RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: An gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively. What is the probability that the plane is hit when all the four shots are fired?
A.0.6976
B.0.7013
C.0.789
D.0.8356
Answer: A.0.6976
Explanation: Required probability:
=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)
=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002
=0.6976=0.6976
Edit: Thank you Vaibhav for providing an alternative method.
Alternate Method:
probability that the plane is hit when all the four shots are fired,
P=1−probability of not hitting the targetP=1−probability of not hitting the target
=1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9)
=1−0.3024=1−0.3024
=0.6976
A
Question: Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 1/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
A.3/140
B.1/280
C.27/280
D.3/35
Answer: C.27/280
Explanation: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*1/8*5/7 + 1/5*7/8*2/7 + 4/5*1/8*2/7 = 27/280.
Answer: C
Question: From a group of 3 MEN and 3 WOMEN, 4 ADULTS are to be randomly selected. What is the probability that equal numbers of men and women will be selected?
A.1/5
B.2/5
C.3/5
D.4/5
Answer: C.3/5
Explanation: Using the first example, here is the probability of THAT EXACT sequence occurring:
MMWW = (3/6)(2/5)(3/4)(2/3) = 36/360 = 1/10
Each of the other 5 options will yield the exact SAME probability....
eg
MWMW = (3/6)(3/5)(2/4)(2/3) = 36/360 = 1/10
So we have 6 different options that each produce a 1/10 chance of occurring.
6(1/10) = 6/10 = 3/5
Final Answer:
C
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get ?
A.57%
B.60%
C.65%
D.90%
Answer: A.57%
Explanation: Solution
Total number of votes polled= (1136 + 7636 + 11628) = 20400.
∴ Required percentage= ( 11628/20400x 100)%= 57%
Answer A
Question: (160)^2 - (161)^2 =
A.1
B.100
C.229
D.323
Answer: D.323
Explanation: Using the formula:
(a+1)^2 - a^2 = 2a+1
So, Answer = 161*2 + 1
= 322+1 = 323 = Answer = D
Question: At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 400-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $200?
A.1,108
B.3,300
C.2,108
D.2,124
Answer: B.3,300
Explanation: We have $200 and we have to maximize the number of hot dogs that we can buy with this amount.
Let's try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money, which in this case is 400 for $22.95.
For the sake of calculation, let's take $23. 23x8 gives 184 ,i.e. a total of 400x8 = 3200 hot dogs . We are left with ~$16. Similarly, let's use $3 for calculation. We can buy 5 20-pack hot dogs (3x5), a total of 20x5 = 100 hot dogs. So we have 3300 hot dogs.
2108 looks far-fetched (since we are not likely to be left with > $1.55). Hence, (b) 3300 (ANSWER B)
Question: A bike covers a certain distance at the speed of 62km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?
A.85 km/h
B.82.66 km/h
C.87.67 km/h
D.90.25 km/h
Answer: B.82.66 km/h
Explanation: Ans.(B)
Sol. Total distance = 62 × 8 = 496 km
Now speed = 496/6 = 82.66 km/h
Question: Cindy paddles her kayak upstream at c kilometers per hour, and then returns downstream the same distance at n kilometers per hour. How many kilometers upstream did she travel if she spent a total of p hours for the round trip?
A.cnp
B.cn/p
C.(c + n)/p
D.cnp/(c + n)
Answer: D.cnp/(c + n)
Explanation: let t1 and t2 be the time taken to row upstream and downstream respectively
now,
t1=distance/speed=d/c
similarly,
t2=d/n (as same distance has to be rowed)
also,
t1+t2=p
therefore,
p=(d/c)+(d/n)
=d(c+n)/cn
d=pcn/(c+n)=D
Question: Three workers have a productivity ratio of 2 to 4 to 8. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?
A.20 to 3
B.6 to 1
C.5 to 1
D.1 to 6
Answer: A.20 to 3
Explanation: The fastest worker who does 8 units of job worked for all 10 hours, so he did 8*10=80 units of job;
The slowest worker who does 2 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 2*6=12 units of job;
The ratio thus is 80 to 12, or 20 to 3.
Answer: A.
Question: There are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then A:D will be?
A.1 : 2
B.3 : 5
C.5 : 7
D.6 : 11
Answer: A.1 : 2
Explanation: Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6
∴A∶B∶C∶D= 3 : 4 : 5 : 6.
Thus, A : D = 3 : 6 or, 1 : 2
A
Question: If (y - 1)(z - 3) + 5(y - 1) = 0, then which of the following must be true?
