RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Aishwarya was first to board to her flight to delhi.
She forgot her seat number and picks a random seat for herself.
After this, every single person who get to the flight sits on his seat if its available else chooses any available seat at random.
Abhishek is last to enter the flight and at that moment 99/100 seats were occupied.
Whats the probability what Abhishek gets to sit in his own seat ?
A.1/2
B.1/5
C.2/9
D.4/7
Answer: A.1/2
Explanation: A
1/2
one of two is the possibility
1. If any of the first 99 people sit in Abhishek seat, Abhishek will not get to sit in his own seat.
2. If any of the first 99 people sit in Aishwarya's seat, Abhishek will get to sit in his seat.
Question: A diagonal of a polygon is an segment between two non-adjacent vertices of the polygon. How many diagonals does a regular 10-sided polygon have?
A. 875
B. 35
C. 1425
D. 2025
Answer: B. 35
Explanation: There's a direct formula for this.
Number of diagonals in a regular polygon = [n*(n-3)] / 2, n = number of sides of the regular polygon.
Here, n = 10.
Plugging it in, we get 35 diagonals!
Answer (B).
Question: To mail a package, the rate is 20 cents for the first pound and 5 cents for each additional pound. Two packages weighing 3 pounds and 5 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
A.Combined, with a saving of 5 cents
B.Separately, with a saving of 5 cents
C.Combined, with a saving of 15 cents
D.Separately, with a saving of 10 cents
Answer: C.Combined, with a saving of 15 cents
Explanation: 3 pounds = 1*20+2*5 = 30
5 pounds = 1*20+4*5 =40
total = 70
8 pound = 1*20+7*5 = 55
dif. 15
Answer : C
Question: Every day Daniel drives 64 miles back from work. On Sunday, Daniel drove all the way back from work at a constant speed of x miles per hour. On Monday, Daniel drove the first 32 miles back from work at (2x) miles per hour, and the rest of the way at (x/2) miles per hour. The time it took Daniel to drive back from work on Monday is longer than the time it took him to drive back from work on Sunday by what percent?
A.15%
B.25%
C.35%
D.45%
Answer: B.25%
Explanation: Let's TEST X = 4....
On Sunday, Daniel drove 64 miles at 4 miles/hour.
D = (R)(T)
64 = (4)(T)
64/4 = 16 = T
It takes 16 hours to drive home
On Monday, Daniel drove the first 32 miles at (2)(4) = 8 miles/hour and the rest of the way (32 miles) at 4/2 = 2 miles/hour
D = (R)(T)
32 = (8)(T)
32/8 = 4 = T
It takes 4 hours for the first part
D = (R)(T)
32 = (2)(T)
32/2 = 16 = T
It takes 16 hours for the second part
Total time to drive home on Monday = 4+16 = 20 hours
We're asked by what percent 20 hours is greater than 16 hours.
20/16 = 1.25, so it is 25% greater.
B
Question: Three fifth of the square of a certain number is 126.15. What is the number?
A.210.25
B.75.69
C.14.5
D.145
Answer: C.14.5
Explanation: Let the number be X
Given, 3/5 X^2 = 126.5
X^2 = 126.15 * 5/3
X^2 = 42.05 * 5 = 210.25
X = 14.5
Answer C.
Question: For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 980, what is the maximum possible sum of the length of x and the length of y?
A.16
B.14
C.18
D.10
Answer: A.16
Explanation: we know that : x > 1, y > 1, and x + 3y < 980,
and it is given that length means no of factors.
for any value of x and y, the max no of factors can be obtained only if factor is smallest no all factors are equal.
hence, lets start with smallest no 2.
2^1 =2
2^2 =4
2^3=8
2^4=16
2^5=32
2^6=64
2^7=128
2^8=256
2^9=512
2^10 =1024 (it exceeds 1000, so, x can't be 2^10)
so, max value that X can take is 2^9 , for which has length of integer is 9.
now, since x =512 ,x+3y<980
so, 3y<468
==> y<156
so, y can take any value which is less than 162. and to get the maximum no of factors of smallest integer, we can say y=2^7
for 2^7 has length of integer is 7.
