divelab/Sys2Bench huggingface dataset:
Question: What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
Options:
A)814
B)800
C)100
D)200
E)456
Rationale: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm2.
Required number of tiles = (1517 x 902)/41 x 41 = 814.
Answer:A
Answer: A
Question: In a group of 44 students, each student is registered for at least one of three classes – History, Math and English. Twenty students are registered for History, twenty students are registered for Math, and thirty students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
Options:
A)13
B)10
C)20
D)8
E)7
Rationale: Each student is registered forat least one of three classesmeans thatthere are no students who are registered for none of the classes.
Total = {people in group A} + {people in group B} + {people in group C} - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups}:
44 = 20 + 20+ 30- {people in exactly 2 groups} - 2*3 + 0-->{people in exactly 2 groups}=20
Answer: C
Answer: C
Question: Can you find the missing number in the sequence given below?
11 16 21 12 17 ? 13 18 23 14 19 24
Options:
A)20
B)21
C)22
D)23
E)24
Rationale: Solution:
22
Explanation :
The sequence is given in the puzzle is :
11 16 21 12 17 ? 13 18 23 14 19 24
Let's break the given series as below:
11 16 21
12 17 22
13 18 23
14 19 24
Now read the number from left hand side from top to bottom as :
So the number that will replace '?' is 22.
Answer C
Answer: C
Question: There are 6 people from different countries namely Germany, Italy, Britain, Spain, Poland and France. They are sitting around a table. Polish sits next to British. German sits next to Italian, or British or both. Italian does not sit next to the Frenchman. Spanish sits immediately after British. Who sits on the either side of the German?
Options:
A)British and Italian
B)Polish and British
C)British and French
D)Italian and French
E)none
Rationale: according to question
the arrangement would be
FGISBP
So the answer is : option (d)
ANSWER:D
Answer: D
Question: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 91 players took part in that tournament. How many matches were played?
Options:
A)90 matches
B)95 matches
C)99 matches
D)85 matches
E)87 matches
Rationale: A 90 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 90 matches were played.
Answer: A
Question: In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:
Options:
A)16
B)17
C)18
D)19
E)20
Rationale: Solution:
Let there were x teams participating in the games, then total number of matches,
nC2 = 153.
On solving we get,
=> n =−17 and n =18.
It cannot be negative so,
n = 18 is the answer.
Answer: Option C
Answer: C
Question: Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 188 cms. What was the ratio of men to women?
Options:
A) 5:2
B) 5:1
C) 4:3
D) 5:4
E) 3:1
Rationale: We're given a few facts to work with:
1) The average height of the females is 170cm
2) The average height of the males is 188cm
3) The average of the GROUP is 180cm
We're asked for the RATIO of men to women.
W = number of Women
M = number of Men
(170W + 188M)/(W+M) = 180
170W + 188M = 180W + 180M
8M = 10W
4M = 5W
M/W = 5/4
The ratio of men to women is 5 tổ 4.
D
Answer: D
Question: If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
Options:
A)331/8%
B)331/3%
C)631/3%
D)332/3%
E)131/3%
Rationale: 100
150
------
150-------50
100-------? => 331/3%
Answer:B
Answer: B
Question: The number of bacteria in a petri dish increased by 50 percent every 1 hour. If there were 108 million bacteria in the dish at 2: 00 p.m., at what time were there 32 million bacteria in the dish?
Options:
A)10: 00 a.m.
B)11: 00 a.m.
C)12: 00 p.m.
D)01: 00 p.m.
E)02: 00 p.m.
Rationale: Given:
he number of bacteria in a petri dish increased by 50 percent every 1 hour
There were 108 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 1 hour, this means that the number is multiplied by 1.5 every 1 hour.
Required: At what time were there 32 million bacteria in the dish?
Assume that there were n intervals of 1 hour between 32 million and 108 million.
32 * (1.5)^n = 108
(3/2)^n = 108/32 = 27/8 = (3/2)^3
Hence n = 3 intervals.
Each interval was of 1 hour. Therefore, the number of hours = 3
Subtracting 3 hours from 2 PM, we get 11 AM as the answer.
Option B
Answer: B
Question: During the break of a football match, the coach will make 3 substitutions. If the team consists of 15 players among which there are 2 forwards, what is the probability that none of the forwards will be substituted?
Options:
A) 21/55
B) 18/44
C) 12/65
D) 28/44
E) 36/55
Rationale: Required probability = no. of favorable outcome/ total no. of outcomes
out of 15 players any 3 can be selected in 15C3 ways
after removing 2 forwards any 3 players can be selected from the remaining 9 players in 9C3 ways
thus required probability = 9C3/15C3 =12/65
Answer: C
Question: Nitin ranks 15th in a class of 47 students. What is rank from the last ?
