divelab/Sys2Bench huggingface dataset:
Question: If 7 men and 2 boys working together, can do six times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?
Options:
A)2:5
B)2:3
C)1:8
D)4:1
E)3:2
Rationale: 7M + 2B = 6(1M + 1B)
7M + 2B = 6M + 6B
1M = 4B
The required ratio of work done by a man and a boy = 4:1
Answer:D
Answer: D
Question: Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
Options:
A)40/9 days
B)20/9 days
C)30/9 days
D)60/9 days
E)10/9 days
Rationale: A's one hour work = 1/8.
B's one hour work = 1/10.
(A+B)'s one hour work = 1/8+1/10 = 9/40.
Both A & B can finish the work in 40/9 days
Answer : A
Answer: A
Question: The compound interest on $2000 at 10% per annum is $662. The period(in years) is?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: A = P(1 + R/100)^T
2662 = 2000(1 + 10/100)^T
(11/10)^T = 2662/2000
(11/10)^T = (11/10)^3
T = 3 years
Answer is B
Answer: B
Question: 45 men can complete a work in 19 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work?
Options:
A)6.2
B)10
C)15
D)7.8
E)8
Rationale: 45*19 men can complete the work in 1 day
1 man's 1 day work = 1/855
45 men 6days work = 6*1/19 =6/19
remaining work = 1-6/19 = 13/19
75 men's 1 day's work = 75/855 = 5/57
13/19 work is done by them in 57/5 * 13/19 = 7.8days
Answer is D
Answer: D
Question: A,B and C are employed to do apiece of work for Rs.529. A and C are supposed to finish 19/23 of the work together. How much shall be paid to B?
Options:
A)10
B)11
C)12
D)14
E)16
Rationale: C
12
12 men can complete a work in 18 days. Six days after they started working, 4 more men joined them. How many days will all of them together complete the remaining work?
Answer: C
Question: A 40-liter solution of alcohol and water is 5 percent alcohol. If 4.5 liters of alcohol and 5.5 liters of water are added to this solution, what percent of the solution produced is alcohol?
Options:
A)7%
B)10%
C)13%
D)16%
E)19%
Rationale: The percent of alcohol in the solution is (0.05(40) + 4.5) / 50 = 6.5/50 = 13%
The answer is C.
Answer: C
Question: A Bus 125 m long passes a man, running at 5 km/hr in the same direction in which the bus is going, in 10 seconds. The speed of the bus is:
Options:
A)100 km/hr
B)50 km/hr
C)55 km/hr
D)60 km/hr
E)35 km/hr
Rationale: speed = 125/10=25/2
==>25/2*18/5
==>45 km/hr
speed of bus x km/hr
x-5 km/hr ==> 45
x = 50 km/hr
ANSWER B
Answer: B
Question: Jim walks 3.3 mph and wants to walk to Dales house that's 3.5 miles away. How long will it take him to get there?
Options:
A)78 minutes approx
B)61 minutes approx
C)34 minutes approx
D)1 hr 6 m approx
E)1 hr 33 min approx
Rationale: 3.5/3.3= 1 hr 6 mins approx
Correct answer D
Answer: D
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
Options:
A)12.8 kmph
B)32.5 kmph
C)18.5 kmph
D)12.5 kmph
E)12.4 kmph
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer:D
Answer: D
Question: A class of students appeared in two different tests of quantitative ability both of which were scored out of 100. The scores of each student in each test could be expressed as a product of two distinct prime numbers. If a student’s scores in the two tests did not have any common prime factors, what is the maximum possible difference between his two scores?
Options:
A)79
B)83
C)88
D)89
E)91
Rationale: I started by listing out the primes
2,3,5,7,11,13,17,19,23,29,31,37
Then I tried to maximize the score--we know the minimum score will be 6 as the product has to be between two distinct primes.
Our max score is 100 so lets try to get as close to 100 as possible. 19*5=95
95-6=89
ANSWER:D
Answer: D
Question: 5 coins are tossed together. What is the probability of getting exactly 2 heads?
