divelab/Sys2Bench huggingface dataset:
Question: If the range T 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?
Options:
A)	0
B)	2
C)	12
D)	13
E)	15
Rationale: The range T 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.
Answer: D
Question: A certain car dealership offers its newest model in ten exterior and ten interior colors. If the five interior colors are identical to the ten exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?
Options:
A)25
B)81
C)90
D)10!/2!
E)10!
Rationale: I lined up the 10 different colours for Exterion and Interior like this:
E: A B C D E F G H I J
I: A B C D E F G H I J
I calculated the number of combinations: 10*10= 100 combinations.
But, from these 100 we need to delete sth: the same colours.
There are 10 possible pairs of coulours that will be the same. So, I deleted these 10 pairs from 100, resulting in 25.
Mind here, that the 10 do not result in 20 colours, because 1 pair is one unit that is not allowed. So, 10 units are not allowed (surprised that 80 wasn't among the answer options to confuse test takers...).
A
Answer: A
Question: In a soccer bet,we play 4 teams.first team odd 1.25,second 5.23,third 3.25,fourth 2.05.we place the bet with 5.00 euros.
how much money we expect to win?
Options:
A)217.78
B)225.5
C)235.01
D)266.74
E)669.0
Rationale: in the case we won the bet,we have:
1.25* 5.23* 3.25* 2.0*5.00=219.50
we will win 217.78
so correct answer is A
Answer: A
Question: 36 men can complete a piece of work in 18 days. In how many days will 81 men complete the same work ?
Options:
A)8
B)77
C)88
D)29
E)21
Rationale: Explanation:
Less Men, means more Days {Indirect Proportion}
Let the number of days be x
then,
81 : 36 :: 18 : x
x = 8
Answer: A) 8 days
Answer: A
Question: If the average (arithmetic mean) of 16 consecutive odd integers is 414, then the least of these integers is
Options:
A)a) 399
B)b) 418
C)c) 519
D)d) 521
E)e) 525
Rationale: A very helpful rule to know in arithmetic is the rule that in evenly spaced sets, average = median. Because the average will equal the median in these sets, then we quickly know that the median of this set of consecutive odd integer numbers is 414.
There are 16 numbers in the set, and in a set with an even number of terms the median is just the average of the two most median terms (here the 7th and 8th numbers in the set). This means that numbers 7 and 8 in this set are 413 and 415. Because we know that number 7 is 413, we know that the smallest number is 7 odd numbers below this, which means that it is 7*2 = 14 below this (every odd number is every other number). Therefore 413-14 = 399, answer choice A.
Answer: A
Question: A photography dealer ordered 30 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 30 cameras?
Options:
A)7% loss
B)13% loss
C)6% profit
D)13% profit
E)15% profit
Rationale: Total cost 30*($250/1.2)=6250;
# of cameras sold is 30-6=24 total revenue is 24*250;
# of cameras returned is 6 total refund 6*(250/1.2)*0.5;
So, total income 24*250+ 6*(250/1.2)*0.5
The dealer's approximate profit is (24*250+ 6*(250/1.2)*0.5-6250)/(6250)*100= 6%
Answer: C.
Answer: C
Question: A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 980gm. for a kg.His gain is …%.
Options:
A)2.04%
B)5.36%
C)4.26%
D)6.26%
E)7.26%
Rationale: His percentage gain is 100*20/980 as he is gaining 20 units for his purchase of 980 units.
so 2.04%..ANSWER:A
Answer: A
Question: A sum 's' is divided into 4 parts. second person gets Rs 10
more than first.3rd person is Rs 10 more than second,4th is 10 more than 3rd.how much amount do 1st person get.?
Options:
A)x = (s-60)/4
B)x = (s-60)/5
C)x = (s-60)/3
D)x = (s-60)/2
E)x = (s-60)/6
Rationale: let x be amount getting by first person,
second person gets x +10,third person gets x + 20,fourth person gets x + 30,
now s = (x)+(x+10)+(x+20)+(x+30)
s = 4x + 60
s - 60 = 4x
or x = (s-60)/4
ANSWER:A
Answer: A
Question: For each hour of production, a certain factory requires 1 assembly line worker for every 10 units to be produced in that hour. The factory also requires 12 managers regardless of the number of units to be produced. Which of the following expressions represents the total number of assembly line workers and managers that this factory requires to produce 50N in one hour, where N is a positive integer?