Options:
A)33
B)38
C)32
D)28
E)19
Rationale: Explanation:
Number students behind the nitin in rank = (47 - 15) = 32
Nitin is 33rd from the last
Answer: A) 33
Answer: A
Question: There are three bags.The first bag has two blue rocks. The second bag has two red rocks. The third bag has a blue and a red rock. All bags are labeled but all labels are wrong.You are allowed to open one bag, pick one rock at random, see its color and put it back into the bag, without seeing the color of the other rock.
How many such operations are necessary to correctly label the bags ?
Options:
A)1
B)2
C)3
D)4
E)None
Rationale: Just One!
example
If u get Blue rock with label as "blue+red" => this is red as all labels are wrong.
In this way u can logically solve this puzzle.
Answer A
Answer: A
Question: When a certain number X is divided by 84, the remainder is 25. What is the remainder when X is divided by 14?
Options:
A)10
B)8
C)9
D)5
E)11
Rationale: Let possible value of x is 109
least possible value of x/14 is 109/14 =>7 quotient with remainder 11
Thus answer is (E) 11
Answer: E
Question: In a village of 2,500 people, 800 people are over 70 years old and 850 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a male or younger than 70 years old?
Options:
A)221/250
B)199/250
C)33/50
D)8/25
E)51/250
Rationale: To solve this we would need to know the number of people who are less than 70 years old, the number of males, and the number of males who are less than 70 years old.
Overlapping sets: quantity of A or B = A + B - (A∩B) = quantity of A + quantity of B - (intersection of A and B)
Number of males = 2500-850 = 1650
Number of people below 70 years old = 2500-800 = 1700
Number of males below 70 years old = 1700-(850*0.4) = 1360
Total number of people who are male OR below 70 = 1650 + 1700 - 1360 = 1990
Probability of male or below 70 = 1990/2500 = 199/250
Answer: B
Answer: B
Question: In a garden there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is
Options:
A)20 m
B)22 m
C)24 m
D)26 m
E)16 m
Rationale: Each row contains 12 plants.
There are 11 gapes between the two corner trees (11 x 2) metres and 1 metre on each side is left.
Therefore Length = (22 + 2) m = 24 m.
ANSWER:C
Answer: C
Question: A restaurant meal cost $30 and there was no tax. If the tip was more than 15 percent but less than 25 percent of the cost of the meal, then the total amount paid must have been between
Options:
A) $40 and $42
B) $39 and $41
C) $38 and $40
D) $34 and $39
E) $36 and $37
Rationale: Hence it will be between 30 * (1+15/100) and 30 * (1+25/100).
i.e b/w 34.5 and 37.5. Hence the answer D (b/w 34 and 39).
Answer: D
Question: Pam had $23. Then she saved $11 from her allowance and spent $6 on a comic book and $8 on a puzzle. How much money does Pam have left?
Options:
A)$33
B)$20
C)$25
D)$60
E)$10
Rationale: Step 1: Find the total amount of money saved.
$23 + $11 = $34
Step 2: Find the total cost of the comic book and the puzzle.
$6 + $8 = $14
Step 3: Find the amount of money left.
$34 – $14 = $20
Pam has $20 left.
Answer is B.
Answer: B
Question: The two lines y=x and x=-9 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x-axis?
Options:
A)32.5
B)36.5
C)40.5
D)44.5
E)48.5
Rationale: The point of intersection is (-9,-9).
The triangle has a base of length 9 and a height of 9.
area = (1/2)*base*height = (1/2)*9*9 = 40.5
The answer is C.
Answer: C
Question: The average weight of 25 persons sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 25 persons?
Options:
A)55 kg
B)48 kg
C)52 kg
D)None
E)55 kg
Rationale: Answer: Option D
25x + 46 = 26(x â€“ 5)
x = 176
Answer: D
Question: The charge for a single room at Hotel P is 70 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G?
Options:
A)100%
B)120%
C)150%
D)200%
E)300%
Rationale: P = 0.3R = 0.9G
R = 0.9G/0.3 = 3G
Thus R is 200% greater than G.
The answer is D.
Answer: D
Question: If q + | q | = 0, which of the following must be true?
Options:
A)q > 0
B)q≥0
C)q < 0
D)q≤0
E)q = 0
Rationale: Manipulate the equations:
q + | q | = 0
|q| = -y
-q > 0 OR -q = 0
This means q could be 0 or q is less than 0.
