RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Two cards are drawn together from a pack of 52 cards. The probability that one is a club and other is a diamond, is:
A.29/34
B.47/100
C.3/20
D.13/102
Answer: D.13/102
Explanation: Explanation :
One card drawn.
Probability of being it club or diamond = (13x2)/52.
Another card drawn.
Now, Probability of being it of other suit(the suit among the two, not selected in first draw) = 13/51.
Hence, probability of event = ((13x2)/52)x(13/51)= 13/102.
Answer : D
Question: Which of the following equations describes a line that is perpendicular to y = x/2 + 5?
A.y = x − 5
B.y = −3 − 2x
C.y = 5x
D.y = 5x - 1
Answer: B.y = −3 − 2x
Explanation: Two perpendicular lines have slopes that are inverse reciprocals of each other.
The slope of y = x/2 + 5 is 1/2 so the slope of a perpendicular line will be -2.
The answer is B.
Question: If b < 2 and 2x - 2b = 0, which of the following must be true?
A.x > -3
B.x < 2
C.x = 3
D.x < 3
Answer: B.x < 2
Explanation: 2x - 2b = 0
Therefore, 2x = 2b
As, b<2
2x < 2(2)
i.e x < 2
Answer : B
Question: By investing in 16 % stock at 64, one earns Rs. 1500. The investment made is:
A.5760
B.7667
C.4445
D.4566
Answer: C.4445
Explanation: Explanation:
To earn Rs., investment = Rs. 64.
To earn Rs. 1500, investment = = Rs. 5760.
Answer: C) 5760
Question: In a forest 140 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
A.150
B.750
C.1,250
D.1,400
Answer: D.1,400
Explanation: The percentage of tagged deer in the second sample = 5/50*100=10%.
So, 140 tagged deers comprise 10% of total # of deers --> total # of deers = 140*10 = 1,400.
Answer: D.
Question: To create paint with a certain shade of gray, one must combine 2.3 liters of black paint with every one liter of white paint. Approximately how many liters of white paint must be combined with 350 liters of black paint to create the certain shade of gray?
A.152.1
B.156.4
C.347.1
D.694.4
Answer: A.152.1
Explanation: Since the ratio of Black to White is 2.3 to 1 this implies that Amount of Black is going to be more than (approximately double) the amount of White. This implies Option C, D and E can not be correct.
Now between A and B:
Black:White = 2.3:1 Since the ratio is more than double, the amount of White Paint should be less than half of Black Paint. B is more than half so can not be the answer, A fits the criteria hence should be the correct answer. No calculation needed whatsoever.
Question: A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 14 cups of tea are prepared, 7 in one way and 7 in other. Find the different possible ways of presenting these 14 cups to the expert.
A.2532
B.2432
C.3032
D.3432
Answer: D.3432
Explanation: Solution:
Since, there are 7 cups of each kind, prepared with milk or tea leaves added first, are identical hence, total number of different people ways of presenting the cups to the expert is,
[14!/(7!x7!)]= 3432
Answer: Option D
Question: If December 3rd, 1999 is a Friday, what day is January 6th, 2000?
A.Wednesday
B.Thursday
C.Friday
D.Saturday
Answer: B.Thursday
Explanation: There is difference of 34 days from Dec. 3rd 1999 to Jan. 6th 2000.
34/7 has a remainder of 6.
Jan. 6th is: Friday + 6 days = Thursday
The answer is B.
Question: In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
A.32
B.52
C.62
D.72
Answer: B.52
Explanation: Total = 100
T= 40 NT= 60
40*(60/100)=24 60*(40/100)=24
24 + 24 = 48 => 100 - 48 = 52%
ANSWER B
Question: The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
A.12
B.24
C.34
D.48
Answer: D.48
Explanation: Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.Answer: Option D
Question: A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
A.288
B.200
C.289
D.267
Answer: B.200
Explanation: The number of ways to select two men and three women
= 5C2 * 6C3
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200
Answer:B
Question: The width of a rectangle is 10 meter and its area is 150 square meter. If length of the rectangle is increased then its new area is 4/3 times of the original area. What is the new perimeter of the rectangle?