A. y = -4 and z = -3
B. y = 4 or z = -3
C. y = -4 or z = 3
D. y = 1 and z = 3
Answer: D. y = 1 and z = 3
Explanation: factor out:
(y-1)(z-3+5)=0
(y-1) (z+2) = 0
So by checking options we get ,
Ans - D
Question: Ravi's brother is 3 years senior to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, what were the ages of Ravi's father and mother respectively when his brother was born ?
A.32 years, 23 years
B.32 years, 29 years
C.35 years, 29 years
D.35 years, 33 years
Answer: A.32 years, 23 years
Explanation: Explanation:
When Ravi's brother was born, let Ravi's father's age = x years and mother's age = y years.
Then, sister's age = (x - 28) years. So, x - 28 = 4 or x = 32.
Ravi's age = (y - 26) years. Age of Ravi's brother = (y - 26 + 3) years = (y - 23) years.
Now, when Ravi's brother was born, his age = 0 i.e. y - 23 = 0 or y = 23.
Answer: Option A
Question: In expressing a length of 81.472 km as nearly as possible with the three significant digits, find the percentage error
A.0.35%
B.0.34%
C.0.034%
D.0.035%
Answer: C.0.034%
Explanation: Explanation:
Error = (81.5 - 81.472) = 0.028
Required percentage =
0.028/ 81.472×100=0.034
Option C
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
A.10 kmph
B.13 kmph
C.65 kmph
D.55 kmph
Answer: A.10 kmph
Explanation: Speed of the boat in still water
= (60+80)/2
= 70 kmph. Speed of the stream
= (80-60)/2
= 10 kmph.
Answer: A
Question: There are 400 wolfs at a large zoo. The number of wolfs is 4 times the number of all the other animals combined. How many more wolfs are there than non wolfs animals at the zoo?
A.450
B.420
C.400
D.390
Answer: D.390
Explanation: Answer is D.
Total wolfs= 400 = 4 * Other Animals (X)
or X = 10.
So, Difference in wolfs and X = 400-10 = 390.
Question: Which of the following is not a leap year?
A.1200
B.800
C.700
D.2000
Answer: C.700
Explanation: Explanation :
1. Every year divisible by 4 is a leap year, if it is not a century.
2. Every 4th century is a leap year, but no other century is a leap year.
800,1200 and 2000 comes in the category of 4th century (such as 400,800,1200,1600,2000 etc).
Hence 800,1200 and 2000 are leap years
700 is not a 4th century, but it is a century. Hence it is not a leap year
Answer : Option C
Question: In a simultaneous throw of 2 dice what is the probability of getting a total of 11?
A.1/4
B.1/18
C.2/11
D.3/13
Answer: B.1/18
Explanation: n(S) = 6*6 = 36
E = {(5,6),(6,5)}
Probability = 2/36 = 1/18
Answer is B
Question: Find the odd man out. 1, 3, 9, 12, 19, 29
A.12
B.9
C.1
D.3
Answer: A.12
Explanation: 12 is an even number. All other given numbers are odd
Answer : Option A
Question: A certain number of men can do a work in 65 days working 6 hours a day. If the number of men are decreased by one-fourth, then for how many hours per day should they work in order to complete the work in 40 days?
A.11
B.12
C.14
D.13
Answer: D.13
Explanation: D
13
Let the number of men initially be x. we have M1 D1 H1= M2 D2 H2
So, x * 65 * 6 = (3x)/4 * 40 * h2
=> h2 = (65 * 6 * 4)/(3 * 40) = 13.
Question: In a certain college, 20% of the boys and 40% of the girls attended the annual college outing. If 35% of all the students are boys, what percent of all the employees went to the outing?
A.33%
B.34%
C.35%
D.36%
Answer: A.33%
Explanation: assume total students =100 in that 35 students are boys ,remaining 65 are girls........
20% of boys(35) =7
40% of girls(65) =26
totally (26+7)=33 mens went to outing...... 33 is 33% in 100
so, the answer is 33%
ANSWER:A
Question: A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
A.7 4/5
B.9 3/5
C.4 1/6
D.7 7/12
Answer: B.9 3/5
Explanation: A + B + C's 1 day's work = 1/4
A's 1 day's work = 1/16
B's 1 day's work = 1/12
Therefore C's 1 day's work = 1/4	- ( A's 1 day's work + B's 1 day's work )
=> C's 1 day's work = 1/4 - ( 1/16 + 1/12 )
=> C's 1 day's work = (12-3-4)/48 = 5/48
So, C alone can do the work in 48/5 = 9 3/5 days.