SO, combined together : 9+7 = 16.
A
Question: If |z|/w = 5,which of the following must be true?
A.z = -5w
B.z = 5w
C.z^2 = 25w^2
D.z^2 = 25w^3
Answer: C.z^2 = 25w^2
Explanation: |z|/w = 5.
|z| = 5w.
Then z = 5w or -5w and so z^2 = 25w^2.
The answer is C.
Question: .3+33+333+33.3=?
A.362.33
B.399.6
C.702.33
D.702
Answer: B.399.6
Explanation: .3
33
333
33.3
----------
399.6
----------
Answer is B
Question: Which of the following will divide evenly into 347,406,520?
A.4
B.11
C.9
D.3
Answer: A.4
Explanation: Rule:
4: Last two digits should be divisible by 4
the last two digits are 00, which are divisible by 4
Answer: A
Question: (1.1 + 1.1 + 1.1 + 1.1) x 1.1 x 1.1 = ? = ? x 0.121
A.54
B.33
C.44
D.22
Answer: C.44
Explanation: Explanation:
? = (1.1 + 1.1 + 1.1 + 1.1) x 1.1 x 1.1/0.121
= (4.4 x 1.1 x 1.1)/0.121 = 44
Answer: Option C
Question: Age of Raghav who is 30 years old is 3/5 times of Ram and Ram is older than Mohan by 35 years.If vijay's age is just between the age of Ramesh and and Mohan and Ramesh is 21 years old.What is age of vijay?
A.20
B.25
C.18
D.17
Answer: C.18
Explanation: Solution:
Raghav's age=3/5 Ram's age
=>30=3/5 Ram's age
=>Ram's age=30/3 * 5=50
Ram's age=Mohan's age +35
=>Mohan's age=Ram's age -35
=>Mohan's age=50-35
=>Mohan's age =15
Vijay's age=(Ramesh's age +Mohan's age)/2
=>Vijay's age=(21+15)/2
=>Vijay's age=18 years.
Answer C
Question: A man walking at the rate of 6km per hour crosses a square field diagonally in 9 seconds the area of the field is
A.110sq.m
B.111.5aq.m
C.112.5sq.m
D.114sq.m
Answer: C.112.5sq.m
Explanation: Explanation:
Distance covered in 9 seconds = (6×1000/3600)×9 = 15m
Diagonal of square field = 15m
Side of square =a then diagonal of that square= √2 a
Hence area of the square = a2= (152)/2 =112.5 sq.m
Answer: Option C
Question: A is half good a work man as B and together they finish a job in 26 days. In how many days working alone B finish the job?
A.98 days
B.21 days
C.17 days
D.39 days
Answer: D.39 days
Explanation: WC = 1:2
2x + x = 1/26 => x = 1/78
2x = 1/78 => 39 days
Answer:D
Question: What approximate value should come in place of (x) in the following question?
139.25 + 223.94 / 4.002 = x
A.195
B.276
C.188
D.166
Answer: A.195
Explanation: Explanation:
Given: 139.25 + 223.94 / 4.002 = x
Approximate 139.25 as 140, 223.94 as 224, 4.002 as 4,
we get, x = 140 + 224 / 4 = 140 + 56 = 196 =>195
ANSWER: A
Question: A and B can do a piece of work in 6 days, B and C in 7 days, C and A in 8 days. How long will C take to do it?
A.12.6 days
B.14.4 days
C.15.2 days
D.16.8 days
Answer: D.16.8 days
Explanation: 2c = 1/7 + 1/8 – 1/6 = 20/168 = 10/84
c = 5/84 => 84/5 = 16.8 days
The answer is D.
Question: Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 5/7 and that of Ravi is 1/5. Find the probability that both of them are selected.
A.2/35
B.2/3
C.7/35
D.1/7
Answer: D.1/7
Explanation: Let A be the event that Ram is selected and B is the event that Ravi is selected.
P(A) = 5/7
P(B) = 1/5
Let C be the event that both are selected.
P(C) = P(A) x P(B) as A and B are independent events:
= 5/7 x 1/5 = 1/7
ANSWER:D
Question: Three business people who wish to invest in a new company. Each person is willing to pay one third of the total investment. . After careful calculation, they realize that each of them would pay $ 7000 less if they could find two more equal investors. How much is the total investment in the new business.
