RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If y is 75% greater than x, than x is what % less than y?
A.30.6%
B.34.4%
C.38.7%
D.42.9%
Answer: D.42.9%
Explanation: y = 1.75x
x = y/1.75 = 100y/175 = 4y/7
x is 3/7 less which is about 42.9% less than y.
The answer is D.
Question: While planning their outing, Abhishek understood that their boat could travel with a speed of 12kmph in still water.The group decided to travel 24 minutes downstream. Aarti had prior experience in that route and mentioned that the speed of stream was 4kmph.How many kms will the group travel downstream?
A.6.4
B.3.2
C.4
D.4.8
Answer: A.6.4
Explanation: Downstream speed= boat speed in still water + speed of stream
Boat speed in Downstream = 12 + 4= 16 km/h
Time spend = 24 min = 24/60 h = 2/5 h
Distance Travel = 16 * 2/5 = 6.4 km
Answer:a
Question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
A.40
B.48
C.45
D.50
Answer: B.48
Explanation: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
ANSWER B
Question: Out of 6 consonants and 3 vowels, how many words of 4 consonants and 2 vowels can be formed?
A.1050
B.25200
C.32400
D.5800
Answer: C.32400
Explanation: Number of ways of selecting (4 consonants out of 6) and (2 vowels out of 3)
= 6C4 * 3C2
= 6C2 * 3C1
= 6*5 *3
2*1
= 15*3= 45
Number of groups, each having 4 consonants and 2 vowels= 45.
Each group consists of 6 letters.
Number of ways of arranging 6 letters among themselves
= 6! = (6*5*4*3*2*1)= 720
Therefore, Required number of words= 45*720= 32400
ANSWER:C
Question: The probability of Sam passing the exam is 1/4. The probability of Sam passing the exam and Michael passing the driving test is 1/7. What is the probability of Michael passing his driving test?
A.1/24.
B.1/2.
C.4/7.
D.2/3.
Answer: C.4/7.
Explanation: 1/4 *1/m= 1/7 , 1/m = 4/7
Answer C
Question: An old priest fell on a bottom of the well of a church.
The well is 15 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ?
A.16-days
B.14-days
C.11-days
D.19-days
Answer: C.11-days
Explanation: C
11-days
In 10-days, he will climb 10-inch and when he climbs 5 inch more, he will be out of the well :-)
Question: Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 6/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
A.6/16
B.14/31
C.7/15
D.17/35
Answer: A.6/16
Explanation: # of basic stereos was 2/3 of total and # of deluxe stereos was 1/3 of total, let's assume total=15, then Basic=10 and Deluxe=5.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 6/5 units. Total time for Basic would be 10*1=10 and total time for Deluxe would be 5*6/5=6 --> total time for both of them would be 10+6=16 --> deluxe/total=6/16.
Answer: A.
Question: If 6a = 7b = 20, then 84ab =
A.50
B.100
C.625
D.800
Answer: D.800
Explanation: 6a * 7b = 20 * 20 = 400
42 ab = 400
i.e. 84 ab = 800
Answer: Option D
Question: A gang of 8 boys goes on an tour in 2 cars, of which 1 canseat 5 & the other only 4. In how many ways can they travel?
A.110
B.123
C.126
D.154
Answer: C.126
Explanation: There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows
Case I: 5 students in the first car and 3 in the second
Or Case II: 4 students in the first car and 4 in the second
Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.
Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.
Therefore, the total number of ways in which 8 students can travel is:
\inline {\color{Blue}8C_{3}+8C_{4}}=56 + 70= 126
C
Question: If a certain number is divisible by 25 and 38, it is NOT necessarily divisible by which of the following?
A.5
B.10
C.19
D.20
Answer: D.20
Explanation: If a certain number is divisible by 25 and 38, it is NOT necessarily divisible by which of the following?
let the certain number be 950, which is both divisible by 25 and 38.
950/20 = 95/2
D. 20
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hours, it must travel at a speed of:
A.150
B.720
C.160
D.80
Answer: B.720
Explanation: Explanation:
Speed = Distance/Time
Speed =1200(5/3)km/hr
Required speed =(1200*(3/5))km/hr=720 km/hr
Answer B
Question: The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
A.91.5 cm
B.91.8 cm
C.61.8 cm
D.91.6 cm
Answer: A.91.5 cm
Explanation: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42 = 91.5 cm
Answer:A
Question: The “d-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^d, where d is the d-number of the result of his die roll, and plots 3^d 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?
A. 3/8
B. 13/36
C. 17/36
D. 19/36
Answer: B. 13/36
Explanation: If you calculate 3^d 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
Question: A can run 4 times as fast as B and gives B a start of 75 m. How long should the race course be so that A and B might reach in the same time?
A.70 m
B.60 m
C.100 m
D.65 m
Answer: C.100 m
Explanation: Speed of A:Speed of B=4:1
means in a race of 4m A gains 3m.
then in a race of 75m he gains 75*(4/3)
I.e 100m
ANSWER:C
Question: A's speed is 15/13 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that B beats A by 40% of the length of the race?
A.44%
B.48%
C.52%
D.42%
Answer: B.48%
Explanation: First calculate the distance, B has covered with his speed in the time, in which A reached 60% of the race.
Then Add the remaining distance as head start for B to win the race.
Its best to apply Ratios concept here.
Since A's speed is 15/13 of B, therefore, B's speed is 13/15 of A
Distance covered by B = speed x time = (13/15) x (0.6) = 0.52%
(Which means B would have covered 0.52 of the race length during the time in which A has covered 0.6 of the race length.