D. q≤0
E. q=0
Answer: D
Answer: D
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
Options:
A)40
B)35
C)45
D)55
E)56
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (27 * 3 + 3 * 3) years = 90 years.
Sum of the present ages of wife and child = (20 * 2 + 5 * 2) years = 50 years.
Husband's present age = (90 - 50) years = 40 years
Answer: Option A
Answer: A
Question: A guy was asked to specify his age in years. He said, “Take my age 3 years hence, multiply it by three and subtract thrice of my age 3 years ago and you will know my age.” What was the age of that guy?
Options:
A)18
B)15
C)13
D)19
E)10
Rationale: A
18
Current age of the guy = A years.
Then, 3 (A + 3) – 3 (A – 3) = A
(3A + 9) – (3A – 9) = A
A = 18
Answer: A
Question: 6, 11, 21, 36, 56, 81, ?
Options:
A)111
B)71
C)81
D)61
E)91
Rationale: The pattern is + 5, + 10, + 15, + 20, + 25, + 30, + 35, + 40, + 45, + 50,....
Answer : A.
Answer: A
Question: If two painters can complete four rooms in two hours, how many painters would it take to do 24 rooms in 8 hours?
Options:
A)7
B)8
C)4
D)6
E)1
Rationale: Explanation:
Two painters can complete four rooms in two hours.So 24 rooms can be painted in 8 hrs by 4 painters
Answer: C) 4 painters
Answer: C
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 60 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)30
B)31
C)18
D)25
E)24
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (60 + 60)/12 => x = 5
Speed of each train = 5 m/sec.
= 5 * 18/5 =18 km/hr.
Answer: Option C
Answer: C
Question: Diana invested $61,293 in an account with a fixed annual percent of interest, compounding quarterly. At the end of five full years, she had $76,662.25 in principal plus interest. Approximately what was the annual percent rate of interest for this account?
Options:
A)1.2%
B)4.5%
C)10%
D)18%
E)25.2%
Rationale: 61,293 (1+(r/4))^20 = 76,662.25
Interest Accrued within Given Time Period: 76,662.25 - 61,293 = (estimated) 15,000
So, Per Year: 15,000/5 = 3000
Next, in order to find the rate:
(estimated) 60,000 * Rate = 3,000
3,000 / 60000 = 5% .... Since 60000 is lower than the actual figure of 61293, the actual rate will be a little less than 5%.
The only answer close to that is Choice B.
Answer: B
Question: Seven children — A, B, C, D, E, F — are going to sit in seven chairs in a row. The children CFE have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?
Options:
A)84
B)720
C)1440
D)4320
E)4800
Rationale: for such questions , we can treat both as one then total person=4..
these 6 can be arranged in 4! ways.. but within these 4 , one consists of two people who can be arranged in 6 ways CFE or FC.. so ans =4!*6=84
ans A
Answer: A
Question: A train traveling at 108 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds. What is the length of the platform in meters?
Options:
A)240 meters
B)360 meters
C)420 meters
D)600 meters
E)Cannot be determined
Rationale: Answer
Distance covered by the train when crossing a man and when crossing a platform
When a train crosses a man standing on a platform, the distance covered by the train is equal to the length of the train.
However, when the same train crosses a platform, the distance covered by the train is equal to the length of the train plus the length of the platform.
The extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover. i.e., length of the platform.
Compute length of platform
Length of the platform = speed of train * extra time taken to cross the platform.
Length of platform = 108 kmph * 12 seconds
Convert 108 kmph into m/sec
1 kmph = 5/18 m/s (This can be easily derived. But if you can remember this conversion, it saves a good 30 seconds).
∴ 108 kmph = 5/18∗108 = 30 m/sec
Therefore, length of the platform = 30 m/s * 12 sec = 360 meters.
Choice B
Answer: B
Question: X Y
+Y X
________
The sum of the two digit numbers above is a three digit number PQ2, where each letter X, Y, P, and Q represents a different non zero digit. Which of the following can be the value of X?
I)	7
II)	8
III)	9
Options:
A)I only
B)II only
C)III only
D)I , II and III
E)I and II only
Rationale: it can be a combination of 9,3 or 8,4 or 7,5
I choose D as an answer.
Answer: D
Question: An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is
Options:
A)4%
B)4.02%
C)4.04%
D)5%
E)5.24%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404 x 100 % = 4.04%
100 x 100
C)
Answer: C
Question: On flipping 3 coins together what is the outcomes for at least one tail, three tail and three head?