Options:
A)12 + 5N
B)12 + 2N
C)62N
D)37N
E)25
Rationale: 10 units = 1 worker;
50N units = 50N/01 = 5N workers.
So, the answer is 5N workers plus 12 managers.
Answer: A.
Answer: A
Question: Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 90 kmph and 70 kmph respectively. In what time will they cross each other completely?
Options:
A)15 sec
B)19 sec
C)12 sec
D)10 sec
E)11.25 sec
Rationale: Explanation:
D = 250 m + 250 m = 500 m
RS = 90 + 70 = 160 * 5/18 = 400/9
T = 500 * 9/400 = 11.25 sec
Answer: Option E
Answer: E
Question: In a chess tournament each of the six players will play with
every other player exactly once. How many matches will be
played during the tournament?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: if 2 players are playing thn no of match= 1
if 3 player are playing thn no of match =2
hence for Pth player no of matches = n-1 where n= no of players
so for 6th player it is 5
for 5th it is 4....
for 1 it is 0.
don't be confuse 1 already played with 6,5,4,3,2
__________________
6--->5,4,3,2,1
5----->4,3,2,1
4---->3,2,1
3---->2,1
2---->1
5+4+3+2+1=15
ANSWER:E
Answer: E
Question: A train is 360 meter long is running at a speed of 90 km/hour. In what time will it pass a bridge of 140 meter length?
Options:
A)65 seconds
B)46 seconds
C)40 seconds
D)20 seconds
E)26 seconds
Rationale: Speed = 90 Km/hr = 90*(5/18) m/sec = 25 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/25)
= 20 seconds
Answer:D
Answer: D
Question: How many 7 in between 1 to 130?
Options:
A)18
B)20
C)22
D)23
E)24
Rationale: 7,17,27,37,47,57,67,
70,71,72,73,74,75,76,77(two 7's),78,79,87,97,107,117,127
23 7's between 1 to 130
ANSWER:D
Answer: D
Question: The median annual household income in a certain community of 21 households is $50,000. If the mean W income of a household increases by 10% per year over the next 2 years, what will the median income in the community be in 2 years?
Options:
A) $50,000
B) $60,000
C) $60,500
D) $65,000
E) Cannot be determined
Rationale: Answer is E, because there are different numbers in the set and we are not sure which side of the numbers in the set will be increased so the mean W is increase by 10%. It could be the case that small number of higher end incomes increased a little or many low end incomes increased - it cannot be identified.
Answer: E
Question: A batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning?
Options:
A)23
B)28
C)27
D)19
E)24
Rationale: Let the average after the 16th inning be P.
So, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 64
= 16P => P
= 19.
Answer: D
Answer: D
Question: The function F is defined for all positive integers n by the following rule: f(n) is the number of position integer each of which is less than n, and has no position factor in common with n other than 2. If p is any prime number then f(p)=
Options:
A)p-1
B)p-2
C)(p+1)/2
D)(p-1)/2
E)2
Rationale: The confusing moment in this question is its wording. Basically question is: how many positive integers are less than given prime number p which has no common factor with p except 1.
Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).
If we consider p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6.
Answer: E.
Answer: E
Question: Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 6 muffins remained. How many guests did Monica plan on?
Options:
A)3.
B)4.
C)5.
D)6.
E)7.
Rationale: Let x be the number of guests.
Number of muffins prepared = 5x + 2
Number of muffins eaten + Number of muffins remaining = Number of muffins prepared
6(x - 1) + 6 = 5x + 2
6x - 6 = 5x + 2
x = 8
Answer: A
Answer: A
Question: If the sides of a triangle are 26 cm, 24 cm and 20 cm, what is its area?
Options:
A)120
B)772
C)288
D)266
E)240
Rationale: The triangle with sides 26 cm, 24 cm and 20 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 20 = 240 cm2
Answer: E
Answer: E
Question: The total age of A and B is 10 years more than the total age of B and C. C is how many year younger than
Options:
A)14 years
B)12 years
C)56 years
D)10 years
E)55 years
Rationale: Given that A+B = 10 + B + C
=> A â€“ C = 10 + B â€“ B = 10
=> C is younger than A by 10 years
Answer:D
Answer: D
Question: In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 28 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?
Options:
A)70
B)245
C)150
D)200
E)350
Rationale: Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7 = 0.14, or 14% of the boys in the camp are from school A and do not study science.
We are told that this number equals to 28, so 0.14*{total} = 28 --> {total} = 200.