Options:
A)10
B)5/16
C)3/16
D)7/16
E)8/16
Rationale: Since 5 coins are tossed, sample space = 20/2=10
Getting exactly 2 heads=32
p(E) = 20/32=5/16
ANSWER:B
Answer: B
Question: A sum of money at simple interest amounts to Rs. 820 in 3 years and to Rs. 854 in 4 years. The sum is:
Options:
A)500
B)718
C)780
D)910
E)None
Rationale: Sol.
S.I. for 1 year = Rs. (854 - 820) = Rs. 34.
S.I. for 3 years = Rs. (34 * 3) = Rs. 102.
âˆ´ Principal = Rs. (820 - 102) = Rs. 718
Answer B
Answer: B
Question: If x + y + z = 0 then,
x^2 + y^2 + z^2/(x-y)^2 + (y-z)^2 + (z-x)^2 = ?
Options:
A)0
B)1
C)xyz
D)x+y+z
E)None
Rationale: =>(x + y + z)² = x² + y² + z² + 2xy + 2xz + 2yz
=> x + y + z = 0 given
=>So, x² + y² + z² = - 2(xy + xz + yz) .....(1)
(x² + y² + z²)
------------------- = ?
(x-y)²+(y-z)²+(z-x)²
(x² + y² + z²)
------------------------------------
2(x² + y² + z²)- 2(xy + xz + yz)
(x² + y² + z²)
------------------------------- [:: from (1)]
2(x² + y² + z²) + x² + y² + z²
(x² + y² + z²)
------------------ .........[::if x,y,z != 0, excluding the trivial case]
3(x² + y² + z²)
=> ans 1/3
ANSWER:E
Answer: E
Question: Rs.525 among A, B and C such that B may get 2/3 of A and C together get. Find the share of C?
Options:
A)228
B)150
C)992
D)277
E)232
Rationale: A+B+C = 590
5A = 6B = 8C = x
A:B:C = 1/5:1/6:1/8
= 24:20:15
15/59 * 590 = Rs.150
Answer: B
Answer: B
Question: The average score of a cricketer in 2 matches is 60 and in other 3 matches is 50. Then find the average score in all the 5 matches?
Options:
A)54
B)27
C)30
D)35
E)42
Rationale: Average in 5 matches = (2*60 + 3*50)/2+3 = 120+150/ 5 = 270/5 = 54
Answer is A
Answer: A
Question: In how many ways can the letters of wordELECTRICALbe arranged such that all the Consonants always appear together?
Options:
A)9!
B)5!*4!
C)5!*6!
D)5!*4!*2!
E)6!*4!
Rationale: Let the arrangment be: _ _ _ _ _ _ _ _ _ _ (10 letters, 4 vowels E, E, I, A and 6 consonant L, C, T, R, C, L)
For all consonants together, consider them as 1 group {L, C, T, R, C, L} E E I A --> this gives us 5! arrangements with {} group considered as 1 . Now {} group can in itself be arranged in 6! ways
Thus total arrangements with all consonants together = 5!*6! --> C is the correct answer.
Answer: C
Question: The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 21. The corrected new mean is :
Options:
A)36.54
B)36.58
C)36.23
D)36.14
E)36.81
Rationale: Explanation:
Correct Sum = (36 * 50 + 48 - 21) = 1827.
Correct mean = = 1827/50 = 36.54
Answer: A) 36.54
Answer: A
Question: A Cuban cigar would cost 6 dollar less than 1.5 times a French cigar, had the French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What is the price of the French cigar?
Options:
A)12.7$.
B)23$.
C)25.5$.
D)35$.
E)11.7$.
Rationale: The three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each.
From the given data we know French cigar < Cuban cigar < Arabic cigar
and each is more expensive 1.5 times. Therefore eliminate options C,D,A straightaway . Since French cigar is at least 1.5 times cheaper we know B cannot be the answer.
Therefore E is the answer.
Answer: E
Question: 23 people are there, they are shaking hands together, How many hand shakes possible, if they are in pair of cyclic sequence ?
Options:
A)20
B)77
C)66
D)88
E)11
Rationale: Answer:A
Answer: A
Question: The weight of a hollow sphere is directly dependent on its surface area. The surface area of a sphere is 4π·R^2, where R is the radius of the sphere. If a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams, a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams R?
