RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 40 miles per gallon, and from Town B to Town C, the car averaged 50 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?
A.42.85
B.40
C.35
D.41
Answer: A.42.85
Explanation: step 1) took LCM of 40 and 50.. came as 200.
step 2) 200 distance between B to C... do 200/50 hence 4 gallons used
step 3) twice distance.. hence 200*2= 400... do as above.. 400/40= 10 gallons used
step 4) total gallons.. 4+10= 14 gallons
step ) total miles= 200+400= 600 miles
hence.. average of whole journey = 600/14 which comes to 42.85
Answer : A
Question: The cost price of a Rs. 100 stock at 4 discount, when brokerage is 15% is
A.Rs. 96.25
B.Rs. 96.2
C.Rs. 97.25
D.Rs. 97.5
Answer: B.Rs. 96.2
Explanation: Explanation :
Cost Price = 100−4+1/5=96.2
Answer : Option B
Question: If a+b+c=13, a2+b2+c2=69, then find ab+bc+ca
A.-50
B.50
C.69
D.75
Answer: B.50
Explanation: (a+b+c)2= a2+b2+c2+2(ab+bc+ca)
2(ab+bc+ca)= (a+b+c)2- a2+b2+c2
=169-69
=100
ab+bc+ca=50
ANSWER B 50
Question: Set S consists of integers {1,3,5,7}. If two numbers are chosen from set S at random, what is the probability that the product of 2 numbers is more than 15?
A.1/2
B.1/3
C.1/5
D.1/6
Answer: B.1/3
Explanation: Number of ways you can choose 2 from 4 = 4C2 = 6
E = event of getting the 2 numbers product is more than 15 = (3,7),(5,7) = 2
probability = 2/6 = 1/3
Answer is B
Question: Which of the numbers below is the odd one out
1,65,190,406,749,950,1261.
A.190
B.406
C.950
D.749
Answer: C.950
Explanation: 950 is the odd man.. diff between sucessive are Cube Numbers
ANSWER:C
Question: Solve the equation for x : 2x - 21 + 3x = 4 + 9 - x
A.4
B.5
C.5.6
D.9.2
Answer: C.5.6
Explanation: C
5.6
5 x + x = 13 + 21
6 x = 34 => x = 5.6
Question: Pipe A can fill a tank in 45 hrs and pipe B can fill it in 36 hrs. If both the pipes are opened in the empty tank. In how many hours will it be full?
A.10 hr
B.15 hr
C.20 hr
D.25 hr
Answer: C.20 hr
Explanation: Part filled A in 1 hr= (1/45)
Part filled B in 1 hr= (1/36)
Part filled by (A+B) together in 1 hr=(1/45)+(1/36)=1/20
So, The tank will be full in 20 hr.
Answer : C
Question: f(x) is a function such that f(2x + 1) = 2f(x) + 1 for all real numbers x and f(0) = 2. Find the value of f(3).
A.9
B.10
C.11
D.12
Answer: C.11
Explanation: f(2x + 1) = 2f(x) + 1 : given
f(3) = 2f(1) + 1 : x = 1 in A
f(1) = 2f(0) + 1 : x = 0 in A
f(3) = 11 : substitute
correct answer is C) 11
Question: The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?
A.3377
B.2997
C.3600
D.2799
Answer: C.3600
Explanation: P = 144(100/5)2 => P
= 3600
Answer:C
Question: A computer program generates a single digit by a random process, according to which the probability of generating any digit is directly proportional to the reciprocal of one more than that digit. If all digits are possible to generate, then the probability E of generating an odd prime digit is between
A.0 and 1/6
B.1/6 and 1/3
C.1/3 and 1/2
D.1/2 and 2/3
Answer: B.1/6 and 1/3
Explanation: K (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9+ 1/10) =1
Note that 1/10 is least value and is equal to 0.1 so we can write above series as
K (1+0.5+0.3+0.25+0.2+0.16+0.5+residual) = 1
K=1/3+
P (3 or 5 or 7) =K*13/24
Required probability E= 13/24 × 1/3+ = 4+/24 > 1/6
Answer should be B
P.s. 3+ denotes a value little greater than 3 .
Same for 4+.
Question: A rhombus has area 432 sq m, one diagonal is 36 cm. find other diagonal ?