Answer: D.
Answer: D
Question: Tough and Tricky questions: Distance/Rate.
On a reconnaissance mission, a state-of-the-art nuclear powered submarine traveled 200 miles to reposition itself in the proximity of an aircraft carrier. This journey would have taken 1 hour less if the submarine had traveled 10 miles per hour faster. What was the average speed, in miles per hour, for the actual journey?
Options:
A)20
B)40
C)50
D)80
E)100
Rationale: Say, if speed is 40, 200/40 = 5 hrs and 200/50 = 4 hrs (a reduction of 1 hr -> Correct answer)
Answer (B)
Answer: B
Question: In how many ways can the letters of the word 'APPLE' be arranged?
Options:
A)48
B)60
C)56
D)32
E)18
Rationale: The word APPLE contains 5 letters
1A,2P,1L AND 1E
required number of ways = 5!/(1!*2!*1!*1!) = 60
Answer is B
Answer: B
Question: There are 400 tigers at a large zoo. The number of tigers is 5 times the number of all the other animals combined. How many more tigers are there than non tigers animals at the zoo?
Options:
A)400
B)390
C)370
D)320
E)90
Rationale: Answer is B.
Total tigers= 400 = 5 * Other Animals (X)
or X = 80.
So, Difference in tigers and X = 400-80 = 320.
Answer: D
Question: ? + 3699 + 1985 - 2047 = 31111
Options:
A)21274
B)27474
C)21224
D)27224
E)None of these
Rationale: Explanation :
Let x + 3699 + 1985 - 2047 = 31111
=> x = 31111 - 3699 - 1985 + 2047 = 27474. Answer : Option B
Answer: B
Question: If x^2 - 4 = 0 and x < 0, which of the following must be equal to 0 ?
Options:
A) x^2 - 9x
B) x^2 - 9x + 20
C) x^2 - 2x + 3
D) x^2 + 2x - 3
E) x^2 + 5x + 6
Rationale: x^2-4 = 0
x= +2 or x = -2
if we substitute x= -2 in the equation x^2 +5x+6 = 4-10+6 = 0
E is also the answer
Answer: E
Question: On Monday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each subsequent day thereafter, Kramer wears one of his new shirts together with one of his new sweaters and one of his new hats. Kramer avoids wearing the exact same combination of shirt, sweater, and hat for as long as possible. On which day is this no longer possible?
Options:
A)Tuesday
B)Wednesday
C)Thursday
D)Friday
E)Saturday
Rationale: Shirt combinations = 3!/1*(3-1)! = 3*2*1/1*2*1 = 3
Sweater combinations = 2!/1*(2-1)! = 2*1/1*1 = 2
Hat combinations = 4!/1!*(4-1)! = 4*3*2*1/1*3*2*1 = 4
Total Combinations = Shirt Combos*Sweater Combos*Hat Combos
3*2*4=24 combinations
24 / 7 (days of the week) = remainder of 3
Purchased on Monday, 3rd day is Thursday. Next day, which he won't have a new combination for, is Friday. (D)
Answer: D
Question: A shopkeeper labeled the price of his articles so as to earn a profit of 30% on the cost price. He then sold the articles by offering a discount of 10% on the labeled price. What is the actual percent profit earned in the deal?
Options:
A)18%
B)20%
C)17%
D)18%
E)None of these
Rationale: Explanation:
Let the CP of the article = Rs.100.
Then labeled price = Rs.130.
SP = Rs.130- 10% of 130 = Rs.130-13 = Rs.117.
Gain = Rs.117 – Rs.100 = Rs.17
Therefore, gain/profit percent = 17%.
Answer: Option C
Answer: C
Question: Certain sales in December were 50% less than they were in January and 50% greater than they were in Febuary. What was the percentage decrease in the stocks from January to February ?
Options:
A)70.1%
B)55%
C)66.7%
D)57.5%
E)45.8%
Rationale: Let stocks value in Feb = 100 => In Jan =50 and March = 50 * 100/150 = 33.3
Thus, percent decrease in stocks from Feb to March = 100 - 33.3 =66.7%
Hence Answer is C
Answer: C
Question: A disease has infected an ant colony that consists ofworkersandsoldiers: 30% of the soldiers and 14% of theworkerswere infected. If that colony is inhabited by 7000 ants, out of which 1580 are infected, how manyworkersinhabit the colony?
