divelab/Sys2Bench huggingface dataset:
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
Options:
A)3630
B)2899
C)277
D)2870
E)2787
Rationale: 6300:4200:10500
3:2:5
3/10 * 12100 = 3630
Answer:A
Answer: A
Question: Find the value of X, Y by solving the below equations
X + Y = 15
X - Y = 5
Options:
A)10, 5
B)8, 7
C)9, 6
D)11, 4
E)12, 3
Rationale: X + Y = 15 ---(I)
X - Y = 5 -----(II) by adding (I) and (II)
------------
2X = 20 ==> X = 20/2 = 10
By Replacing the value of X in (I) we get 10 + Y = 15 ==>
Y = 15 -10 = 5.
So, X = 10, Y = 5
Answer A) 10, 5
Answer: A
Question: A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 64 chose brand C. Which of the following could be the number of customers who preferred brand D?
Options:
A) 1
B) 8
C) 14
D) 20
E) 27
Rationale: I get D, but I'm not sure that my method is sound.
You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote.
x = total number of testers
A + B + C + D
.61x + (.5)(.61x) + 65 + D = x
.61x + .305x + 65 + D = x
I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D.
x = 400
A = 244, B = 122, C = 65..also over 400
x = 600
A = 366, B = 183 C = 65....also over 600
x = 800
A = 488, B = 244, C = 65...D = 3...not an option on the list.
x = 1000
A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question.
E
Answer: E
Question: John had a stock of 1400 books in his bookshop. He sold 62 on Monday, 62 on Tuesday, 60 on Wednesday, 48 on Thursday and 40 on Friday. What percentage of the books were not sold?
Options:
A)81.57%
B)36.5%
C)80.67%
D)56.5%
E)80.57%
Rationale: Let N be the total number of books sold. Hence
N = 62 + 62 + 60 + 48 + 40 = 272
Let M be the books NOT sold
M = 1400 - N = 1400- 272= 1128
Percentage
Books not sold / total number of books = 1128/1200 = 0.81 = 80.57%
correct answer E
Answer: E
Question: Find the maximum value of the function f(x)=x−5 if x is a number between -5 and 13.
Options:
A)6
B)7
C)8
D)9
E)None
Rationale: Solution:
Since f(x) is a linear function whose slope is 1, a positive number, it is strictly increasing for all x. Therefore its maximal value is reached for the largest value of x, x=13 and f(x)=13-5=8.
Answer C
Answer: C
Question: A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?
Options:
A)6
B)5
C)4
D)9
E)6
Rationale: 9 a.m.
Answer: C
Answer: C
Question: Tough and Tricky questions: Percents.
Over the course of a year, a certain microbrewery increased its beer output by 60 percent. At the same time, it decreased its total working hours by 30 percent. By what percent did this factory increase its output per hour?
Options:
A)228.5
B)228
C)229.5
D)220
E)229
Rationale: Lets assume the initial production was 100 litres of beer for 100 hr.
With the 60% increase the total amount of beer production will be 160 litres and with 30 % decrease in total hours will be reduced to 70 hr.
100hr ----> 100 lts
1hr -----> 1 lts
70hr -----> 160 lts
1hr -----> 2.28 lts
Total Increase in production for 1 hr = 228%
Answer B
Answer: B
Question: A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 25% impurities to the product. Find the net profit percentage of the dealer?
Options:
A)44%
B)40%
C)50%
D)56.25%
E)36.25%
Rationale: The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight.
It means that he is selling $4 worth of product for $5.
The dealer then further added 25% impurities to the product.
It means that he is selling $5 worth of product for $6.25.
So his profit is $6.25-$4 = $2.25
and his profit percent is
(2.25/4)*100 = 56.25%
Answer:- D
Answer: D
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
Options:
A)16 2/7%
B)16 2/6%
C)16 2/3%
D)16 7/3%
E)12 2/3%
Rationale: 10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer: C
Answer: C
Question: 5n + 2 > 12 and 7n - 5 < 37; n must be between which numbers?