A.48 m
B.52 m
C.54 m
D.60 m
Answer: D.60 m
Explanation: Let length of new rectangle be x m
Then x×10=150×4/3=200 or, x=20 m
Hence new perimeter=2(10+20)=60 m
ANSWER:D
Question: A train 600 m long passed a pole in 12 sec. How long will it take to pass a platform 450 m long?
A.19
B.20
C.21
D.22
Answer: C.21
Explanation: Speed = 600/12
= 50 m/sec.
Required time
= (600 + 450)/50
= 21 sec.
Answer:C
Question: The traffic lights at 3 different roads change after every 48 sec, 72 sec, 108 sec respectively. If they all change simultaneously at 9:15 AM then at what time will they again change simultaneously.
A.9:22:12
B.9:42:15
C.10:15:24
D.9:54:12
Answer: A.9:22:12
Explanation: LCM of 48,72,108 = 432 = 7mnts 12sec
The lines will change every 7m 12sec
The light will change again after 9:15 AM is = 9:15+0:07:12 = 9:22:12
Answer is A
Question: What is the units digit of (147^17)^48 ?
A.1
B.3
C.5
D.7
Answer: A.1
Explanation: The units digit of the exponents of 7 repeat in a cycle of four, which is {7,9,3,1}. The number 17 has the form 4n+1 so the units digit is 7 inside the bracket. The exponent 48 has the form 4n, so the units digit is 1. The answer is A.
Question: The cost price of 4 notebooks is equal to the selling price of 6 notebooks. What is the % profit or loss.
A.32.3 %
B.33.3 %
C.12.3 %
D.23.3 %
Answer: B.33.3 %
Explanation: Let the cost price of 1 notebooks be Rs 1
Cost of 6 notebooks = Rs 6
Selling price of 6 apples = 4
Gain/loss = 6 - 4 = 2
%=2/6âˆ—100= 33.3
Answer: B
Question: Bill is golfing with three friends and can either buy generic golf tees that are packaged by the dozen or the higher quality Aero flight tees that come by the pair. What is the minimum number of packages of Aero flight tees Bill must purchase to ensure that he has at least 20 golf tees for each member of his foursome, if he will buy no more than 2 packages of the generic golf tees?
A.16
B.10
C.28
D.4
Answer: C.28
Explanation: At least 20 golf tees for each member of his foursome = total of at least 4*20 = 80 tees.
2 packages of the generic golf tees, that are packaged by the dozen = 2*12 = 24 tees.
So, Bill must by at least 16 Aero tees. They come by the pair, hence he must by at least 56/2 = 28 packages of Aero flight tees.
Answer: C.
Question: A father was as old as his son's present at the time of your birth. If the father's age is 42 years now, the son's age 5years back was?
A.10 years
B.12 years
C.14 years
D.16 years
Answer: D.16 years
Explanation: Let the son's present age be x years. Then, (42 - x) = x
2x = 42.
x = 21.
Son's age 5 years back (21 - 5) = 16 years.
D
Question: The sum of the first n positive perfect squares, where n is a positive integer, is given by the formula n3/3 + cn2 + n/6, where c is a constant. What is the sum of the first 15 positive perfect squares?
A.1,010
B.1,164
C.1,240
D.1,316
Answer: C.1,240
Explanation: For n=1,
1=1/3 + c + 1/6
1=1/2 + c
=> c = 1/2
15*15*15/3 + 1/2*15*15 + 15/6=1240
ANSWER:C
Question: What is the range of all the roots of |x^2 - 1| = x ?
A.4
B.3
C.2
D.1
Answer: D.1
Explanation: we get 2 quadratic equations here ..
1) x^2-x-1=0 ....... roots 2 , -1
2) x^2+x-1=0 ........ roots -2, 1
Inserting each root in given equation , it can be seen that -1 and -2 do not satisfy the equations .