Options:
A)1500
B)2500
C)2750
D)3000
E)3250
Rationale: From two question we get wo equations:
(1) 0,3s + 0,14w = 1580
(2) s + w = 7000
From (2) we get w=7000-s
In (1) 0,3s + 980-0,14s= 1580
0,16s=600
60000:16= 3750 =s
In (2) 3750 + w = 7000
w= 3250 E
Answer: E
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
Options:
A)7
B)9
C)8
D)11
E)10
Rationale: Explanation:
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
⇒ 5x = 25
⇒ x = 5.
Hence, B's age = 2x = 10 years.
Answer: E
Answer: E
Question: A certain fruit stand sold jackfruit for $0.70 each and bananas for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase ?
Options:
A)16
B)15
C)14
D)13
E)11
Rationale: Some multiple of 7 + Some multiple of 5 should yield 63. To get to a some multiple of 5, we should ensure that a 3 or 8 (5+3) should be a multiple of 7.
63 is a direct multiple of 7, however in this case there won't be any bananas. Hence the next option is to look for a multiple of 7 that has 8 as the unit digit. 28 satisfies this hence no. of apples is 4 and no of bananas is 7 .
E
Answer: E
Question: jeya travels the first 8 hours of her journey at 50 mph speed and the remaining 2 hours at 30mph speed. What is the average speed of jeya's travel in mph?
Options:
A)41mph
B)43mph
C)44mph
D)42mph
E)46mph
Rationale: Explanation :
Average speed=Total Distance/Time.
Total distance travelled by jeya= Distance covered in the first 8 hours + Distance covered in the next 2 hours.
Distance covered in the first 8 hours = 8Ã—50=400 miles
Distance covered in the next 2 hours= 2Ã—30=60 miles
Therefore, total distance travelled = 400+60=460 miles.
The total time taken = 8+2=10hours.
Hence, the average speed =460/10= 46mph.
Answer : E
Answer: E
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 21 seconds, what is the ratio of their speeds?
Options:
A)1:3
B)3:1
C)2:3
D)3:2
E)3:4
Rationale: Let the speed of the trains be x and y respectively
length of train1 = 27x
length of train2 = 17y
Relative speed= x+ y
Time taken to cross each other = 21 s
= (27x + 17 y)/(x+y) = 21
= (27x + 17 y)/ = 21(x+y)
= 6x = 4y
=x/y = 4/6 = 2/3 i.e 2:3
Answer :C
Answer: C
Question: What is the four-digit number in which the first digit is 1/3 of the second,the third is the sum of the first and second, and the last is three times the second?
Options:
A)1349
B)1347
C)1449
D)2349
E)1399
Rationale: It is given that the first digit is 1/3 of the second. There are 3 such possibilities 1)1 and 3
2)2 and 6
3)3 and 9
Now, the third digit is the sum of the first and second digits.
1)1 + 3 = 4
2)2 + 6 = 8
3)3 + 9 = 12
It is clear that option 3 is not possible. So we are left with only two options.Also, the last digit is three times the second, which rules out the secondoption. Hence, the answer is 1349
ANSWER:A
Answer: A
Question: If w is a positive integer and 10^w – 74 in decimal notation has digits whose sum is 440, what is the value of w?
Options:
A)40
B)44
C)45
D)46
E)50
Rationale: Answer E = 50
We have (10^w)-74, where the sum of the digits is 440.
100-74 = 26, so we already have 2+6 = 8 from the 440.
Because we have a power of 10, we will have numbers like 100, 1000, 10000 and so on. This minus 74 rests 26 and a lot of 9s. E.g: 1000-74 = 9926.
So dividing the 432/9 = 48, that`s the number of 9s. and we have 2 other numbers (2 and 6) wich were 00 before the subtraction.
So we have 48 + 2 as an w = 50
Answer: E
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options:
A)87 Kmph
B)97 Kmph
C)72 Kmph
D)28 Kmph
E)19 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer: C
Answer: C
Question: What is the area of square field whose side of length 15 m?
Options:
A)225 sq m
B)297 sq m
C)167 sq m
D)112 sq m
E)981 sq m
Rationale: 15 * 15
= 225 sq m
Answer: A
Answer: A
Question: Find the value of 72519 x 9999=m?
Options:
A)678994226
B)357900042
C)567890900
D)725117481
E)567788990
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: D
Question: My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 100 years. Can you tell my grandson age in years?