A.2400m
B.2500m
C.2600m
D.2700m
Answer: A.2400m
Explanation: area of rhombus =1/2*d1*d2
432=1/2*d1*.36
d1=2400m
ANSWER:A
Question: In the Forestside summer camp there are 50 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 5% of the total number of children in the camp. How many more boys must she bring to make that happen?
A.50.
B.45.
C.40.
D.30.
Answer: A.50.
Explanation: Given there are 50 students In the Forestside summer camp , 90% of 50 = 45 boys and remaining 5 girls.
Now here 90% are Boys and 10% are Girls.
Now question is asking about how many boys do we need to add, to make the girls percentage to 5 or 5%..
If we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it.
Now boys are 95% and girls are 5%. ( out of 100 students = 95 boys + 5 girls ).
IMO option A is correct.
Question: Sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum. Sandy attempts 30 sums and obtains 65 marks. How many sums did Sandy get correct?
A.19
B.21
C.23
D.25
Answer: D.25
Explanation: Let x be the correct sums and (30-x) be the incorrect sums.
3x - 2(30-x) = 65
5x = 125
x = 25
The answer is D.
Question: Length of a rectangular plot is 26 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
A.53 m
B.63 m
C.73 m
D.83 m
Answer: B.63 m
Explanation: Let breadth = x metres.
Then, length = (x + 26) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 26) + x] = 200
2x + 26 = 100
2x = 74
x = 37
Hence, length = x + 26 = 63 m
B
Question: A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
A.0.75D
B.0.76D
C.0.765D
D.0.775D
Answer: C.0.765D
Explanation: Successive doscounts = - a - b +ab/100
Putting the values,
Total discount = -15 - 10 + 150/100 = -25 + 1.5 = 23.5% discount
Hence the final price of the dress = D - 0.235D = 0.765D
Correct Option: C
Question: George is 8 years more than Christopher and Ford is 2 years younger than Christopher. The sum of their ages is 60. Find the ages of Christopher.
A.18
B.19
C.20
D.21
Answer: A.18
Explanation: Christopher age = x
George age, y = x + 8---------->(1)
Ford age, z = x - 2------------>(2)
Sum of their ages, x+y+z=60---->(3)
Substitute z and y values in equation (3)
Therefore, x+(x+8)+(x-2)=60
=> 3x+8-2=60
=> 3x=60-6
=> 3x=54 =>x=54/3
x=18
ANSWER:A
Question: A person was asked to state his age in years. His reply was , "Take my age 3 years hence, multiply it by 4 and subtract 4 times my age 3 years ago and you will know how old I am." What was the age of the person ?
A.18
B.92
C.27
D.24
Answer: D.24
Explanation: Explanation:
Let the present age of person be x years.
Then, 4(x + 3) - 4(x - 3 ) = x <=> (4x + 12) - (4x - 12) = x <=> x = 24..
Answer: D
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
A.22
B.25
C.66
D.77
Answer: B.25
Explanation: 800 --- 200
100 --- ? => 25%
Answer: B
Question: A 250 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
A.230 m
B.240 m
C.250 m
D.320 m
Answer: C.250 m
Explanation: Relative speed = (120 + 80) km/hr
=	(200 x(5/18))m/sec
=	(500/9)m/sec.
Let the length of the other train be x metres.
Then,	(x + 250)/9 = 500/9
x + 250 = 500
x = 250.
C
Question: In the x- y plane, there are 4 points (0,0), (0,4), (4,4), and (4,0). If these 4 points makes a rectangle, what is the probability that x+y<4?
A.1/2
B.1/3
C.1/4
D.1/5
Answer: A.1/2
Explanation: If x+y<4, then y<-x+4.
The line y=-x+4 intersects the rectangle and these three points of intersection (0,0), (0,4) and (4,0) form a triangle.
The points below the line y=-x+4 satisfy x+y<4.
The area of this triangle is (1/2)(4)(4)=8
The area of the rectangle is 16.
P(x+y<4) = 8/16 = 1/2
The answer is A.
Question: If the area of circle is 684 sq cm then its circumference?
A.11
B.88
C.93
D.266
Answer: C.93
Explanation: 22/7 r2 = 684 => r = 14.8
2 * 22/7 * 14.8 = 93 Answer: C
Question: If the length of the diagonal of a square is 20cm,then its perimeter must be
A.40
B.38
C.27
D.29
Answer: A.40
Explanation: Explanation:
d=√2l
Answer: A) 40
Question: The simple form of the ratio 5/8:3/2 is?