Options:
A)1/7
B)3/8
C)3/11
D)4/13
E)5/8
Rationale: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Favorable outcomes for at least two heads
= favorable outcomes for exactly two heads and favorable outcomes for more than two heads
= {HHT,HHH,THH,HTH,TTT}
5/8
E
Answer: E
Question: A man can row downstream at 18 kmph and upstream at 16 kmph. Find the speed of the man in still water and the speed of stream respectively?
Options:
A)13, 3
B)12, 6
C)15, 3
D)14, 4
E)17, 1
Rationale: Explanation:
Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 16 --- (2)
From (1) & (2) 2x = 34 => x = 17, y = 1.
Answer: Option E
Answer: E
Question: To furnish a kitchen in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 120 different combinations are possible, how many tables are there in the warehouse?
Options:
A)A)5
B)B)8
C)C)10
D)D)15
E)E)30
Rationale: Total number of ways to choose 2 chairs from 5= 5C2=10
Total number of combination=100
That means we need get 10 combinations from the selection of tables....
Screening through the answers.... 5C2=10..... 10*10=100
Answer is 6... A
Answer: A
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 7 years and that for 11 years?
Options:
A)8 : 11
B)9 : 11
C)7 : 11
D)Data inadequate
E)None of these
Rationale: Let the principal be P and rate of interest be R%.
∴ Required Ratio = [(P×R×7/100) /(P×R×11/100)]=1PR/11PR=7/11=7:11
Answer D
Answer: D
Question: A boat can travel with a speed of 42 km/hr in still water. If the speed of the stream is 10 km/hr, find the time taken by the boat to go 80 km downstream
Options:
A)1 hour 40 min
B)2 hour 40 min
C)1 hour 20 min
D)1 hour 30 min
E)1 hour 50 min
Rationale: Speed of the boat in still water = 42 km/hr
speed of the stream = 10 km/hr
Speed downstream = (42+10) = 52 km/hr
Distance travelled downstream = 80 km
Time taken =distance/speed
=80/52
= 1.54 hours
= 1 hour 30 min.
ANSWER:D
Answer: D
Question: A train m leaves meerut at 5 a.m. and reaches delhi at 9 a.m. another train leaves delhi at 7 a.m. and reaches meerut at 10.30 a.m. at what time do the two trains_lavel3 cross each other ?
Options:
A)7:56am
B)7:58am
C)7:46am
D)8:56am
E)6:56am
Rationale: Let the total distance be x
so the speed of 1st train is x/4 and 2nd train x/3.5
In 2 hours 1st train covers half of the total distance .
so remaining is only half of the total distance(ie x/2).
let t be the time taken
t*x/4 + t*x/3.5 = x/2
t=14/15 i.e. 56 min
ie
total time taken= 2 hrs + 56 min
time they cross each other is 7:56am
ANSWER:A
Answer: A
Question: How many boxes do we need if we have to carry 250 apples into boxes that each hold 25 apples?
Options:
A)A)9
B)B)5
C)C)7
D)D)10
E)E)None of the above
Rationale: Sol.
Apples 250
Each carries 25
= 250/25
= 10
Answer : D
Answer: D
Question: A set S = {x, -8, -6, -5, 5, 7, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?
Options:
A)Cannot be determined
B)-1
C)1
D)2
E)0
Rationale: Median of the set = (-5+5)/2 = 0
As per statement, Mean of the set = 0
Mean of the set
|y|- |x| +21-19 = 0 (where x is negative n y is positive)
|y|- |x| = -2
So the absolute difference between two numbers is 2
Answer D
Answer: D
Question: Insert the missing number
2, 9, 28, 65, ...
Options:
A)126
B)195
C)121
D)103
E)101
Rationale: the series are 2,9,28,65,126
logic is 1cube+1,2cube+1, 3cube+1,4cube+1, 5cube+1
so the answer is 126
ANSWER:A
Answer: A
Question: When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. When the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?
Options:
A)11
B)17
C)13
D)23
E)None of these
Rationale: Explanatory Answer
When 242 is divided by a certain divisor the remainder obtained is 8.
Let the divisor be d.
When 242 is divided by d, let the quotient be 'x'. The remainder is 8.
Therefore, 242 = xd + 8
When 698 is divided by the same divisor the remainder obtained is 9.
Let y be the quotient when 698 is divided by d.
Then, 698 = yd + 9.
When the sum of the two numbers, 242 and 698, is divided by the divisor, the remainder obtained is 4.
242 + 698 = 940 = xd + yd + 8 + 9
940 = xd + yd + 17
As xd and yd are divisible by d, the remainder when 940 is divided by d should have been 17.