A.a)	$ 64,000
B.b)	$ 54,000
C.c)	$ 21,000
D.d)	$ 52,500
Answer: D.d)	$ 52,500
Explanation: Initially each invest in x. Hence total investment is 3x.
Total investment is also 5(x-7000).
3x = 5(x-7000)
x= 5*7000/2 = 17500
3x = 52500 and the answer is D.
Question: Ron walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long W would it have taken for him to walk both ways.
A.8 h 45 min
B.7 h 45 min
C.6 h 45 min
D.5 h 30 min
Answer: A.8 h 45 min
Explanation: 1.Walking to to a viewpoint+Driving back=6 hours 45 minutes
2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes.
3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes.
4.Walking to to a viewpoint+Walking back W=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes.
Answer: A.
Question: Can anyhow help me with an easy solution for this
3, 4, 81, 4, 5, 121, 6, 7, ?
A.144
B.121
C.256
D.225
Answer: D.225
Explanation: 3, 4, 81, 4, 5, 121, 6, 7, ?
3+4=7 and 7+2=9 and 9^2=81
4+5=9 and 9+2=11 and 11^2=121
6+7=13 and 13+2=15 and 15^2=225
ANSWER:D
Question: If the range E of the six numbers 4,3,14,7,10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?
A.	0
B.	2
C.	12
D.	13
Answer: D.	13
Explanation: The range E of a set is the difference between the largest and smallest elements of a set.
Without x, the difference between the largest and smallest elements of a set is 14-3=11<12, which means that in order 12 to be the range of the set x must be either the smallest element so that 14-x=12 ---> x=2 OR x must the largest element so that x-3=12 --> x=15.
The the difference between the greatest possible value of x and least possible value of x is 15-2=13.
Answer: D.
Question: The mean of 50 observations is 200. But later he found that there is decrements of 47 from each observations. what is the the updated mean is ?
A.165
B.185
C.153
D.198
Answer: C.153
Explanation: 153
Answer is C
Question: Car R and Car Y traveled the same 80-mile route. If Car R took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car R, how many hours did it take Car Y to travel the route?
A. 2/3
B. 1
C. 4/3
D. 8/5
Answer: C. 4/3
Explanation: The speed of car R is (distance)/(time) = 80/2 = 40 miles per hour.
The speed of car Y = 3/2*40 = 60 miles per hour --> (time) = (distance)/(speed) = 80/60 = 4/3 hours.
Answer: C.
Or: to cover the same distance at 3/2 as fast rate 2/3 as much time is needed --> (time)*2/3 = 2*2/3 = 4/3 hours.
Answer: C.
Question: A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
A.10
B.6
C.5
D.4
Answer: C.5
Explanation: Explanation:
Speed of the motor boat =15 km/hr
Let speed of the stream =v
Speed downstream =15+v km/hr
Speed upstream =15-v km/hr
Time taken downstream =30/15+v
Time taken upstream =30/15-v
Total time =30/15+v + 30/15-v
Given that total time is 4 hours 30 minutes
=4 1/2hour =9/2hour
ANSWER IS C
Question: Find the missing number in the series.
2 , 3 , 6 , 0 , 10, -3 , 14...
A.-6
B.8
C.7
D.67
Answer: A.-6
Explanation: Explanation:
There are two series in the question
1.	Add 4 : 2+3 = 6, 6+4 = 10
2.	Subtract 3 : 3-3 = 0, 0-3 - -3
Thus, following the series:
-3-3 = -6
ANSWER: A
Question: Solve the given two equations and find the inequality of X and Y.(a) x^2-7x+12=0 and (b) y^2+y-12=0
A.If x>y
B.If x>=y
C.If x < y
D.If x<=y
Answer: B.If x>=y
Explanation: Solution:-
X=4,3
Y=-4,3
So, X>=Y
B
Question: A car travels at a speed of 65 miles per hour. How far will it travel in 7 hours?