A.5:8
B.5:5
C.5:9
D.5:3
Answer: A.5:8
Explanation: 5/8 : 3/2 = 5:8
Answer: A
Question: What is the tens' digit T of the sum of the first 40 terms of 1, 11, 111, 1111, 11111, 111111, ...?
A.T=2
B.T=3
C.4
D.8
Answer: B.T=3
Explanation: All of the first 40 terms have 1 at the units place.
Except the first term, the tens digit of all the remaining 39 terms is 1.
So now if you do the addition
1 1
1 1
. . .
. . .
. . .
1 1
0 1
3 0
Answer is B
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
A.4 years
B.5 years
C.11 years
D.15 years
Answer: A.4 years
Explanation: Explanation:
Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years.
Answer: A
Question: Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 20 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?
A.20%
B.80%
C.100%
D.180%
Answer: D.180%
Explanation: We can use fractional equivalents here to solve the problem
80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears
10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours
Now we come to productivity
Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour
Hence the productivity is double with the assistant i.e. the increase in productivity is 180%
D
Question: What should come in place of the question-mark (?) in the following number series?
5690 5121 4552 3983 3414 2845?
A.2276
B.2516
C.2746
D.2356
Answer: A.2276
Explanation: the diff of the numbers in the series is same i.e 569.
5690-5121=569
5121-4552=569
4552-3983=569
3983-3414=569
3414-2845=569
so,2845-2276=569
so ans is 2276.
ANSWER:A
Question: An old truck uses 16 gallons of diesel fuel in traveling 224 miles. In order for the truck to travel the same distance using 8 gallons of diesel fuel, by how many miles per gallon must the truck’s fuel mileage be increased?
A.16
B.8
C.14
D.12
Answer: C.14
Explanation: There are two sets 16G1 gallons and 8G2 gallons details given.
16 gallons covering 224 miles
Then 1 G1 is used to cover 14 miles.
Now for 8 G2 covering 224 miles.
then 1 G2 is used to cover 28 miles.
There must 28 - 14 = 14 miles per gallon increment is needed for 8 gallons to improve the mileage to cover 224 miles.
IMO C is correct answer.
Question: Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 3 hours. How long would it take Taimour to paint the fence alone?
A.6 hours
B.9 hours
C.14 hours
D.24 hours
Answer: B.9 hours
Explanation: I believe the answer is B. Please see below for explanation.
if Jamshid can paint a dence in 50 percent less time then Taimour we can infer the following rate J = 2T
if working together they can do the job in 8 hours we can infer 1 = 2T+T * 3 => 1/9
Working alone Taimour can do the job in 1 = 1/9 * hours => 9
Answer B
Question: How many prime numbers K exist such that 90 < K < 106 and K is a factor of 99999919?
A.1. Zero
B.2. One
C.3. Two
D.4. Three
Answer: C.3. Two
Explanation: I found that considering the constraint..K is a prime num in between 90 to 106 not inclusive , only 3 numbers (91,97 and 101) are present but those numbers are not the factors of the number mentioned....Therefore, i doubt the answer.C
Question: Twelve percent of the programmers in a startup company weigh 200 pounds or more. Twenty-five percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less. What percent of the programmers in the startup company weigh between 100 and 200 pounds?
A.15%
B.20%
C.25%
D.66%
Answer: D.66%
Explanation: Initially 88% and 12% split
80% is further divided as 25% and 75%
Q is asking about that 75%
let total be '100' then that 75% is (3/4)∗88
so, the required % is [(3/4)∗88/100]∗100 = 66%
ANSWER:D
Question: Equal weights of two alloys containing tin, copper and lead in the ratio 5:2:7 and 8:11:9 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy?
A.35:81:45
B.33:91:81
C.17:28:27
D.18:15: 23
Answer: D.18:15: 23
Explanation: Let the weight of the two alloys be w each
Required ratio =
(5w/14 +8w/28): ( 2w/14+11w/28 ): (7w/14+9w/28)
= 18w/28 : 15w/28 : 23w/28
=18:15: 23
ANSWER:D
Question: Working simultaneously and independently at an identical constant rate, 10 machines of a certain type can produce a total of x units of product P in 4 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 6 days?