Options:
A)1 and 8
B)2 and 6
C)0 and 9
D)2 and 7
E)2 and 6
Rationale: 5n > 10 --> n > 2
7n < 42 --> n < 6
2 < n < 6
Answer: E
Answer: E
Question: At 15:00 there were 20 students in the computer lab. At 15:03 and every three minutes after that, 4 students entered the lab. If at 15:10 and every ten minutes after that 8 students left the lab, how many students were in the computer lab at 15:44 ?
Options:
A)7
B)14
C)25
D)27
E)30
Rationale: Initial no of students + 3 * (1 + No of possible 3 minute intervals between 15:03 and 15:44) -
8 *(1 + No of possible 10 minute intervals between 15:10 and 15:44)
20 + 3*14 -8 * 4 = 27
D
Answer: D
Question: There are 10 balls in a box: 5 balls are green, 3 are blue and 2 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a white ball is selected at random from the box?
Options:
A)1/13
B)4/13
C)3/13
D)5/13
E)2/8
Rationale: If 1 green and 1 blue ball are taken from the box, then there are 4 green, 2 blue and 2 white balls, a total of 8 balls. If one ball is selected at random, the probability that it is white is given by 2 / 8
Answer : E
Answer: E
Question: Each of the 43 points is placed either inside or on the surface of a perfect sphere. If 16% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?
Options:
A)3
B)11
C)13
D)23
E)38
Rationale: Maximum number of points on the surface is 16%*43 = 6.88 ... or 6 since it has to be an integer
Now note that if two points form a diameter, they cannot be part of any other diameter.
So in the best case we can pair up the points
We have 6 points, so at best we can form 3 pairs (6).
So, answer is (A)
Answer: A
Question: On a certain scale of intensity, each increment of 10 in magnitude represents a tenfold increase in intensity. On this scale, an intensity corresponding to a magnitude of 160 is how many times an intensity corresponding to a magnitude of 125?
Options:
A)40
B)100
C)400
D)1000
E)10 000
Rationale: Increase of 40 in magnitude corresponds to 10^4 increase in intensity:
If intensity for 125 is x then for 135 it'll be 10*x, for 145 it'll be 10*10*x=10^2*x, for 155 it'll be 10*10*10*x=10^3*x and for 160 it'll be 10*10*10*10*x=10^3*x.
Answer: D.
Answer: D
Question: Working together, printer M and printer N would finish the task in 24 minutes. Printer M alone would finish the task in 60 minutes. How many pages does the task contain if printer N prints 5 pages a minute more than printer M?
Options:
A)400
B)450
C)600
D)1200
E)1500
Rationale: 24*M + 24*N = x pages
in 24 mins printer M will print = 24/60 * x pages = 2/5*x pages
thus in 24 mins printer printer N will print x - 2/5*x = 3/5*x pages
Also it is given that printer N prints 5 more pages per min that printer M. In 24 mins printer N will print 120 more pages than printer M
thus 3/5*x - 2/5*x = 120 => x = 600 pages
C)
Answer: C
Question: If 'a' and 'b' are non-zero numbers such that their sum is ten times the product, what is the value of 1/a + 1/b?
Options:
A)2
B)5
C)10
D)15
E)20
Rationale: a+b = 10ab
1/a + 1/b = (b + a)/(ab) = 10.
The answer is C.
Answer: C
Question: Two friends plan to walk along a 22-km trail, starting at opposite ends of the trail at the same time. If Friend P's rate is 20% faster than Friend Q's, how many kilometers will Friend P have walked when they pass each other?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: If Q complete x kilometers, then P completes 1.2x kilometers.
x + 1.2x = 22
2.2x=22
x = 10
Then P will have have walked 1.2*10=12 km.
The answer is C.