So value of x for given equation .... x=2 or x=1
I guess range is 2-1 =1
D
Question: Find value of X: 5216 × 51 = X
A.265016
B.343546
C.266016
D.353546
Answer: C.266016
Explanation: Normal way of multiplication may take time. Here is one alternative.
5216×51=(5216×50)+5216=(5216×1002)+5216=5216002+5216=260800+5216=266016
C
Question: By walking at 3/4th of his usual speed, a man reaches office 16 minutes later than usual. What is his usual time?
A.48min
B.50min
C.65min
D.60min
Answer: A.48min
Explanation: let T be the usual time.
time spent=4T/3
therefore, 4T/3=T+16
4T=3T+48...therefor T=48min
ANSWER:A
Question: When an amount was distributed among 14 boys, each of them got rs 80 more than the amount received by each boy when the same amount is distributed equally among 18 boys. What was the amount?
A.Rs. 5040
B.Rs. 6040
C.Rs. 7040
D.Rs. 5440
Answer: A.Rs. 5040
Explanation: If 18 boys got Rs x, then
18x = 14*(x+80)= 14x+1120
or
4x =1120
x= 280
so total amt = 280*18 = Rs. 5040
ANSWER:A
Question: If the remainder is 10 when positive integer n is divided by 14, what is the remainder when n is divided by 7?
A.0
B.1
C.2
D.3
Answer: D.3
Explanation: Assume x is quotient here,
n=14x+7 ----------(1)
and n=7x+ ?
We can also write equation (1) as:
n=(14x+7)+3.
ie 7(2x+1)+3 ie the first term is perfectly divisible by 7.
So,the remainder left is 3.
So,answer (D) is right choice.
Question: A cistern can be filled in 9 hours but due to a leak at its bottom it takes 10 hours. If the cistern is full, then the time that the leak will take to make it empty will be ?
A.20 hours
B.19 hours
C.90 hours
D.80 hours
Answer: C.90 hours
Explanation: Explanation:
Part filled without leak in 1 hour = 1/9
Part filled with leak in 1 hour = 1/10
Work done by leak in 1 hour
=1/9âˆ’1/10=1/90
We used subtraction as it is getting empty.
So total time to empty the cistern is 90 hours
ANSWER IS C
Question: Consider a Number 3.1n6
n represent the hundredths digit in the number shown above. If the number is rounded to the nearest hundredth, which of the following could be the tenths digit in the rounded number?
A.4
B.3
C.1
D.2
Answer: D.2
Explanation: In this ques we are given the thousandth digit as 6, so the hundreth digit can take any value from 0-9. For the hundreth digit i considered 2 set of values (i) 0, 1, 2, 3 and (ii) 4, 5, 6, 7, 8, 9. Given that the thousandth digit is 6, the hundreth digit has to go up by 1, and correspondingly, the tenth digit should increase by one.i.e 0-9.say 2
D
Question: In a certain kindergarten, every child has got either a dog or a cat or both. 18 children have got dogs only and 6 children have got both dogs and cats. If there are 30 children in the kindergarten, how many of them have cats?
A.6
B.12
C.14
D.16
Answer: B.12
Explanation: A : Only Cats
B : Both Cats and Dogs
C : Only Dogs
As per question, A + B + C =30
C = 18
B = 6, so A = 6. Hence, A + b = 12. Answer is B
Question: I. j; k; m; n; p
II. j - 10; m; m; m; p + 15
III. j + 2; k + 1; m; n - 1; p - 2
If j, k, m, n, and p are consecutive positive integers such that j < k < m < n < p, the data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation H in which of the following?
A. I, III, II
B. II, I, III
C. II, III, I
D. III, I, II
Answer: B. II, I, III
Explanation: Range of 1st Set = (p-j)
Range of 2nd Set = P+15 - j +10 = (p-j) +25
Range of 3rd Set = P -2 - j - 2 = (p-j) - 4
R2 > R1 > R3 ==> SD2 > SD1 > SD3
Since, H=Higher the Range -> More Dispersion in the Set -> More Standard Deviation.B
Question: When the price of an article is reduced by 30%, the sales increases by 50%. The percentage change in the total amount of receipts is?