So correct answer is B
Question: If |4x+6| = 46, what is the sum of all the possible values of x?
A.2
B.-2
C.4
D.-5
Answer: B.-2
Explanation: There will be two cases
4x+6= 46 or 4x+6 = -46
=> x =10 or x= -12
sum of both the values will be -12 +10 = -2
Answer is B
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 60 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
A.17 1/4 min
B.28 1/7 min
C.15 min
D.17 1/8 min
Answer: C.15 min
Explanation: 1/20 + 1/30 - 1/60 = 4/60 = 1/15
15/1 = 15
Answer:C
Question: Mr. David manufactures and sells a single product at a fixed price in a niche market. The selling price of each unit is Rs. 30. On the other hand, the cost, in rupees, of producing x units is 240 + bx + cx2, where b and c are some constants. Mr. David noticed that doubling the daily production from 20 to 40 units increases the daily production cost by 66.66%. However, an increase in daily production from 40 to 60 units results in an increase of only 50% in the daily production cost. Assume that demand is unlimited and that Mr. David can sell as much as he can produce. His objective is to maximize the profit.
How many units should Mr. David produce daily ?
A.130
B.100
C.70
D.150
Answer: B.100
Explanation: Explanation :
Cost price function f(x) = cx2 + bx + 240.
When x = 20, f(20) = 400c + 20b + 240.
=> f(40) = 1600c + 40b + 240
66.67% is 2/3.
=> f(40) – f(20) = 2/3 * f(20).
Substituting f(40) and f(20), we get, 1200c+ 20b =(2/3) * (400c + 20b + 240)
Solving, we get 20b + 2800c = 480.
Now, f(60) = 3600c + 60b + 240.
f(60) – f(40) = ½ * f(40)
Substituting, and solving, we get, 360 + 60b + 2400c = 240 + 60b + 3600c
c = 1/10.
Substituting we get, b = 10.
So, the cost function f(x) = 0.1x2 + 10x + 240.
Selling price = 30 * x. ( Each unit SP is 30)
So, profit = SP – CP = 30x – (0.1x2 + 10x + 240) = -x2/10 + 20x – 240.
For maximum profit, differentiating this should give 0.
dp/dt = 0, dp/dt = -x/5 + 20
20 – x/5 = 0. x= 100.
Also double differentiating d2p / dt2, we get a negative number, so profit is maximum.
So, profit is maximum when 100 units are produced daily.
Answer : B
Question: In a building there are 5 rooms.Each having a equal area .The length of the room is 4m and breadht is 5 m.The height of the rooms are 2m. If 17 bricks are needed to make a square meter then how many bricks are needed to make the floor of a particular room ?
A.320
B.340
C.300
D.310
Answer: B.340
Explanation: Area of the floor = 4m x 5m = 20 m2
17 bricks are needed to make 1 m2 area.
So to make 20 m2 no of bricks needed = 17 x 20 = 340 Answer : B
Question: A boy & a girl appear for an interview against 2 vacant posts in an office. The probability of the boy's selection is 1/5 and that of the girl's selection is 1/3. What is the probability that only 1 of them is selected?
A.1/3
B.2/5
C.2/7
D.3/8
Answer: B.2/5
Explanation: Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected)
= = 2/5
B
Question: Find the no.of ways of arranging the boy and 9 guests at a circular table so that the boy always sits in a particular seat?
A.3!
B.8!
C.7!
D.9!
Answer: D.9!
Explanation: Ans.(D)
Sol. Total number of persons = 10 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 9 places in 9P9 = 9! Ways ... The number of required arrangements = 9! x 1= 9! = 9! ways
Question: Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 50 miles apart. One and a half hours later, they are again 50 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour?
A.a) 66.67-x
B.b) 40-x
C.c) 80-2x
D.d) 120-x
Answer: A.a) 66.67-x
Explanation: Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same.
Here, the two cars approach a distance 50 mi, then move away from each other another distance of 50 miles. That's a total distance of 100 miles in 1.5 hr, which gives a rate of:
R = (100 mi)/(1.5) = 66.67 mph
That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars.
One of the speeds is x, and let's call the other y. We want y.
x + y = 66.67
y = 66.67 - x
Answer =(A)
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 150 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
A.2989
B.2765
C.5800
D.2989
Answer: C.5800
Explanation: Total production of salt by the company in that year
= 5000 + 5150 + 5300 + .... + 6650 = 70050.