Answer: C
Question: 1100 boys and 700 girls are examined in a test; 42% of the boys and 30% of the girls pass. The percentage of the total who failed is ?
Options:
A)63.3%
B)52.4%
C)81.2%
D)75.4%
E)69.1%
Rationale: Total number of students = 1100+700 = 1800
Number of students passed = (42% of 1100+30% of 700) = 462+210 = 672
number of failures = 1128*100/1800 = 190/3%= 63.3%
Answer is A
Answer: A
Question: The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
Options:
A)36
B)27
C)72
D)29
E)22
Rationale: Sum of the 10 numbers = 230
If each number is increased by 4, the total increase =
4 * 10 = 40
The new sum = 230 + 40 = 270 The new average = 270/10
= 27.
Answer:B
Answer: B
Question: Find the odd man out. 18, 16, 12, 24, 11, 34, 46
Options:
A)16
B)46
C)16
D)11
E)12
Rationale: Explanation :
11 is the only odd number in the given series. Answer : Option D
Answer: D
Question: Out of a world population of approximately 6.6 billion, 1.2 billion people live in the richer countries of Europe, North America, Japan and Oceania and is growing at the rate of 0.25% per year, while the other 5.4 billion people live in the lees developed countries and is growing at the rate of 1.5%. What will be the world population in 5 years if we assume that these rates of increase will stay constant for the next 5 years. (round answer to 3 significant digits)
Options:
A)7.02 billion.
B)7.03 billion.
C)7.04 billion.
D)7.05 billion.
E)7.06 billion.
Rationale: Solution to Problem 12:
Let us first calculate the population PR in 5 years in the richer countries
PR = (1.2 + 0.25% * 1.2) = 1.2(1 + 0.25%) after one year
PR = 1.2(1 + 0.25%) + 0.25% * 1.2(1 + 0.25%)
= 1.2(1 + 0.25%) 2after two years
Continue with the above and after 5 years, PR will be
PR = 1.2(1 + 0.25%) 5 after 5 years
Similar calculations can be used to find the population PL in less developed countries after 5 years.
PL = 5.4(1 + 1.5%) 5 after 5 years
The world population P after 5 years will be
P = PR + PL = 1.2(1 + 0.25%) 5 + 5.4(1 + 1.5%) 5 = 7.03 billion.
Answer B
Answer: B
Question: A right triangle AWC has to be constructed in the xy-plane so that the right angle is at A and AW is parallel to x axis. The coordinates of A, W and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties?
Options:
A)63
B)336
C)567
D)3024
E)5040
Rationale: All the cordinates are integer hence,
possible AW values are
{-1,0}, {-1,1} ....{-1,7}: 8 ways
....
{7,-1}, {7,0} ......{7,6}: 8 ways
9*8 ways = 72
for AC values can be
{1,2}, {1,3} .... {1,7} : 6ways
......
{7,1}, {7,2} ..... {7,6} : 6 ways
7*6 = 42
Total = 72 * 42 = 3024 hence D
Answer: D
Question: At a wedding reception, 125 guests ate chicken and 75 guests ate beef. If exactly 100 guests ate only one of the two types of meat, how many guests ate both types of meat?
Options:
A)5
B)100
C)7
D)4
E)50
Rationale: Say x guests ate both types of meat.
(125 - x) + (75 - x) = 100 --> x = 50.
Answer: E.
Answer: E
Question: After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago.What is the difference between the ages of the replaced and the new member?
Options:
A)2 years
B)4 years
C)8 years
D)15 years
E)25 years
Rationale: the age 5 members will be 13,14,15,16 and 17
3 years before there age was 10,11,12,13 and 14 hence the average is 12(10+11+12+13+14/5=60/5=12).
now if the oldest man 17 is replaced by 2 the the average is become same as three years ago the are .
as (13+14+15+16+2)/5 = 60/5=12.
hence the difference between the ages of the replaced and the new member is 17-2=15.