Options:
A)16
B)R=32
C)R=64
D)128
E)512
Rationale: Weight directly proportional to 4 pi r^2
Now, 4pi is constant, so, weight is directly proportional to r^2.
When radius = 0.15, weight = 8, so (0.15) ^ 2 proportional to 8;
(0.15)^2 * 4 proportional to 8*4, solving further
(0.15)^2 * 2 ^2 = (0.15*2)^2 = 0.3 ^ 2; so answer = 32 (B)
Answer: B
Question: A broker invested her own money in the stock market. During the first year, she increased her stock market wealth by 60 percent. In the second year, largely as a result of a slump in the stock market, she suffered a 30 percent decrease in the value of her stock investments. What was the net increase or decrease on her overall stock investment wealth by the end of the second year?
Options:
A)−5%
B)5%
C)12%
D)20%
E)80%
Rationale: The actual answer is obtained by multiplying 160% by 70% and subtracting 100% from this total. That is: 160% × 70% = 112%; 112% − 100% = 12%.
Answer: C
Answer: C
Question: The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 32 years, then find the age of the person sitting in the middle of the row?
Options:
A)9 years
B)29 years
C)25 years
D)19 years
E)17 years
Rationale: Total age seven persons = (28 * 7)years
Total age of the first three persons and the last three persons are (25 * 3) years and (32 * 3) years respectively.
Age of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 32 * 3 = 196 - 75 - 96 = 25 years.
ANSWER:C
Answer: C
Question: Consider a right circular cone of base radius 4 and height 10 cm. A cylinder is to be placed inside the cone with one of the flat surface resting on the base of the cone. Find the largest possible total surface area (in sq cm) of the cylinder.
Options:
A)100π/3
B)80π/3
C)120π/7
D)130π/9
E)110π/7
Rationale: Explanation :
Let the radius of cylinder be r and its height is h.
So, the height remained above cylinder is 10-h
Also, triangles ABC and ADE are similar. so ratio of corresponding sides must be equal
i.e AB/AD = BC/DE.
i.e. (10-h)/10 = r/4.
so 40 - 4h = 10r (by cross multiply)
h = (40-10r)/4 = 10-2.5r
Now we have total surface area of cyl = 2*π*r*h + 2*π*r2.
Putting value of h = 10 - 2.5r here, we get S = 2*π*r*(10-2.5r) + 2*π*r2.
S = 20*π*r- 5 * π * r2 + 2 * π * r2 .
S = 20 *π*r- 3*π*r .
Now, we have to maximize S, so differentiate it w.r.t r, we get
S = 20*π - 6 * π * r setting it to zero, we get
=> 20*π - 6 * π * r= 0
=> r = 20/6 = 10/3.
So, h = 10 - 2.5r = 10 - 2.5*10/3 = 5/3
So,
=> S = 2 * π * r * h + 2 * π * r2.
=> S = 2 * π * 10/3 * 5/3 + 2 * π* 100/9.
=> S = 2 * π * 50/9 + 2 * π* 100/9.
=> S = 2π150/9.
=> S = 100π/3.
Answer : A
Answer: A
Question: An article is bought for Rs.675 and sold for Rs.1100, find the gain percent?
Options:
A)65%
B)64%
C)63%
D)62%
E)61%
Rationale: 675 ---- 425
100 ---- ? =>
=63%
Answer:C
Answer: C
Question: A two digit no is 18 less than square of the sum of its digit.how many such no are there?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 63=(6+3)^2-18=81-18
82=(8+2)^2-18=100-18
ANSWER:A
Answer: A
Question: If a/b = 5/2, b/c = 1/2, c/d = 1, d/e = 3/2 and e/f = 4/3, then what is the value of abc/def ?
Options:
A) 15/8
B) 14/3
C) 41/7
D) 3/18
E) 18/4
Rationale: Say a = 2. Then:
a/b = 5/2 --> b = 2/5;
b/c = 1/2 --> c = 4/5;
c/d = 1 --> d = 4/5;
d/e = 3/2 --> e = 8/15;
e/f = 4/3 --> f = 2/5.
abc/def = (1*2/5*4/5)/(4/5*8/15*2/5) = 15/8.