A.5% decrease
B.5% increase
C.10% decrease
D.15% decrease
Answer: B.5% increase
Explanation: We have, receipts = Price x Sales
Therefore, net % change in receipts
= (x + y + xy/100) %
= [ - 30 + 50 + (-30 x 50)/100]%
= 5% increase.
ANSWER:B
Question: The average (arithmetic man) of three integers a, b, and c is exactly half the median. If a < b < c and a = 0, what is the value of c/b?
A.2
B.3/2
C.4
D.5
Answer: B.3/2
Explanation: The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=1b/2 --> since a=0, then (0+b+c)/3=1b/2 --> c=3b/2 --> c/b=3/2.
Answer: B.
Question: Tough and Tricky questions: Decimals.
The value of x is derived by summing a, b, and c and then rounding the result to the tenths place. The value of y is derived by first rounding a, b, and c to the tenths place and then summing the resulting values. If a = 5.43, b = 2.98, and c = 3.76, what is y – x?
A.0
B.0.04
C.0.05
D.0.1
Answer: A.0
Explanation: To find x, we first sum a, b, and c, then round to the tenths place. 5.43 + 2.98 + 3.76 = 12.17, which rounds to 12.2.
To find y, we first round a, b, and c to the tenths place and them sum them. so 5.4 + 3.0 + 3.8 = 12.2.
We are looking for y - x, which gives us 12.2 - 12.2 = 0, or
answer choice A.
Question: If a certain sample of data has a mean of 15 and a standard deviation of 2, which of the following is not within 2 standard deviations?
A.11
B.15
C.10
D.12
Answer: C.10
Explanation: If a data distribution is normal then the 68% data values are within one standard deviation of the mean (i.e., μ ± σ), and about 95 percent are within two standard deviations (μ ± 2σ).
Here, mean = 15 and standard distribution is 2.
Numbers which are within two standard distribution will be in the range of 15±(2*2) i.e. 11 to 19.
Only only which does not follow this range is 10
Answer is C
Question: In the manufacture of a certain product, 9 percent of the units produced are defective and 5 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
A.0.15%
B.0.45%
C.0.8%
D.1.25%
Answer: B.0.45%
Explanation: 0.09*0.05 = 0.0045 = 0.45%
The answer is B.
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
A.50
B.87
C.17
D.98
Answer: A.50
Explanation: A+B+C = 500
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 500
----------------
C = 50
Answer: A
Question: Find the remainder W when 12^190 is divided by 1729 ?
A.12
B.1
C.1728
D.1717
Answer: D.1717
Explanation: 12^(190) can be written as. ((12^3)^63)* 12. 12^3 when divided by 1729 gives a remainder W -1. so in the numerator we have -12. Now acccording to remainder theorm the answer will be 1729-12=1717.D
Question: A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
A.525
B.665
C.412
D.235
Answer: B.665
Explanation: Answer: Option B
8 * 84 = 672 â€“ 7 = 665
Question: Two trains for Palwal leave Kanpur at 10 a.m and 10:30 am and travel at the speeds of 60 Kmph and 75 Kmph respectively. After how many kilometers from Kanpur will the two trains be together?
A.150
B.160
C.170
D.180
Answer: A.150
Explanation: Let two train meet at X km distance.
Time taken by first train to cover X km=x/75 h
Time taken by 2nd train to cover X km=x/60 h
Now, x/60 - x/75=1/2
thus, x=150.
ANSWER:A
Question: If the number is divided by 3, it reduced by 30. The number is
A.A)51
B.B)50
C.C)45
D.D)40
Answer: C.C)45
Explanation: Explanation:
Let the number be x. Then,
x - (x/3) = 30 => 2x/3 = 30
=> x = 45
Answer: Option C
Question: The least number which when increased by 6 each divisible by each one of 24, 32, 36 and 54 is :
A.858
B.859
C.869
D.4320
Answer: A.858
Explanation: Solution
Required number = (L.C.M. of 24, 32, 36, 54) - 5 = 864 - 6 = 858. Answer A
Question: Tom covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time?