Average monthly production of salt for that year
= 70050/12
= 5837.
Answer:C
Question: A and B are 90 km apart they start to move each other simultaneously A at speed 10 and B at 5 km/hr if every hour they double their speed what is distance that A pass until he meet B?
A.30 km
B.40 km
C.50 km
D.60 km
Answer: D.60 km
Explanation: in 2 hours a covers (10+20)=30 km
b covers( 5+10)=15 km, total covered=45
in the next hour they have to cover (90-45) km with the speeds 40km/hr and 20 km/hr respectively
let them take another t hrs to meet
so sum of the distance to be covered by both is 45km
(40*t)+(20*t)=45km
gives t= (3/4) hrs
we need to fid out the distance covered by a
which equals to =30+(40*(3/4))=60 km
ANSWER:D
Question: For all numbers u and v, the operation @ is defined by u@v = u^2 - uv. If xy ≠ 0, then which of the following can be equal to zero?
I. x@y
II. (xy)@y
III. x@(x + y)
A.II
B.I and II
C.I and III
D.II and III
Answer: B.I and II
Explanation: u@v = u^2 - uv=u(u-v).... so u@v will be zero if u=v or u=0.. but u cannot be equal to 0.. as per Q, x and y can take any int value except 0...
now lets look at the choices..
when x=y, it will be 0... so ok...
when we put xy=y, it is possible when x=1 and y any integer... so ok again
when we put x=x+y.... only possibility when y=0 and it is given x and y cannot be 0....so not possible
only l and ll possible
answer: B
Question: Based on this year's costs, an orchard grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to decrease 50% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be:
A.100% less than N
B.200% less than N
C.Equal to N
D.100% greater than N
Answer: D.100% greater than N
Explanation: Correct answer is (D).
This year, the price of a tree is price1=P/N.
If this price decreases by 50% it becomes Price2=P/N*0.5
Then with P dollars, you can grow P/Price2 trees i.e. P/(P/N*0.5) i.e. N/0.5 i.e. 2*N
Which is 100% greater than N.
Question: If S = {1, 2, 3, 4, 5, 6, 7}, how much less is the mean of the numbers in S than the median of the numbers in S?
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: Mean = (1 + 2 +3 + 4 + 5 + 6 + 7)/7 = 4
Median = 4
Difference = 4-4 = 0
Option A
Question: If x/y is an integer, which of the following must also be not an integer?
I. xy
II. y/x
III. x
A.I alone
B.II alone
C.III alone
D.I, II and III
Answer: D.I, II and III
Explanation: Let's take X = 4/3 and Y = 2/3
Then X/Y = 2 which is an integer.
But XY = 4/3 * 2/3 = 8/9 --> Not an integer.
Y/X = 2/3 divided by 4/3 = 2/4 = 1/2 Not an integer.
X alone is 4/3. Not an integer.
Hence D.
Question: In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Chuck and Bob are not seated next to each other?
A.24
B.48
C.72
D.74
Answer: C.72
Explanation: When the constraint on an arrangement says,Two people should not be seated together,we do just the opposite. We make them sit together! Kind of tie them with a thread and assume they are one unit!
Let's see why....
These 5 people can be arranged in 5! ways. These are the total number of ways you get.
Now, when we tie 2 people together, we have only 4 entities to arrange. We can do this in 4! ways. But in each of these entities, the two people can sit in two different ways (AB and BA). So number of ways in which these two people sit together is 4!*2!.
Now, the ways in which these two people will not be together will be 5!- 4!*2! = 4!(5 - 2) = 72
Answer :C
Question: Bottle R contains 250 capsules and costs $8.25. Bottle T contains 130 capsules and costs $2.99. What is the difference between the cost per capsule for bottle R and the cost per capsule for bottle T?
A. $0.25
B. $0.01
C. $0.05
D. $0.03
Answer: B. $0.01
Explanation: Cost per capsule in R is 8.25/250=0.825/25=0.033
Cost per capsule in T is 2.99/130=0.023
The difference is 0.01
The answer is B
Question: In the rectangular coordinate system, what is the area of triangle CDE with points
C=(7,2)
D=(3,9)
E=(1,4)
A.17
B.16.3
C.18
D.19
Answer: A.17
Explanation: Use the formula of the distance formula
square root (x2-x1)^2+(y2-y1)^2
Do this for each of the sides and then the value is given as A.