A.14
B.15
C.18
D.20
Answer: D.20
Explanation: The rate of 10 machines is rate=job/time=x/4 units per day --> the rate of 1 machine 1/10*(x/4)=x/40 units per day;
Now, again as {time}*{combined rate}={job done}
then 6*(m*x/40)=3x --> m=20.
Answer: D.
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: Explanation:
Area of the park = (60 x 40) = 2400m2
Area of the lawn = 2109m2
Area of the crossroads = (2400 - 2109) = 291m2
Let the width of the road be x metres. Then,
60x +40x - x2 = 291
x2 - 100x + 291 =0
(x - 97)(x - 3) = 0
x = 3. Answer: C
Question: A trader sells 85 meters of cloth for $8925 at the profit of $15 per metre of cloth. What is the cost price of one metre of cloth?
A.$69
B.$78
C.$90
D.$86
Answer: C.$90
Explanation: C
$90
SP of 1m of cloth = 8925/85 = $105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= $105 - $15 = $90.
Question: If a and n are integers, and a^3=360n, then n must be divisible by which of the following?
A.2
B.6
C.25
D.27
Answer: C.25
Explanation: a^3=360n = 2^3*3^2*5*n
and a^3 is a perfect cube due to a being an integer
hence 360n must have powers of each prime number as multiple of 3
hence 360n = 2^3*3^2*5*(3*5^2) for least value of n
i.e. n must have 5^2
Answer: Option C
Question: Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in
A.7 days
B.7 days
C.9 days
D.3 days
Answer: D.3 days
Explanation: Explanation:
Let x men can do the in 12 days and the required number of days be z
More men, Less days [Indirect Proportion]
Less work, Less days [Direct Proportion ]
Answer: D
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is ?
A.1 : 2
B.3 : 2
C.3 : 1
D.4 : 7
Answer: B.3 : 2
Explanation: Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27 x meters, and
length of the second train = 17 y meters.
(27 x + 17 y) / (x + y) = 23
=> 27 x + 17 y = 23 x + 23 y
=> 4 x = 6 y
=> x/y = 3/2.
Answer : B
Question: Adam can do a job in 15days, John can do the same job in 20days. If they work together for 4days on this job. What fractionof job is incomplete ?
A.3/11
B.4/11
C.13/13
D.8/15
Answer: D.8/15
Explanation: Adam can do 1/15 of the job per day
John can do 1/20 of the job per day
If they work together they can do 7/60 of the work together
Remaining job 1 - 4*7/60 = 32/60 = 8/15
(D)
Question: In how many ways Chief Minister and Minister be elected from a team of 6 members?
A.28
B.20
C.36
D.30
Answer: D.30
Explanation: To do this, if captain is elected first, then we have 6 ways of doing this.
For election of vice-captain, we have only 5 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 6*5 = 30 ways.
D
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 2 min, then the length of the tunnel is?
A.2898
B.1800
C.500
D.297
Answer: B.1800
Explanation: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 2 min = 120 sec.
Let the length of the train be x meters.
Then, (800 + x)/120 = 65/3
x = 1800 m.
Answer: B
Question: Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 80 miles apart. One and a half hours later, they are again 80 miles apart, driving away from each other. If Otto drives at a speed of m miles per hour, then, in terms of m, Han drives at a speed of how many miles per hour?
A.a) 106.67-m
B.b) 40-m
C.c) 80-2m
D.d) 120-m
Answer: A.a) 106.67-m
Explanation: Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same.
Here, the two cars approach a distance 60 mi, then move away from each other another distance of 60 miles. That's a total distance of 160 miles in 1.5 hr, which gives a rate of:
R = (160 mi)/(1.5) = 106.67 mph
That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars.
One of the speeds is m, and let's call the other n. We want n.
m + n = 106.67
n = 106.67 - m
Answer =(A)
Question: The no. of girls in a class are 7times the no. of boys, which value cannever be the of total students?
A.20
B.35
C.30
D.40
Answer: C.30
Explanation: Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.
C
Question: The ratio of boarders to day students at a school was originally 5 to 12. However, after a number of new boarders join the initial 150 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school?
A.30
B.50
C.70
D.80
Answer: A.30
Explanation: Let x be the number of new boarders.
The ratio changed from 5:12 up to 1:2 = 6:12.
150 / (150+x) = 5/6
x = 30
The answer is A.
Question: A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses' back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70, how many horses are there ?
A.10
B.12
C.14
D.16
Answer: C.14
Explanation: Explanation:
Let number of horses = number of men = x.