A.15 Kmph
B.29 Kmph
C.25 Kmph
D.30 Kmph
Answer: A.15 Kmph
Explanation: Total distance = 8 Km
Total time = 50 Km
Time taken to cover the distance of 3 Km = 50*2/5 = 20 min = 1/3 hours
Remaining distance = 8 - 3 = 5 Km
Required speed = 5/1/3 = 15 Kmph
A
Question: Find the fourth proportion to 5,6,15
A.18
B.12
C.6
D.9
Answer: A.18
Explanation: Explanation:
5:6 :: 15:x
=> 5/6 = 15/x
=> x = 15*6/5
=> x = 18
Answer:A
Question: In what time will a train 20 m long cross an electric pole, it its speed be 144 km/hr?
A.2.5 sec
B.2.8 sec
C.0.5 sec
D.2.3 sec
Answer: C.0.5 sec
Explanation: Speed = 144 * 5/18
= 40 m/sec
Time taken = 20/40
= 0.5 sec.
Answer:C
Question: Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 3/4 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
A.6/22
B.5/22
C.7/22
D.4/22
Answer: C.7/22
Explanation: # of basic stereos was 3/4 of total and # of deluxe stereos was 1/4 of total, let's assume total=16, then Basic=12 and Deluxe=4.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be 12*1=12 and total time for Deluxe would be 4*7/5=28/5 --> total time for both of them would be 12+28/5=88/5 --> deluxe/total=28/5 / 88/5= 28/88 =7/22
C
Question: If the ratio of x to y is 3 to 7, then (y-x)/(x+y)?
A.-7/3
B.-3/7
C.4/10
D.1
Answer: C.4/10
Explanation: I believe this problem can be solved using algebra.
The ratio of x to y is 3 to 7 means
(x/y)=(3/7)
Cross-multiply
3x = 7y
x = (3/7)*y
Then, substitute x in the original equation in the problem with the value we just found.
(y - (3/7)*y) / ((3/7)*y + y)
= ((4/7)*y) / ((10/7)*y)
Simplify by canceling the y in the numerator with the y in the denominator.
(4/7) / (10/7)
= (4/7) * (10/7)
The 7s cancel each other out, and you are left with 4/10.
Question: A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: Blue, Green, Yellow Or Pink. The store packs the notepads in pacakages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
A.6
B.8
C.16
D.24
Answer: C.16
Explanation: Packages can be prepared in following 2 ways:
1) 3 notepads of same size and same color
2) 3 notepads of same size and of 3 different colors
Lets go step by step.
1) 3 notepads of same size and same color:
We know that there are 2 sizes of pads and 4 colors in total. We want to keep the size and color same. so there are 2*4 = 8 ways to create package.
2) 3 notepads of same size and of 3 different colors:
We want to select 3 colors out of 4 available = 4C3 = 4
And there are 2 sizes of notepad available. So the total ways in which a package can be created is = 4C3*2 = 8
So total 8+8 = 16 packages can be created. Answer is C.
Question: Out of 7 fruits in a basket, 2 are rotten. If two fruits are drawn at random from the basket, the probability of both being rotten is
A.1/21
B.10/21
C.20/21
D.11/21
Answer: A.1/21
Explanation: The number of exhaustive events = 7C2 = 21.
Let E be event of the 2 fruits being rotten. The number of favourable cases are
2C2 = 1 way.
Required probability = 1/21.
ANSWER:A
Question: A man covers a certain distance on bike. Had he moved 4 kmph faster, he would have taken 72 minutes less. If he moves slow by 4 kmph, he will take hours more to cover the distance. What is the distance travelled by him ?
A.48 km
B.56 km
C.64 km
D.96 km
Answer: D.96 km
Explanation: Explanation :
Let the distance be 'D' and the speed be 'x' kmph.