Answer: A.
Answer: A
Question: If 3x < 2y < 0, which of the following must be the greatest?
Options:
A)2y - 3x
B)3x - 2y
C)-(3x - 2y)
D)-(3x + 2y)
E)0
Rationale: Plugging in -1 for both x and y we get
A. 2y - 3x = 2
B. 3x - 2y = -1
C. -(3x - 2y) = 3
D. -(3x + 2y) = 15
E. 0
Answer: D
Answer: D
Question: TOM traveled the entire 60 miles trip. If he did the first 15 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 45 miles per hour, what is the his average speed, in miles per hour?
Options:
A)35.62mph
B)25.45mph
C)34.52mph
D)36.92mph
E)36.29mph
Rationale: avg speed = total distance/ total time = (d1+d2)/(t1+t2) = (15+45) / ((15/24)+(45/45)) = 60*2/3 = 36.92mph
D
Answer: D
Question: There are X persons and Y chocolates. If each person is given 1 chocolate then 1 chocolate is left, if each person is given 2 chocolates then 1 person will be left. So how many persons and chocolates are there??
Options:
A)3,2
B)3,3
C)3,4
D)4,5
E)4,4
Rationale: X person, Y chocolates
1st equation ==> (Y-1)/x = 1
2nd equation ==> Y/(X-1) = 2
Solving we get x = 3 , Y =4
ANSWER:C
Answer: C
Question: 23 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
Options:
A)None of these
B)506
C)512
D)524
E)542
Rationale: Explanation :
He can go in any bus out of the 23 buses.
Hence He can go in 23 ways.
Since he can not come back in the same bus that he used for travelling,
He can return in 22 ways.
Total number of ways = 23 x 22 = 506. Answer : Option B
Answer: B
Question: (x-2) men can do a piece of work in x days and (x+7) men can do 75% of the same work in (x-10)days. Then in how many days can (x+10) men finish the work?
Options:
A)27 days
B)12 days
C)25 days
D)18 days
E)None of these
Rationale: Explanation:
(3/4) × (x - 2)x = (x + 7)(x - 10)
=> x2 - 6x - 280 = 0
=> x= 20 and x=-14
so, the acceptable values is x=20
Total work = (x - 2) × x = 18 × 20 = 360 unit
Now 360 = 30 × k (30 = 20 + 10)
k = 12 days
Answer: B
Answer: B
Question: If 20,374 + x is a multiple of 5, which of the following could be the value of x?
Options:
A)1
B)2
C)3
D)4
E)6
Rationale: Sum of the digits of 20,374 is 2+0+3+7+4 = 16
Now 16 is not a multiple of 5, the next multiple of 5 close to 16 is 20, which is 4 added to 16.
So the least number to be added to 20,374 is 4.
D
Answer: D
Question: There are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then A:D will be?
Options:
A)1 : 2
B)2 : 3
C)3 : 5
D)4 : 7
E)4 : 9
Rationale: Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6
∴A∶B∶C∶D= 3 : 4 : 5 : 6.
Thus, A : D = 3 : 6 or, 1 : 2
A
Answer: A
Question: Pat, kate and mark charged a total of 198 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate.
Options:
A)18
B)36
C)72
D)110
E)108
Rationale: Let Kate charge for x hours,
then Pat charged for 2x and Mat - for 6x.
So, 2x+6x+x = 198 -total hours charged for,
x= 22.
Mat charged 6x-x or 5x for more hours than kate, or for 110 hours .
D is correct
Answer: D
Question: According to the directions on the can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounces cans of the concentrate are required to prepare 240 6 ounces servings of orange juice?
Options:
A)a) 25
B)b) 34
C)c) 50
D)d) 67
E)e) 30
Rationale: Its E.
Total juice rquired = 240*6 = 1440 ounce
12 ounce concentate makes = 12 * 4 = 48 ounce juice
Total cans required = 1440/48 = 30.
Answer E
Answer: E
Question: 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 47, then how old is B?