However, because we know that the remainder is 4, it would be possible only when 17/d leaves a remainder of 4.
If the remainder obtained is 4 when 17 is divided by 'd', then 'd' has to be 13.
Choice C
Answer: C
Question: A grocer has a sale of Rs. 6400, Rs. 3545, Rs. 9500, Rs. 7500 for 4 consecutive months. How much sale must he have in the fifth month so that he gets an average sale of Rs. 5500?
Options:
A)Rs. 480
B)Rs. 555
C)Rs. 499
D)Rs. 490
E)Rs. 500
Rationale: Total sale for 4 months = Rs. (6400 +3545 +9500 + 7500 ) = Rs. 26945.
Required sale = Rs. [ (5500 x 5) - 26945 ]
= Rs. (27500 - 26945)
= Rs. 555.
B)
Answer: B
Question: the average distance between the sun and a certain planet is approximatly 4.7 10^8 inches. which of the following is the closest to the average distence between sun and the planet in kelometers? (1 km is approx 3.9 x 10^4 inches)
Options:
A)12.05 x(10)^3
B)22.05 x(10)^4
C)14.05 x(10)^6
D)13.05 x(10)^8
E)12.05 x(10)^9
Rationale: No need to solve entire problem.
Distance in KM = 47*(10)^8/39*(10)^4 which is -470*(10)^7/39*(10)^4 = 12.05 x(10)^3
Answer : A
Answer: A
Question: A man spends 35% of his income on food, 25% on children education and 80% of the remaining on house rent. What percent of his income he is left with?
Options:
A)1%
B)8%
C)12%
D)5%
E)4%
Rationale: Let the total income be x
then, income left = (100-80)% of x - [100-(35+25)]% of x = 20% of 40% of x = 8% of x
Answer is B
Answer: B
Question: A and B invests Rs.3000 and Rs.8000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
Options:
A)9:6
B)9:8
C)9:16
D)9:9
E)9:5
Rationale: (3*6 + 6*6): (8*12)
54:96 => 9:16.Answer:C
Answer: C
Question: At a summer camp with 2100 participants, 1/2 of the campers are aged 8 to 12. Next year, the number of campers aged 8 to 12 will increase by 1/3. After this change, what percentage of the total 2100 campers will the 8- to 12-year-olds represent?
Options:
A)62
B)68
C)66
D)64
E)66 2/3
Rationale: Total - 2100 participants
campers are aged 8 to 12 = (1/2)*2100 = 1050
Next year, campers are aged 8 to 12 = (4/3)*1050 = 1400
Percentage = (1400/2100)*100 = 66 2/3%
Answer: Option E
Answer: E
Question: The sum of the present ages of a father and his son is 42 years. Six years ago, father's age was four times the age of the son. After 6 years, son's age will be:
Options:
A)14
B)16
C)18
D)20
E)22
Rationale: Let the present ages of son and father be x and (42 - x) years respectively.
Then, (42 - x) - 6 = 4(x - 6)
36 - x = 4x - 24
x = 12
The son's age after 6 years will be 18.
The answer is C.
Answer: C
Question: For integers x and y, if 91x = 8y, which of the following must be true?
I. x > y
II. y is not an integer
III. The cube root of x is an integer
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: Statement 1: y>x
When y=x=0, equation holds but y is not greater than x
When x=-8 and y=-91, equation again holds but x>y
TRUE
Statement 2: y is not an integer
Since x and y are integers, 91x and 8y must also be integers.
It is given that 91x=8y
or 13*7*x = 8 y
or 13x = 8y/7
To balance the equation, y must be an integer
NOT TRUE
Statement 3: The cube root of x is an integer
x can be equal to 2*2*2*3 and for this value of x,y will be 13*7*3
So, x may or may not be a cube root.
NOT TRUE
Answer:-A
Answer: A
Question: In the game of Yahtzee, a "full house" occurs when a player rolls five fair dice and the result is two dice showing one number and the other three all showing another (three of a kind). What is the probability that a player will roll a full house on one roll of each of the three remaining dice if that player has already rolled a pair on the first two?
Options:
A)1/3
B)5/54
C)5/72
D)5/216
E)1/1296
Rationale: We have that the player rolled XX on the first two dice. To get a "full house" the next three dice must show YYY or XYY in any combination.
The probability of YYY is 5/6*1/6*1/6 = 5/216.
The probability of XYY is 3*1/6*5/6*1/6 = 15/216 (multiply by 3 because XYY can occur in three ways: XYY, YXY, YYX).
The overall probability is 5/216 + 15/216 = 20/216 = 5/54.
Answer: B.
Answer: B