Then, number of legs = 4x + 2 x (x/2) = 5x.
So, 5X = 70 or x = 14.
Answer: C
Question: In a rectangular axis system, what is the area of a parallelogram with the coordinates: (5,7), (12,7), (2,3), (9,3) ?
A.21
B.28.
C.35.
D.49.
Answer: A.21
Explanation: Area of parallelogram = b*h.
Base = Distance in x coordinates between (2,3) and (9,3) = 7
Height = Difference in y coordinates between (5,7) and (2,3) = 3.
Area = 7*3 = 21.
ANSWER:A
Question: A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
A.7.2
B.4.2
C.6.1
D.7.2
Answer: A.7.2
Explanation: Explanation:
distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distance/time = 600/300 = 2m/s
= 2×185 km/hr = 365 km/hr = 7.2 km/hr
Answer: Option A
Question: A photo-mat shop charges $0.50 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $24 if each film contains 36 photos?
A.2 films and 6 photos
B.5 films and 6 photos
C.5 films and 14 photos
D.6 films and 4 photos
Answer: A.2 films and 6 photos
Explanation: 1st photo = 0.50
Subsequent = 0.50*0.6=0.3
Price of 1 full film=0.50+0.3*35=11
Price of 2 full film = 11*2=22
24-22=2
2=0.5+0.3x
x=5
24--->2 full films and 1+5=6 photos
Answer: A
Question: In the Biotechnology class of 2000, there were Q graduates. 32 of the graduates found a job, 45 continued on to their second degree and 13 did both. If only 9 people didn't do both, What is Q equal to?
A.69.
B.71.
C.73.
D.75.
Answer: C.73.
Explanation: Total = 32 +45 -13 +9 = 73 .... My first post on the forum... I hope I am correct
C is correct choice.
Question: The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is
A.1677
B.1683
C.2523
D.3363
Answer: B.1683
Explanation: Explanation:
L.C.M of 5, 6, 7, 8 = 840
therefore Required Number is of the form 840k+3.
Least value of k for which (840k+3) is divisible by 9 is k = 2
therefore Required Number = (840 x 2+3)=1683. Answer: B
Question: A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?
A.300 m
B.400 m
C.200 m
D.100 m
Answer: C.200 m
Explanation: Speed=40 km/hr =40Ã—5/18=100/9 m/s
Time =18 seconds
Distance Covered
=100/9Ã—18
=200 m
Therefore, length of the train =200 m
Answer: C
Question: The price of a book is increased from $300 to $330. What is the % of increase in its price?
A.10%
B.20%
C.40%
D.50%
Answer: A.10%
Explanation: Explanation: Change in the price = Rs 330 â€“ Rs 300
= Rs 30
Percentage of increase = Change in the price Initial Price
* 100.
Percentage increase in price =( 30 300
) *100 = 10%
A
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability y that the World Series will consist of fewer than 7 games?
A. 12.5%
B. 25%
C. 31.25%
D. 68.75%
Answer: D. 68.75%
Explanation: In order to determine the probability y that the World Series will last less than 7 games, we can first determine the probability that the World Series WILL last exactly 7 games and then subtract this value from 1.
In order for the World Series to last exactly 7 games, the first 6 games of the series must results in 3 wins and 3 losses for each team.
Let's analyze one way this could happen for Team 1:
Game 1 Game 2 Game 3 Game 4 Game 5 Game 6
T1 Wins T1 Wins T1 Wins T1 Loses T1 Loses T1 Loses
There are many other ways this could happen for Team 1. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for Team 1 to win 3 games and lose 3 games in the first 6 games.
Logically, there are also 20 ways for Team 2 to win 3 games and lose 3 games in the first 6 games.
Thus, there are a total of 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is:
Thus the probability that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D.
Question: For a finite sequence of non zero numbers, the number of variations in the sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence -1, -3, 2,-5, 4, -6,10,-3?
A.6
B.2
C.3
D.4
Answer: A.6
Explanation: The questions basically asks: how many pairs of consecutive terms are there in the sequence such that the product of these consecutive terms is negative.
-3*2=-6=negative;
2 * -5 = -10 > negative
-5*(4)=-20=negative.
4 * (-6) = -24 > negative
-6 * 10 = -60 > negative
-3 * 10 = -30 > negative
So there are 6 pairs of consecutive terms.
Answer: A.