30 dollars
correct answer is C)$30
Answer: (C) $30
Question: If x = 3d, where d is a prime number greater than 2, how many different positive even divisors does x have, including x?
(A) 0
(B) 1
(C) 2
(D) 3
(E) It cannot be determined from the information given
Rationale: d is prime greater than 2 thus d is odd
3d is odd
Thus no even factors
Ans:A
Answer: (A) 0
Question: 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?
(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%
Rationale: 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 = 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 C.
Answer: (C) 6 days and 40%
Question: How many different positive integers are factors of 36 ?
(A)  4
(B)  6
(C)  7
(D)  9
(E)  11
Rationale: 6×6=3^2 × 2^2
So total factors = (2+1)(2+1) = 9
Answer: D
Answer: (D)  9
Question: What is the maximum number of pieces that a circular pizza can be cut into with 6 linear cuts?
(A) 12
(B) 13
(C) 16
(D) 20
(E) 22
Rationale: 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
E
Answer: (E) 22
Question: 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?
(A)  $215,000
(B)  $365,000
(C)  $115,000
(D)  $200,000
(E)  $160,000
Rationale: 24,000 = 0.18 *(50000) + 0.10 (x - 50000)
24000 - 9000 = 0.10 (x-50000)
150000 = x - 50000
x = 2,00,000
Answer : D
Answer: (D)  $200,000
Question: Five times a number equals one hundred. The number is
(A) 50
(B) 10
(C) 15
(D) 25
(E) 20
Rationale: Since five times the number equals one hundred, then the number equals one hundred divided
by five. Therefore the number is 100/ 5 = 20.
correct answer E
Answer: (E) 20
Question: Fill in the missing number:
18 14 ? 11 10.5 10.25
(A) 10.1
(B) 12
(C) 10.2
(D) 10.5
(E) 10.3
Rationale: 12
Divide each number by 2 and then add 5 to it.
ANSWER B
Answer: (B) 12
Question: 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?
(A) 15 DAYS
(B) 12 DAYS
(C) 10 DAYS
(D) 18 DAYS
(E) 20 DAYS
Rationale: P's 2 day's work =	1/20*2=1/10
P+Q+R)'S 1 DAY'S WORK = 1/20+1/30+1/60 = 6/60 = 1/10
WORK IN DAYS = 1/5
NOW 1/5 DONE IN 3 DAYS
WHOLE WORK WILL BE DONE IN(3*5) = 15 DAYS
ANSWER A
Answer: (A) 15 DAYS
Question: 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?
(A) 32
(B) 86
(C) 44
(D) 22
(E) 87
Rationale: 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 = 144.
B + B -30 = 144
B = (144 + 30)/2 = 87
Answer:Option E
Answer: (E) 87
Question: A train 300 m long passed a pole in 14 sec. How long will it take to pass a platform 540 m long?
(A) 12 sec
(B) 59 sec
(C) 40 sec
(D) 45 sec
(E) 46 sec
Rationale: Speed = 300/14
= 21 m/sec.
Required time = (300 + 540)/21
= 40 sec.
Answer: C
Answer: (C) 40 sec
Question: Which is greater than 99?
(A) 9
(B) 99
(C) 9.9
(D) 999
(E) 909
Rationale: 999 greater than 99.
Answer: D
Answer: (D) 999
Question: 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?
(A) 115
(B) 230
(C) 460
(D) 575
(E) 690
Rationale: 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 = 230.
Answer: B.
Answer: (B) 230
Question: Find the value of 72516 x 9999 = m?
(A) 345434667
(B) 246465757
(C) 465767867
(D) 725087484
(E) 645354643
Rationale: 72516 x 9999 = 72516 x (10000 - 1)
= 72516 x 10000 - 72516 x 1
= 725160000 - 72516
= 725087484
D
Answer: (D) 725087484
Question: 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?
(A) A.3/16
(B) 1/4
(C) C.1/2
(D) 5/8
(E) 7/8
Rationale: Area of the rectangular rug = 4*6 = 24
Fraction not covered by the rug = (Total Area - Rug area) / Total Area
= (64 - 24)/64
= 5/8=D
Answer: (D) 5/8
Question: 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.