D/x + 4 = D/x - 72/60
D/x - D/(x - y) = 6/5 = D(x + 4 - x)/x(x - 4) = 6/5
∴ D/x(x + 4) = 3/10 ......(i)
D/x - 4 - D/x = 2
∴ Dx - Dx + 4D/x(x - 4) = 2
∴ D/x(x - 4) = 1/2 .....(ii)
From equation (i) and (ii):
3/10 x (x + 4) = 1/2 x(x - 4)
∴ 3(x + 4) = 5(x - 4) = 3x + 12 = 5x - 20
2x = 32 ∴ x = 16 kmn-1
∴ D = x(x - 4)/2 = 16x12/2 = 16x6 = 96 km
Answer : Option D
Question: Amita is taller than Rita but not as tall as Sapna, who is shorter than Farida. Sumedha is shorter than Farida but not as short as Rita. Who is the shorest among them?
A.Amita
B.Sumedha
C.Rita
D.Cannot be determined
Answer: C.Rita
Explanation: here sumedha is shorter than Farida but not as short as rita
So sumedhaa will be placed in between farida and rita
hence rita is shortest among them
ANSWER:C
Question: A scale 7 ft. 12 inches long is divided into 4 equal parts. Find the length of each part.
A.20 inches
B.77 inches
C.24 inches
D.97 inches
Answer: C.24 inches
Explanation: Explanation:
Total length of scale in inches = (7*12) + 12 = 96 inches
Length of each of the 4 parts = 96/4 = 24 inches
ANSWER:C
Question: Winson's shop runs a sale on goldfish and platys. If one customer buys 13 goldfish and 12 platys for $5.60, and another buys 14 goldfish and 21 platys for $8.05, what is the ratio of the price of goldfish to platys?
A.0.8
B.0.75
C.c) 8/9
D.5/7
Answer: D.5/7
Explanation: The approach of plugging in the numbers is a fine approach. But, in this case, the answer was the first option and thus, by plugging in a number in the ration given, we arrived at the answer quickly!
However, what if the correct ratio was option D or C?
In any case, the algebraic solution isn't that complex if you realize a key concept:
The number 7 can be factored out of the second equation!
Here's the working:Winson's shop runs a sale on goldfish and platys.
13x + 12y = 5.60 <<<<< Equation 1
14x + 21y = 8.05 <<<<< Equation 2
2x + 3y = 1.15 [Factor Out 7 from equation 2] <<<<< Equation 3
8x + 12y = 4.6 [Multiply Equation 3 with 4]
5x = 1.0 [Equation 1 - Equation 2]
x = 0.2
3y = 1.15 - 0.4 = 0.75 [Substitute for x in Equation 1]
y = 0.25
x/y = 0.2/0.25 = 20/25 = 4/5 = 0.8 [Answer A]
The whole thing must have taken me about 45 s :D
Question: In a stack of cards, 6 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 8/11. What is the number of cards in the stack?
A.7
B.11
C.12
D.15
Answer: A.7
Explanation: This question can be solved by TESTing THE ANSWERS.
We're told that we have 6 blue cards and an unknown number of red cards. We're also told that if 2 cards are to be chosen at random from the stack WITHOUT replacement, then the probability that the cards chosen will BOTH be BLUE is 8/11. We're asked for the TOTAL number of cards.
Probability of pulling two blue cards is...
(6/7)(5/6) = 30/42~ 8/11
A
Question: In a renowned city, the average birth rate is 4 people every two seconds and the death rate is 3 people every two seconds. Estimate the size of the population net increase that occurs in one day.
A. 43,100
B. 43,200
C. 43,300
D. 43,400
Answer: B. 43,200
Explanation: This question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds.
For this particular question : Increase in the population every 2 seconds = 4-3 = 1 people.
Total 2 second interval in a day = 24*60*60/2 = 43,200
Population increase = 43,200 * 1 = 43,200. Hence B.
Question: A train running at the speed of 20 km/hr crosses a post in 10 seconds. What is the length of the train?
A.150
B.250
C.415
D.200
Answer: D.200
Explanation: Speed=(20x5/18)=50/9 m/sec.
Length of the train=(Speed x Time).
Length of the train=50/9 x10m=200 m.
Answer: D