A.125 miles
B.225 miles
C.455 miles
D.425 miles
Answer: C.455 miles
Explanation: During each hour, the car travels 65 miles. For 7 hours it will travel
65 + 65 + 65 + 65 + 65+ 65 + 65 = 7 × 65 = 455 miles
correct answer is C) 455 miles
Question: Triangle ATriangle B are similar triangles with areas 1536 units square and 1734 units square respectively. The ratio of there corresponding height would be
A.9:10
B.17:19
C.23:27
D.16:17
Answer: D.16:17
Explanation: Let x be the height of triangle A and y be the height of triangle of B.
since triangles are similar, ratio of area of A and B is in the ratio of x^2/y^2
Therefore, (x^2/y^2)=1536/1734
(x^2/y^2)=(16*16*6)/(17*17*7)
(x^2/y^2)=16^2/17^2
x/y=16/17
Ans=D
Question: Kyle, David, and Catherine each try independently to solve a problem. If their individual probabilities for success are 1/3, 2/7 and 5/9, respectively, what is the probability that Kyle and Catherine, but not David will solve the problem?
A.35/189
B.33/129
C.25/189
D.24/113
Answer: C.25/189
Explanation: P(Kyle will solve)=1/3
P(David will not solve)= 1 - 2/7 = 5/7
P(Catherine will solve) = 5/9
P= (1/3)*(5/7)*(5/9) = 25/189
Answer:C
Question: A and B invests Rs.5000 and Rs.6000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
A.2:3
B.82:31
C.32:45
D.34:89
Answer: A.2:3
Explanation: A : B
(5000*4)+(2500*8) : (6000*6)+(4000*6)
40000 : 60000
2 : 3
Answer:A
Question: A car traveled from San Diego to San Francisco at an average speed of 63 miles per hour. If the journey back took twice as long, what was the average speed of the trip?
A.24.
B.32.
C.36.
D.42.
Answer: D.42.
Explanation: Let the time taken be = x
One way distance = 63x
Total distance traveled = 2 * 63x = 126x
Total time taken = x + 2x = 3x
Average speed = 126x/3x = 42
Answer: D
Question: If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?
A.Rs. (xd/y)
B.Rs. xd
C.Rs. (yd/x)
D.Rs. yd
Answer: C.Rs. (yd/x)
Explanation: Explanation :
cost of x metres of wire = Rs. d
cost of 1 metre of wire = Rs.(d/x)
cost of y metre of wire = Rs.(y × (d/x)) = Rs. (yd/x).. Answer : Option C
Question: Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 14 miles, how many miles was Mike's ride?
A.28
B.30
C.32
D.34
Answer: D.34
Explanation: The cost of Annie's ride was 2.5+5+(0.25*14) = $11
Let x be the distance of Mike's ride.
The cost of Mike's ride is 2.5+(0.25*x) = 11
0.25*x = 8.5
x = 34 miles
The answer is D.
Question: The rowing athletes in a rowing conference voted for coach of the year. Each rower who voted chose exactly 3 coaches to vote for among the 36 coaches in the conference. If each of the 36 coaches received exactly 5 votes (a 36 way tie), how many rowers voted for coach of the year?
A.60
B.70
C.75
D.84
Answer: A.60
Explanation: There were 36*5 = 180 total votes made. If each voter picked 3 coaches, there were 180/3 = 60 voters. A
Question: A seller uses 900 gm in place of one kg to sell his goods. Find
his actual % profit or loss When he sells his articles at 5 % profit
on cost price ?
A.15.5 %
B.16.5 %
C.16.67 %
D.17 %
Answer: C.16.67 %
Explanation: Explanation :
=[100-x]*z/y-100
=[100+5]1000/900-100=16.67 %
Answer : C
Question: Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
A.Rs. 1(2/7)
B.Rs. 2(1/9)
C.Rs. 3(2/11)
D.Rs. 2(2/13)
Answer: B.Rs. 2(1/9)
Explanation: Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)
B
Question: By selling an shirt for $300, a shop keeper gains 20% . During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is:
A.2
B.14
C.8%
D.12
Answer: C.8%
Explanation: C
8%
Marked price = $300
C.P. = 100/120 * 300 = $250
Sale price = 90% of $300 = $270
Required gain % = 20/250 * 100 = 8%.