Options:
A)50 years
B)20 years
C)5 years
D)10 years
E)90 years
Rationale: Let m be my age in years. If s is my son's age in years, then my son is 52s weeks old. If g is my grandson's age in years, then my grandson is 365g days old. Thus,365g = 52s.Since my grandson is 12g months old,12g = m.Since my grandson, my son and I together are 120 years,g + s + m = 100.The above system of 3 equations in 3 unknowns (g, s and m) can be solved as follows:g + 365g / 52 + 12g = 100 or52g + 365g + 624g = 5,200 org = 5,200 / 1,041 = 5 yearsAnswer : C
Answer: C
Question: A new ram material product $2.67 raw , $0.67 to manufacture, $4.73 to packing and sell price $9.03. How many unit order sold with profit 44000?
Options:
A)4583.33
B)4683.33
C)4783.33
D)4883.33
E)4983.33
Rationale: CP = 2.67 + 0.67 + 4.73 = 8.07
SP =9.03
Profit = 9.03 - 8.07 = 0.96
Unit order sold = 44000/0.96
=4583.33 unit order
ANSWER:A
Answer: A
Question: In an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 65520000 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
Options:
A)130000000
B)12500
C)14000
D)12000
E)None of these
Rationale: Explanation :
Solution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 65520000.
(75/100 * 96/100 * 70/100 * x) = 65520000.
=> x = (65520000*100*100*100)/(75*96*70) = 130000000
Answer : A
Answer: A
Question: City A to city B, Andrew drove for 1hr at 40 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
Options:
A)55
B)57.5
C)61
D)61.5
E)62.5
Rationale: The total distance is 1×40+3×60=220
And the total time is 4 hours. Hence,
Average Speed=(Total Distance/Total Time)
=220/4=55
A
Answer: A
Question: You and your friend spent a total of $15 for lunch. Your friend spent $5 more than you. How much did your friend spend on their lunch?
Options:
A)$9
B)$3
C)$4
D)$6
E)$10
Rationale: My lunch = l, my friends lunch = l+5
(l)+(l+5)=15
l+l+5-5=15-5
2l=10
l=5
My friends lunch l+5 = 5+5=$10, the answer is E
Answer: E
Question: Machine A produces 100 parts twice as fast as Machine B does. Machine B produces 100 parts in 20 minutes. If each machine produces parts at a constant rate, how many parts does Machine A produce in 8 minutes?
Options:
A)100
B)90
C)80
D)30
E)50
Rationale: Machine B produces 100 part in 20 minutes. Machine A produces 100 parts twice as fast as B, so Machine A produces 100 parts in 20/2=10 minutes.
Now, Machine A produces 100 parts in 10 minutes which is 100/10 = 10 parts/minute.
10 parts X a total of 8 minutes = 80
C
Answer: C
Question: A boy has to cover a total distance of 300 kms. in 6 hours. He travels at the rate of 60 kmph. for first 90 minutes and next 100 kms. at the rate of 50 kmph. At what average speed must he travel now in order to complete the journey in 6 hours?
Options:
A)25 kmph.
B)32 kmph
C)44 kmph
D)58 kmph
E)None of these
Rationale: Explanation:
The boy travels 60 kmph for 90 min, this means he travels 90 km.
Next 100 km at the rate of 50 kmph, this means he travels 100 km.
Total distance traveled till now = 100 + 90 = 190 km
Time spent = 1.5 + 2 = 3.5 hr
Required speed = Remaining distance/ Time
= (300 – 190) /(6 – 3.5)
= 110/ 2.5 = 44 kmph
ANSWER: C
Answer: C
Question: On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?
Options:
A)0.008
B)0.125
C)0.128
D)0.512
E)0.64
Rationale: Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probability of rain = 0.2
Therefore, probability of no rain = 0.8
0.8*0.8*0.2 = 0.128
Hence C
Answer: C
Question: A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
Options:
A)1/5
B)1/3
C)3/7
D)2/7
E)3/7
Rationale: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
B)
Answer: B
Question: A tap can fill a tank in 16 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
Options:
A)2 hrs
B)1 hrs
C)10 hrs
D)5 hrs
E)4 hrs
Rationale: Explanation:
A tap can fill a tank in 16 hours.
Therefore the tap can fill half the tank in 8 hours.
One tap take time to fill half of the tank = 8 hrs
4 taps take time to fill half of the tank =8/4 hrs = 2 hrs
Total time taken to fill the tank = 8 hr+2 hr = 10 hrs
Answer : C
Answer: C