Options:
A)7
B)8
C)9
D)18
E)11
Rationale: Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 47
5x = 45 => x = 9
Hence, B's age = 2x = 18 years.
ANSWER:D
Answer: D
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1215 as rent for parking his cars, what is the total rent paid by all the four agencies?
Options:
A)6642
B)2778
C)1279
D)6150
E)2771
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1215
45k = 1215 => k = 27
246k = 246(27) = Rs. 6642
Thus the total rent paid by all the four agencies is Rs. 6642.
Answer: A
Answer: A
Question: Last year the range of the annual bonus of the 100 employees at Company X was $20,000. If the annual bonus of each of the 100 employees this year is 10 percent greater than it was last year, what is the range of the annual bonus of the 100 employees this year?
Options:
A) $27,000
B) $22,000
C) $33,000
D) $16,000
E) $43,000
Rationale: let the lowest bonus be x.
Therefore, highest bonus is x +20000.
Now bonus of each employee is increased by 10%.
Therefore the bonus will remain arranged in the same order as before.
or Lowest bonus = 1.1x and Highest = 1.1 * (x+20000)
or Range = highest - lowest = 1.1 * (x+20000) - 1.1x
= 22000, Hence, B
Answer: B
Question: (150% of 1265) ÷ 7 = ?
Options:
A)A)125
B)B)175
C)C)271
D)D)375
E)E)524
Rationale: Explanation :
? = (150 x 1265/100) ÷ 7 = 189750/700 = 271
Answer : Option C
Answer: C
Question: A fruit seller had some apples. He sells 40% and still has 420 apples. Originally, he had ?
Options:
A)588 apples
B)600 apples
C)672 apples
D)700 apples
E)None
Rationale: Answer
∵ 60% of N = 420
∴ N = (420 x 100)/60 = 700
Correct Option: D
Answer: D
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40 sec
B)11 sec
C)88 sec
D)19 sec
E)10 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Answer: A
Answer: A
Question: After running a series of television advertisements, a leading beverage producer saw its sales increase by 25% to $3 million dollars per month. Prior to the advertising campaign, about how many dollars in sales did the company average per day?
Options:
A)$1.25 million
B)$80,000
C)$750,000
D)$27,000
E)$10,000
Rationale: Let sales in previous month = X
1.25 X=2,000,000
5/4 X= 2,000,000 ..........> X=2,400,000
sales per day= 2,400,000/30= less than 80,000
Answer:B
Answer: B
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform.
Options:
A)310 meter
B)335 meter
C)345 meter
D)350 meter
E)None of these
Rationale: Explanation:
Speed = Distance/time = 300/18 = 50/3 m/sec
Let the length of the platform be x meters
then
Distance=Speed∗Time
x+300=50/3∗39
=>3(x+300)=1950
=>x=350 meters
Option D
Answer: D
Question: By selling 45 lemons for Rs 40, a man loses 20 %. How many should he sell for Rs 24 to gain 20 % in the transaction ?
Options:
A)33
B)18
C)99
D)27
E)36
Rationale: Explanation:
Let S.P. of 45 lemons be Rs. x.
Then, 80 : 40 = 120 : x or x = = 60
For Rs.60, lemons sold = 45
For Rs.24, lemons sold == 18.
Answer: B
Answer: B
Question: I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?
Options:
A)25
B)37
C)54
D)65
E)72
Rationale: Explanation:
Clearly, the required number would be such that it leaves a remainder of 1 when divided by 2, 3 or 4 and no remainder when divided by 5. Such a number is 25.
Answer: A
Answer: A
Question: A work as fast as B. If B can complete a work in 36days independently,the number of days in which A and B can together finish the work in?
Options:
A)12days
B)3days
C)4days
D)5days
E)6days
Rationale: Ratio of rates of working of A and B = 2:1
ratio of times taken = 1:2
A's 1day work = 1/18
B's 1day work = 1/36
A+B 1day work = 1/18 + 1/36 = 3/36 = 1/12
A and B can finish the work in 12days
Answer is A
Answer: A
Question: If an object travels at six feet per second, how many feet does it travel in one hour?