Question: The probability that A will not tell truth is 75% and the probability that B will tell truth is 60%.what is the probability that an incident described by them is true?
A.10%
B.12%
C.15%
D.17%
Answer: C.15%
Explanation: A truth....> 25%
B truth.....> 60%
a&b truth...> 0.25*0.6=0.15=15%
ANSWER:C
Question: A and B Started a business with Rs.15000 and 12000 respectively. After 6 months B puts Rs.1000 more in his capital while after 8 months A puts Rs.5000 more in his capital. If there is a profit of Rs.35,000 after one year then B will get
A.Rs.15,000
B.Rs.18,000
C.Rs.16,000
D.Rs.20,000
Answer: A.Rs.15,000
Explanation: Ratio of A and B
=15000*8+20,000*4 : 12000*6+1300*6
= 4 :3
Then B will get
= 3/7*35,000
=15,000
ANSWER:A
Question: How long does a train 130 m long running at the speed of 65 km/hr takes to cross a bridge 150 m length?
A.15.7 sec
B.15.1 sec
C.15.5 sec
D.17.1 sec
Answer: C.15.5 sec
Explanation: Speed = 65 * 5/18
= 18.1 m/sec
Total distance covered
= 130 + 150 = 280 m.
Required time = 280/18.1 '
= 15.5 sec.
Answer:C
Question: Find the value of 72519 x 9999 = m?
A.723437481
B.725465481
C.625117481
D.725117481
Answer: D.725117481
Explanation: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Question: In how many ways can 4 rings be arranged in 5 finger (no finger has more than 1 ring)?
A.5C4
B.5P4
C.(5C4)4!
D.B and C
Answer: C.(5C4)4!
Explanation: No. of ways of selecting 4 fingers from 5(considering a non-mutant) = 5C4.
No. of ways of arranging the 4 rings= 4!
Answer: (5C4).4!
ANSWER:C
Question: If the number 517*326 is completely divisible by 7, then the smallest whole number in the place of * will be:
A.3
B.1
C.2
D.4
Answer: D.4
Explanation: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 6) = (24 + x), which must be divisible by 7.
x = 4.
D
Question: What approximate value should come in place of question mark (?) in the following equation?
of 857 of 14% – 5.6 × 12.128 = ?
A.48
B.36
C.60
D.52
Answer: D.52
Explanation: ? = 857 of 14% – 5.6 × 12.128
≈ 857 of 14% – 5.6 × 12 ≈ 120 – 67 ≈ 52
Answer D
Question: How many numbers greater than 5000 can be formed with four of the digits 3, 4, 5, 6, 7 where no digit can be repeated.
A.62
B.72
C.82
D.90
Answer: B.72
Explanation: 3*4*3*2=72
ANSWER:B
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 32 cm?
A.276 sq.cm
B.268 sq.cm
C.640 sq.cm
D.297 sq.cm
Answer: C.640 sq.cm
Explanation: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE = √(625 - 225)
= √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus
= 1/2 * d1d2
= 1/2 * 40 * 32
= 640 sq.cm.
Answer:C
Question: By selling a bat for Rs.450/- a man loses 10% what is that bat cost price
A.s.600/-
B.s.500/-
C.s.700/-
D.s.780/-
Answer: B.s.500/-
Explanation: 90 % ------> 450 (90 * 5 = 450)
100 % ------>500 (100 * 5 = 500)
Cost price = Rs.500/-
B)
Question: The sum of the first 40 positive even integers is 1,640. What is the sum of the first 40 odd integers?
A.1500
B.1600
C.1400
D.1200
Answer: B.1600
Explanation: Sum of first n even numbers = n(n+1) =1640
Sum of first n odd numbers = n^2 = 40*40 = 1600 (here n=40)
Answer : B
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 42, the dividend is:
A.5330
B.5336
C.5343
D.4452
Answer: D.4452
Explanation: Divisor = (5 * 42) = 210
= 10 * Quotient = Divisor
=> Quotient = 210/10 = 21
Dividend = (Divisor * Quotient) + Remainder
Dividend = (210 * 21) + 42 = 4452.