ANSWER:D
Answer: D
Question: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
Options:
A)50
B)874
C)168
D)578
E)120
Rationale: Explanation:
Let speed of the car be x kmph
hen, speed of the train =150/100X=3/2X kmph
75/x-75/(3/2)x=125/(10*60)
75/x-50/x=5/24
x=25*24/5=120 kmph
Answer E
Answer: E
Question: 70 students are required to paint a picture. 52 use green color and some children use red, 38 students use both the colors. How many students use red color?
Options:
A)53
B)54
C)55
D)56
E)57
Rationale: 70 = red +green -both
Red = 70-green+both = 70-52+38=56
ANSWER:D
Answer: D
Question: A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many science books were there at the starting?
Options:
A)500
B)560
C)670
D)800
E)900
Rationale: science books sold = 2x × 0.2 = 0.4x
science books unsold = 2x – 0.4x = 1.6x
art books sold = 5x × 0.2 = x
art books unsold = 5x – x = 4x
total books unsold = 1.6x + 4x = 5.6x
5.6x = 2240
x = 400
2x science = 800
D
Answer: D
Question: A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as remainder. The number is
Options:
A)22030
B)220030
C)23030
D)24030
E)20303
Rationale: Explanation:
(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030
Option B
Answer: B
Question: The Racing magic takes 40 seconds to circle the racing track once. The Charging bull makes 40 rounds of the track in an hour. If they left the starting point together, how many minutes will it take for them to meet at the starting point for the second time?
Options:
A)3
B)6
C)9
D)12
E)15
Rationale: Time taken by Racing magic to make one circle = 40 seconds
Time taken byCharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds
LCM of 90 and 40 seconds = 360 seconds = 6 mins
Time taken for them to meet at the starting point for the second time = 6 mins *2 = 12 mins
Answer D
Answer: D
Question: Balls are bought at 11 for Rs.10/- and sold at 10 for Rs.11/-. Find the gain or loss percentage?
Options:
A)21 % Profit
B)22 % Profit
C)24 % Profit
D)31 % Profit
E)32 % Profit
Rationale: 11 balls -----> Rs.10/-
10 balls -----> Rs.11/-
Note: Number of articles bought is must equal to number of articles sold.
10(11 10) ==> 110 100 = Cost price
11(10 11) ==> 110 121 = Selling price
Then, 21/100 × 100 = 21 % Profit
A)
Answer: A
Question: if there is one larger cube with surface area 600 and no. of smaller cubes with surface area 24.then how many small cubes are required to make a larger cube with surface area of 600?
Options:
A)5
B)125
C)4
D)100
E)24
Rationale: the ratio between larger and smaller is
6a12:6a22=600:24
a12:a22=100:4
a1:a2=10:2
then length of cube is 10 and 2
so make a cube with length 10, we have to 5 small cubes each in length, breadth and height. so total 125 cubes are required.
then the answer is B
Answer: B
Question: In a village the average age of n people is 42 years. But after the verification it was found that the age of a person had been considered 20 years less than the actual age, so the new average, after the correction,increased by 1. The value of n is?
Options:
A)11
B)20
C)28
D)17
E)13
Rationale: Explanation:
It is the same as a person with 20 years more age replaces an existing person of the group ( or village)
Since the total age of the village having n persons, is being increased by 20 years and the average age of village is being increased by 1 year, hence there are total 20 people in the village.
Alternatively : ( n x 42 ) + 20 = ( n x 43 )
=> n=20
Answer: B
Answer: B
Question: Harry started a 7-mile hike with a full 11-cup canteen of water and finished the hike in 3 hours with 2 cup of water remaining in the canteen. If the canteen leaked at the rate of 1 cup per hour and Harry drank 3 cups of water during the last mile, how many cups did he drink per mile during the first 6 miles of the hike?