Question: I bought two books; for Rs.460. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
A.337.33
B.280.33
C.299.33
D.268.33
Answer: D.268.33
Explanation: x*(85/100) = (460 - x)119/100
x = 280
Answer: D
Question: The train travels at an average speed of 16km/h, to the top of the hill where the midpoint of the trip is. Going down hill, train travels at an average speed of 8km/h. Which of the following is the closest approximation of train's average speed, in kilometers per hour, for the round trip?
A.9.6
B.10.6
C.4.3
D.2.5
Answer: B.10.6
Explanation: Since we're not given a distance to work with, we can TEST any distance that we like. Here, since the speeds are 16km/hour and 8 km/hour, using a multiple of both 16 and 8 would make the math easiest.
Let's set the Distance up the hill at 64 km.
So, going uphill, we have....
D = (R)(T)
64 = (16)(T)
64/16 = 4 = T
4 hours to go uphill
Going downhill, we have....
D = (R)(T)
60 = (20)(T)
64/8 = 8 = T
8 hours to go downhill
Total Distance = 120 km
Total Time = 4+8 = 12 hours
Average Speed = 128/12 = 10.6 km/hour
B
Question: If 25% of x is 15 less than 15% of 1500, then x is?
A.657
B.765
C.865
D.840
Answer: D.840
Explanation: 25% of x = x/4 ; 15% of 1500
= 15/100 * 1500 = 225
Given that, x/4 = 225 - 15
=> x/4 = 210 => x = 840.
Answer:D
Question: What is the least number of square tiles required to pave the floor of a room
15 m 17 cm long and 9m 2 cm broad?
A.814
B.802
C.836
D.900
Answer: A.814
Explanation: L = 15 M 17 CM =1517 CM
B = 9 M 2 CM = 902 CM^2
AREA = 1517 * 902 CM^2
FIND OUT HCF = 41
AREA OF SQUARE = 41 * 41 = 1517 * 902 / 41 * 41 = 37 * 22
=407 * 2 =814
ANSWER A
Question: 2 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
A.12/9 days
B.30/11 days
C.82/8 days
D.22/76 days
Answer: B.30/11 days
Explanation: 2M = 6W ---- 20 days
12M + 8W -----?
36W + 8 W = 44W ---?
6W ---- 20 44 -----?
6 * 20 = 44 * x => x = 30/11 days
Answer:B
Question: A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days Q will the work get over?
A.Q=60
B.Q=70
C.Q=75
D.80
Answer: C.Q=75
Explanation: We can also use the concept of man-days here
100 days -->10men so the job includes 100*10=1000 man-days
After 20 days
1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done
Now the Balance Job=1000-250=750 man-days worth of Job
Since 2 men are fired so B/L men=8
Therefore Total no. of days of Job=750 man-day/8 days = 375/4=94 days (approx.)
Now since this is total and Ques. is asking for additional no. of days,
So 94-20=74 days
The nearest approx. to answer is 75
Ans: C (75 days)
Question: R-R-R-G-G-G-G-Y-Y-Y-B-R-R-R-G-G-G-G-Y-Y-Y-B… B-R-R
The preceding is a representation of the different colored beads on a string. The beads follow a repeating pattern and the colors Red, Green, Yellow, and Blue are represented by R, G, Y, and B respectively. Which of the following is a possible number of beads in the missing section of the string represented above?
A.64
B.65
C.66
D.67
Answer: B.65
Explanation: The repeated pattern R-R-R-G-G-G-G-Y-Y-Y-B has 11 beads.
But the missing section includes R-R-R-G-G-G-G-Y-Y-Y at the end.
Thus the number of beads in the missing section has the form 11k + 10.
The answer is B.
Question: If 20 men can build a wall 66 metres long in 10 days, what length of a similar can be built by 86 men in 8 days?
A.227.04 mtrs
B.378.4 mtrs
C.478.4 mtrs
D.488.4 mtrs
Answer: A.227.04 mtrs
Explanation: If 20 men can build a wall 66 metres long in 10 days,
length of a similar wall that can be built by 86 men in 8 days = (66*86*8)/(10*20) = 227.04 mtrs
ANSWER:A
Question: Two trains of equal are running on parallel lines in the same direction at 49 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
A.50
B.88
C.65
D.55
Answer: C.65
Explanation: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 49 - 36 = 13 km/hr.
= 13 * 5/18 = 65/18 m/sec.
2x/36 = 65/18 => x = 65.
Answer:C