(A) 5
(B) 6
(C) 8
(D) 9
(E) 7
Rationale: 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:B
Answer: (B) 6
Question: A fruit seller sells 8 oranges at a cost price of 9. The profit percent is
(A) 12 1⁄2
(B) 11 1⁄9
(C) 5 15⁄17
(D) 8 2⁄3
(E) None of these
Rationale: 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%
Answer A
Answer: (A) 12 1⁄2
Question: 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?
(A) 50
(B) 49
(C) 53
(D) 54
(E) 51
Rationale: 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
= 51
Answer is E.
Answer: (E) 51
Question: By selling an article at Rs.300, a profit of 25% is made. Find its cost price?
(A) s.486
(B) s.455
(C) s.240
(D) s.480
(E) s.489
Rationale: SP = 300
CP = (SP)*[100/(100+P)]
= 300* [100/(100+25)]
= 300* [100/125]
= Rs.240
Answer: C
Answer: (C) s.240
Question: 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?
(A) 1:3
(B) 3:4
(C) 2:5
(D) 3:7
(E) 2:1
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
5000 : 15000 => 1:3
ANSWER:A
Answer: (A) 1:3
Question: 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?
(A) 114
(B) 126
(C) 134
(D) 144
(E) None of these
Rationale: 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) = 126. Answer : Option B
Answer: (B) 126
Question: 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
(A) 5,00,000 kg
(B) 4,00,000 kg
(C) 4,50,000 kg
(D) None of these
(E) Cannot be determined
Rationale: 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 = 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 = 400000 kg hematite.
Answer: Option B
Answer: (B) 4,00,000 kg
Question: 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?
(A) 11
(B) 12
(C) 15
(D) 16
(E) 17
Rationale: 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.
C
Answer: (C) 15
Question: If the largest three digit number is subtracted from the smallest five digit number, then the remainder is
(A) 9000
(B) 9001
(C) 90001
(D) 9009
(E) NOne
Rationale: Sol.
Required number = (10000 - 999) = 9001.
Answer B
Answer: (B) 9001
Question: 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 ?
(A) 4
(B) 8
(C) 5
(D) 2
(E) 9
Rationale: 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: B
Answer: (B) 8
Question: P is a prime number. If 6p is between 15 and 95, which of the following T can be a value of 7p + 2?
(A) T=15
(B) T=79
(C) 121
(D) 65
(E) 21
Rationale: [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.B
Answer: (B) T=79
Question: 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?
(A) x + 1
(B) 3x + 3
(C) 5x + 1
(D) 5x + 4
(E) 6x + 8
Rationale: 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 E.
Answer: (E) 6x + 8
Question: 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?
(A) 19
(B) 29
(C) 39
(D) 49
(E) 59
Rationale: let the average after 17th inning =x
Then average after 16th inning=(x-3)
Therefore 16(x-3)+87=17x
Therefore x=39
ANSWER:C
Answer: (C) 39
Question: 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?
(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
Rationale: In 48 hours Pat's watch will gain an extra 48/2*10 = 240 seconds.
In 48 hours Kim's watch will lose 48/3*6 = 96 seconds.
Hence the difference will be 240 + 96 = 336 seconds.
Answer: E.
Answer: (E)  5 min 36 sec
Question: 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?
(A) 10 meters
(B) 25 meters
(C) 45 meters
(D) 15 meters
(E) 35 meters
Rationale: 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 = 35 m.
Choice E
Answer: (E) 35 meters
Question: 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
(A) 26
(B) 40
(C) 29.25
(D) 27
(E) None of the above
Rationale: 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 C
Answer: (C) 29.25
Question: If x^2 + 1/x^2 = √20 what is the value of x^4 + 1/x^4 ?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = √20 andSQUAREboth sides:
(x² + 1/x²)²= 20
So, (x² + 1/x²)(x² + 1/x²) = 20
Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 20
Simplify: x⁴ + 1/x⁴ = 18
Answer: E
Answer: (E) 18
Question: 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?
(A) 2.86
(B) 2.88
(C) 2.89
(D) 2.834
(E) 2.81
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer: B
Answer: (B) 2.88
Question: 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?
(A) 56%
(B) 50%
(C) 57%
(D) 10%
(E) 80%
Rationale: 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: B
Answer: (B) 50%
Question: 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.