Options:
A)2/6
B)3/6
C)4/6
D)6/4
E)5/6
Rationale: No of cups leaked during the trip = 3 cups.
No of cups Harry drank = 6 cups.
No of cups harry drank during the first 6 miles = 3.
drink / mile = 3/6
Answer: B
Answer: B
Question: A, B and C enter into a partnership. A invests 3 times as much as B invests and 2/3 of what C invests. At the end of the year, the profit earned is Rs. 55000. What is the share of C?
Options:
A)Rs. 12250
B)Rs. 13375
C)Rs. 16750
D)Rs. 15000
E)None of these
Rationale: Explanation:
Let the investment of C be Rs. x.
The inverstment of B = Rs.(2x/3)
The inverstment of A = Rs. (3 × (2/3)x) = Rs. (2x)
Ratio of capitals of A, B and C = 2x : 2x/3 : x = 6 : 2 : 3
C's share = Rs. [(3/11) × 55000] = Rs. 15000
Answer: Option D
Answer: D
Question: A man invested Rs. 14,400 in Rs. 100 shares of a company at 25% premium.If the company declares 5% dividend at the end of the year,then how much does he get ?
Options:
A)Rs. 576
B)Rs. 600
C)Rs. 650
D)Rs. 720
E)None
Rationale: Solution
Number of shares = (14400/125) = 115.2.
Face value = Rs. (100x115.2 ) = Rs. 11520.
Annual income = Rs.(5/100x11520) = Rs. 576.
Answer A
Answer: A
Question: X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
Options:
A)2
B)6
C)7
D)8
E)5
Rationale: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000
Let investment period of Z be x months.
Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)
= 240 : 300 : 30x = 8 : 10 : x
The share of Z in the annual profit of Rs. 50000 is Rs. 14000.
=> [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7
=> 25x = 7x + (18 * 7) => x = 7 months.
Z joined the business after (12 - 7) months. i.e., 5 months.
Answer: E
Answer: E
Question: If the sum and difference of two numbers are 5 and 10 respectively, then the difference of their square is:
Options:
A)50
B)28
C)160
D)180
E)18
Rationale: Let the numbers be x and y.
Then, x + y = 5 and x - y = 10
x2 - y2 = (x + y)(x - y) = 5 * 10 = 50.
ANSWER:A
Answer: A
Question: 47% of the students in a class of 38 students has glasses or contacts. How many students in the class have either glasses or contacts?
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: a=r⋅b
47%=0.47a
=0.47⋅34
a≈18
Option D is correct.
Answer: D
Question: A person travels at a speed of 10 mph from one city to another. However while returning as there was not much traffic. He came with a speed of 15mph. what is his average speed?
Options:
A)10Kmph
B)11Kmph
C)12Kmph
D)13Kmph
E)14Kmph
Rationale: Average speed = 2xy/(x+y) = (2*15*10)/25 = 12Kmph
ANSWER:C
Answer: C
Question: In a barrel of juice there is 20 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?
Options:
A)3:2.
B)2:1.
C)3:1.
D)4:3.
E)3:4
Rationale: Price of 20 L juice= 3x
1L= 3x/20
Price of 80 L beer= 4x
1L= 4x/80
Ratio of 1 L price = 3x/20/4x/80= 3:1
C is the answer
Answer: C
Question: A fruit seller had some oranges. He sells 10% oranges and still has 360 oranges. How many oranges he had originally?
Options:
A)420
B)700
C)220
D)400
E)None of these
Rationale: Explanation :
He sells 10% of oranges and still there are 360 oranges remaining
=> 90% of oranges = 360
⇒ (90 × Total Oranges)/100 = 360
⇒ Total Oranges/100 = 4
⇒ Total Oranges = 4 × 100 = 400
Answer : Option D
Answer: D
Question: A dog takes 2 leaps for every 3 leaps of a hare. If one leap of the dog is equal to 5 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
Options:
A)9 : 3
B)3 : 10
C)2 : 3
D)6 : 3
E)10 : 3
Rationale: Explanation:
Dog : Hare = (2*5) leaps of hare : 3 leaps of hare = 10 : 3
Answer: E
Answer: E
Question: A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ?