D
Question: If a = (1/2)b and c = 8a, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of a ?
A. a + 4
B. (11/3)a
C. 4a
D. (4 1/7)a
Answer: B. (11/3)a
Explanation: Official Answer: B
The average of the three variables isa + b + c/3. However, we need to solve in terms of a, which means we must convert b and c into something in terms of a.
Were told that a =1/2b, which is equivalent to b = 2a. We can plug that in and simplify the average to:a + 2a + c/3
We also know that c = 8a, which we can plug directly into the average expression:
a + 2a + 8a/3
= 11a/3=(11/3)a , choiceB.
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
A.33 1/9%
B.33 1/2%
C.33 1/3%
D.33 5/3%
Answer: C.33 1/3%
Explanation: 675 ---- 225
100 ---- ? => 33 1/3%
Answer:C
Question: 5358 x 56 = ?
A.272258
B.272358
C.300048
D.274258
Answer: C.300048
Explanation: 5358 x 51	= 5358 x (50 + 6)
= 5358 x 50 + 5358 x 6
= 267900 + 32148
= 300048.
C)
Question: If @ is a binary operation defined as the difference between an integer n and the product of n and 5, then what is the largest positive integer n such that the outcome of the binary operation of n is less than 10?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: the product of n and 5 =5n..
the difference between an integer n and the product of n and 5=5n-n=4n..
the outcome of the binary operation of n is less than 10?
so 4n<10...
max value that n can take as an integer is 2
ANSWER:B
Question: If 5x = 3y and xy ≠ 0, what is the ratio of 1/5*x to 1/6*y ?
A. 25/6
B. 36/25
C. 18/25
D. 5/6
Answer: C. 18/25
Explanation: 5x = 3y => x/y = 3/5
1/5*x to 1/6*y = x/y * 6/5 =(3/5)* (6/5)=18/25
Ans: C
Question: In a group of cows and chickes, the number of legs was 14 more than twice the number of heads . the number of cows was:
A.7
B.5
C.11
D.12
Answer: A.7
Explanation: no of cows x and their legs 4x, no of chicke y and their legs 2y, total no of legs= 4x + 2y, total nof heads = x + y, the no of legs was 14 mor than twice the number of heads. 2x + 2y +14 = 4x + 2y, 14= 4x-2x+ 2y -2y, therefore, 14 = 2x , x = 7, correct answer : (A)
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles.
A.3566
B.5467
C.4132
D.3526
Answer: C.4132
Explanation: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
Answer: Option C
Question: Arun obtained 76, 65, 82, 67 and 85 marks (out in 100) in English, Mathematics, Chemistry, Biology and Physics. What is his average mark?
A.53
B.54
C.72
D.75
Answer: D.75
Explanation: Explanation:
Average mark = 76+65+82+67+85/5=375/5=75
Answer: Option D
Question: How many 6 digit number contain number 4 ?
A.317608
B.327608
C.337608
D.427608
Answer: D.427608
Explanation: total 6 digit no. = 9*10*10*10*10*10 = 900000
not containing 4 = 8*9*9*9*9*9 = 472392
total 6 digit number contain 4 = 900000 - 472392 = 427608
ANSWER:D
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability w that the World Series will consist of fewer than 7 games?
A. 12.5%
B. 25%
C. 31.25%
D. 68.75%
Answer: D. 68.75%
Explanation: In order to determine the probability that the World Series will last less than 7 games, we can first determine the probability w that the World Series WILL last exactly 7 games and then subtract this value from 1.
In order for the World Series to last exactly 7 games, the first 6 games of the series must results in 3 wins and 3 losses for each team.
Let's analyze one way this could happen for Team 1:
Game 1 Game 2 Game 3 Game 4 Game 5 Game 6
T1 Wins T1 Wins T1 Wins T1 Loses T1 Loses T1 Loses
There are many other ways this could happen for Team 1. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for Team 1 to win 3 games and lose 3 games in the first 6 games.
Logically, there are also 20 ways for Team 2 to win 3 games and lose 3 games in the first 6 games.
Thus, there are a total of 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is:
Thus the probability that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D.