Options:
A)21600
B)3778
C)12788
D)18000
E)2881
Rationale: Explanation:
If an object travels at 6 feet per second it covers 6x60 feet in one minute, and 6x60x60 feet in one hour.
Answer = 21600
Answer: A) 21600
Answer: A
Question: A certain restaurant offers 7 different salads, 4 different main courses, and 6 different desserts. If customers choose one salad, one main course, and two different desserts for their meal, how many different meals are possible?
Options:
A)340
B)380
C)420
D)460
E)500
Rationale: The number of possible choices for desserts is 6C2 = 15
The number of possible meals is 7*4*15 = 420
The answer is C.
Answer: C
Question: A profit of Rs. 20000 is to be distributed among A, B, C in the proportion 2 : 3 : 5. What will be the difference between B’s and C’s shares
Options:
A)4000
B)3000
C)5500
D)4500
E)None of these
Rationale: Explanation :
B's share = Rs 20000 *(3/10) = Rs 6000
C's share = Rs 20000 * (5/10) = Rs 10000
Difference in B's and C's shares = Rs 4000
Answer : A
Answer: A
Question: In a room filled with 8 people, 6 people have exactly 2 siblings in the room and 2 people have exactly one sibling in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
Options:
A)5/8
B)3/8
C)3/5
D)2/3
E)3/4
Rationale: The 8 people consist of two sets of 3 siblings and 1 set of 2 siblings.
The number of ways to choose 2 people is 8C2 = 28.
The number of ways to choose 2 from the first group of siblings is 3C2 = 3.
The number of ways to choose 2 from the second group of siblings is 3C2 = 3.
The number of ways to choose 2 from the third group of siblings is 2C2 = 1.
The number of ways to choose 2 people who are siblings is 3+3+1 = 7.
The number of ways to choose 2 people who are not siblings is 28-7=21.
P(the two people are not siblings) = 21/28 = 3/4
The answer is E.
Answer: E
Question: Tom, working alone, can paint a room in 20 hours. Peter and John, working independently, can paint the same room in 10 hours and 5 hours, respectively. Tom starts painting the room and works on his own for two hour. He is then joined by Peter and they work together for two hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
Options:
A)5/7
B)7/8
C)2/5
D)3/5
E)1/5
Rationale: Let the time when all three were working together be t hours. Then:
Tom worked for t+4 hour and has done 1/20*(t+4) part of the job;
Peter worked for t+2 hour and has done 1/10*(t+2) part of the job;
John worked for t hours and has done 1/5*t part of the job:
1/20*(t+4)+1/10*(t+2)+1/5*t=1 --> multiply by 20 --> (t+4)+(2t+2)+4t=20 --> t=2;
Hence Peter has done 1/10*(2+2)=4/10 =2/5
Answer: C
Answer: C
Question: The probability that a family with 6 children has exactly four boys is:
Options:
A)1/3
B)1/64
C)15/64
D)3/8
E)none of the above
Rationale: Now let's find the # of combinations where there's a BGB combination. Let the sequence of BG=A:
BBAA
BAAB
BABA
ABBA
ABAB
AABB
So there are 6 combinations here. But since BG can also be GB, we have to multiply by 2. We have to multiply by another 2 because there are 2 As. Therefore, there are 6x2x2=24 combinations.
We also have to include the instances where GG occurs at the end or the front, that is:
GGBBBB
BBBBGG
(all the other instances such as BBGGBB have been taken care of in the calculation at the top)
So we have 24+2=26 possibilities of 4 boys and 2 girls.
The total number of possibilities is 2^6=64. Therefore, the probability is 26/64, which is 13/32. The answer is E
Answer: E
Question: A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently nine spaces behind player B, what is the probability that player B will be frozen after player A rolls?
Options:
A)1/12
B)5/36
C)1/9
D)1/3
E)17/36
Rationale: no. of possible outcomes = 6*6 = 36
no. of outcomes that result a total of 9 (as A is 9 spaces behind B) = 4 ( (3,6), (4,5), (5,4), (6,3) )
So, the probability = 4/36=1/9 (Option C)
Answer: C