Options:
A)1/3
B)2by3
C)2/5
D)3/5
E)4/5
Rationale: Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol.
Let x ml be the amount removed ---> total alcohol left = 4-0.4x
New quantity of whiskey added = x ml out of which 0.19 is the alcohol.
Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x = 20/3 ml.
Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (20/3)/10 = 2/3.
Hence, B is the correct answer.
Answer: B
Question: A train passes a station platform in 36 sec and a man standing on the platform in 25 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)288
B)165
C)881
D)1277
E)121
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 25 = 375 m.
Let the length of the platform be x m . Then,
(x + 375)/36 = 15 => x = 165 m.
Answer: B
Answer: B
Question: What is 2/5 of 5/9 of 1/2?
Options:
A)1/4
B)1/9
C)9/16
D)5/8
E)16/9
Rationale: 2/5 * 5/9 * 1/2= 1/9
Answer: B
Answer: B
Question: If q = 50! + 1, which of the following cannot be a prime factor of q?
I. 11
II. 29
III. 41
Options:
A)I​ only
B)III only
C)II and III
D)I and II
E)I​, II, and III
Rationale: The numbers 11, 29, and 41 are all factors of 50!
Therefore they can not be factors of 50! + 1.
The answer is E.
Answer: E
Question: There are 19 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season?
Options:
A)1710
B)1920
C)2440
D)2860
E)3260
Rationale: The number of ways to choose two teams is 19C2 = 19*18/2 = 171
The total number of games in the season is 10*171 = 1710.
The answer is A.
Answer: A
Question: The food in a camp lasts for 36 men for 45 days. If twelve more men join, how many days will the food last?
Options:
A)80 days
B)30 days
C)65 days
D)34 days
E)15 days
Rationale: one man can consume the same food in 36*45 = 1620 days.
12 more men join, the total number of men = 48
The number of days the food will last = 1620/48
= 34 days.
Answer:D
Answer: D
Question: The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago ?
Options:
A)71 years
B)72 years
C)74 years
D)77 years
E)78 years
Rationale: Required sum = (80 - 3 x 3) years = (80 - 9) years = 71 years.
Answer: Option A
Answer: A
Question: The “c-number” of a number x is defined as the ones digit of 2^x. Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^c, where c is the c-number of the result of his die roll, and plots 3^c on a number line as the point A. Finally, he repeats this entire process, this time plotting the result as the point B. What is the probability that the distance between A and B is greater than the value of B?
Options:
A) 3/8
B) 13/36
C) 17/36
D) 19/36
E) 23/36
Rationale: If you calculate 3^c for 1st roll, all 6 results will be 9, 81, 6561, 729, 9, 81. This result is the same for 2nd roll. 9, 81, 6561, 729, 9, 81.
About distance: If the first result is 9 and the second is also 9, the distance is 9-9=0 which is smaller than 9. If the first result is 9 and the second is 81, the distance is 81-9=72 which is also smaller than B which has the value of 81. If the first result is 81 and the second is 9, the distance will be greater than B. Distance 81-9=72>9.
On the first roll, the probability of getting result 9 is 2/6. In this case no other alternative values for second roll which would make the distance greater than B. So probability is 0. So next estimations are:
probability of getting 81 on the first roll (2/6) * probability of getting 9 on the second roll (2/6) = 1/9
probability of getting 729 on the first roll (1/6) * probability of getting 9, 81 on the second roll (4/6) = 1/9
probability of getting 6561 on the first roll (1/6) * probability of getting 9, 81, 729 on the first roll (5/6) = 5/36
All together: 1/9 + 1/9 + 5/36 = 13/36=B
Answer: B