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: 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:B
Answer: (B) 21
Question: 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???
(A) 40
(B) 45
(C) 50
(D) 60
(E) 15
Rationale: 15 men using chain rule
ANSWER:E
Answer: (E) 15
Question: In expressing a length 810472 km as nearly as possible with three significant digits, find the percentage error.
(A) 0.034
(B) 0.024
(C) 0.352
(D) 0.063
(E) 0.026
Rationale: Error = (81.5 – 81.472)km = 0.028.
Required percentage = [(0.028/81.472)*100]% = 0.034%.
Answer A.
Answer: (A) 0.034
Question: 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?
(A) 1/8!
(B) 3!/8!
(C) 5!/8!
(D) 1/3!
(E) 1/2!
Rationale: 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: D
Answer: (D) 1/3!
Question: 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?
(A) 240
(B) 65
(C) 110
(D) 130
(E) 200
Rationale: 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 = 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 = 65
Answer: Option B
Answer: (B) 65
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 6 m wide at the top and 4 m wide at the bottom and the area of cross-section is 10290 sq m, the depth of cannel is?
(A) 258
(B) 260
(C) 262
(D) 264
(E) 266
Rationale: 1/2 * d (6+4)
= 10290
d = 258
Answer: A
Answer: (A) 258
Question: How many four-digit numbers that do not contain the digits 2, 3, 4, or 6 are there?
(A) 1025
(B) 1080
(C) 2096
(D) 3040
(E) 4200
Rationale: 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 B.
Answer: (B) 1080
Question: 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?
(A) 2299
(B) 2699
(C) 2670
(D) 6725
(E) 8000
Rationale: CP = SP * (100/(100 + profit%))
= 8800(100/110) = Rs. 8000
Answer:E
Answer: (E) 8000
Question: 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?
(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
Rationale: 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
A)
Answer: (A) 3 1/5 Km
Question: Calculate the average of first 16 even numbers is?
(A) 16
(B) 15
(C) 12
(D) 17
(E) 11
Rationale: Explanation:
Sum of 10 even numbers = 16 * 17 = 272
Average = 272/16 = 17
Answer: Option D
Answer: (D) 17
Question: 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?
(A) 9:8
(B) 15:8
(C) 27:8
(D) 8:9
(E) 8:15
Rationale: 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:C
Answer: (C) 27:8
Question: A paper is in a square form whose one side is 20 cm. Two semi circles are drawn on its opposites as diameters. If these semi circles are cut down what is the area of the remaining paper?
(A) 8.79
(B) 8.77
(C) 8.75
(D) 8.72
(E) 8.723
Rationale: (5 * 3.5)/2 = 8.75
Answer: C
Answer: (C) 8.75
Question: 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?
(A) 640
(B) 277
(C) 500
(D) 297
(E) 435
Rationale: 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.
Answer: A
Answer: (A) 640
Question: 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?
(A) 22
(B) 60
(C) 27
(D) 21
(E) 19
Rationale: 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=B
Answer: (B) 60
Question: If ten persons sit in a row, then the probability that three particular persons are always together is?
(A) 1/5
(B) 1/4
(C) 1/9
(D) 1/6
(E) 1/15
Rationale: 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:E
Answer: (E) 1/15
Question: "A" and "B" run around a circular track starting from the same point simultaneously in the same direction. "A" meets "B" for the first time when "A" is exactly in the middle of his 5th round. If "A" is faster than "B" and take 70 seconds to complete 1 lap, how long will B take to complete 1 lap?
(A) 90 seconds
(B) 54.44 seconds
(C) 110 seconds
(D) 63 seconds
(E) 77 seconds
Rationale: A is faster than B. Every second he increases distance between A and B. They will meet for the first time again when he increases distance between them by one full circle. (Say the lap is of 100m. He keeps increasing distance between them. When he is 90 m ahead of him, it is the same as 10 m behind him because they are moving in a circle. Finally when he is 100 m ahead of him, he is exactly 1 lap ahead and hence both are at the same point).
A takes 70 secs for one full lap. So he covers 4.5 laps in exactly 70*4.5 = 315 seconds.
In 315 secs, B completes 3.5 laps. So for each lap, he takes 315/3.5 = 90 secs
Answer (A)
Answer: (A) 90 seconds