Therefore to win, B needs a headstart of (1 - 0.52 = ) 0.48 of the race length.
So the answer is B
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
A.237
B.480
C.882
D.271
Answer: B.480
Explanation: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.160
SP = CP - Loss = 640 - 160 = Rs.480
Answer:B
Question: A, B and C can do a piece of work in 7 days, 21 days and 28 days respectively. How long will they taken, if all the three work together?
A.2
B.4 8/19
C.5
D.67
Answer: B.4 8/19
Explanation: 1/7 + 1/21 + 1/28 = 19/84 => 84/19 => 4 8/19 days
Answer: B
Question: A man can row his boat with the stream at 24 km/h and against the stream in 10 km/h. The man's rate is?
A.1 kmph
B.6 kmph
C.7 kmph
D.4 kmph
Answer: C.7 kmph
Explanation: Explanation:
DS = 24
US = 10
S = ?
S = (24-10)/2 =7 kmph
Answer: C
Question: The cost of 9 kgs. of sugar is Rs.279. What is the cost of .153 kgs. of sugar?
A.Rs.3.377
B.Rs.4.473
C.Rs.4.377
D.Rs.4.743
Answer: D.Rs.4.743
Explanation: Explanation:
The cost of .153 kgs. of sugar = 279x .153/9 = Rs.4.743
Answer: Option D
Question: It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 440 cubic metres in 10 minutes. The inner radius of the pipe should be :
A.√2 m
B.2 m
C.1⁄2 m
D.1⁄√2 m
Answer: A.√2 m
Explanation: Let inner radius of the pipe be r.
Then, 440 = 22⁄7 × r2 × 7 × 10
or r2=440/22×10=2
or r = √2 m
Answer A
Question: What is the next number of the following sequence.
6, 9, 18, 45, 108, 351, ..
A.952
B.972
C.985
D.548
Answer: B.972
Explanation: For odd place values
6*3=18
18*6=108
108*9=972
and for even place values
6*1+ 3^1=9
18*2+3^2=45
108*3+3^3=351
972*4+3^4=39699(so ans is 972)
ANSWER:B
Question: If x/4 – (x – 3)/5 = 1, then find the value of x.
A.3
B.6
C.8
D.11
Answer: C.8
Explanation: Explanation:
x/4 – (x - 3)/5 = 1
(5x – 4(x – 3))/20 = 1
5x - 4x + 12 = 20
x = 8
ANSWER: C
Question: In the first M games of a team's season, the ratio of the team's wins to its losses was 1:3. In the subsequent N games, the ratio of the team´s wins to losses was 2:3. If M:N = 4:5, what was the ratio of the team's wins to its losses for all M+N games?
A.7:18
B.3:7
C.1:2
D.2:5
Answer: C.1:2
Explanation: M = 4/9 of total games
N = 5/9 of total games
Wins = 1/4*4/9 + 2/5*5/9 = 1/9 + 2/9 = 1/3
Losses = 1 - 1/3 = 2/3
The ratio of wins to losses is 1:2.
The answer is C.
Question: 10 camels cost as much as 24 horses, 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants. If the cost of 10 elephants is Rs.170000, find the cost of a camel?
A.Rs.6867
B.Rs.6818
C.Rs.6810
D.Rs.6800
Answer: D.Rs.6800
Explanation: Cost of the camel = P
10 camels = 24 horses
16 horses = 4 oxen
6 oxen = 4 elephants
10 elephants = Rs.170000
P = Rs.[(24 * 4 * 4 * 170000)/(10 * 16 * 6 * 10)]
P = Rs.(65280000/9600) => P = Rs.6800
Answer: D
Question: A 12% item produces 20%. The market value of the item is:
A.Rs. 55
B.Rs. 60
C.Rs. 40
D.Rs. 65
Answer: B.Rs. 60
Explanation: Let the face value of the item is Rs.100
It produces Rs.12
Market value of the stock=(12/20)*100=Rs.60
ANSWER:B
Question: What is the value of âˆš25% ?
A.10%
B.50%
C.25%
D.45%
Answer: B.50%
Explanation: Explanation: br>âˆš25%
=âˆš25/âˆš100
=5/10
=50/100=50%
correct answer is B)50%
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
A.5.79
B.5.73
C.5.76
D.5.75
Answer: C.5.76
Explanation: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
\Answer:C
Question: The sale price sarees listed for Rs.400 after successive discount is 15% and 5% is?
A.338
B.323
C.342
D.882
Answer: B.323
Explanation: 400*(85/100)*(95/100) = 323
Answer: B
Question: If a, b and c are even integers, which of the following could be the value of a^2 + b^2 + c^2?
A.a)98
B.b)101
C.c)102
D.d)204
Answer: D.d)204
Explanation: a, b and c are even integers which means that, supposing that x, y and z are integers, then a=2x, b=2y and c=2z
Therefore we have: a^2+b^2+c^2=2^2*x^2+2^2*y+2^2*z=4x^2+4y^2+4z^2=4(x^2+y^2+z^2).
Which means that the total a^2+b^2+c^2 must be divisible by 4.
The only choice which is divisible by 4 is: D)
204=10^2+10^2+2^2
Answer: D.
Question: A train traveling at 36 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?
A.120 meters
B.360 meters
C.420 meters
D.600 meters
Answer: A.120 meters
Explanation: 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 = 36 kmph * 12 seconds
Convert 36 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).
∴ 36 kmph = 5/18∗36 = 10 m/sec
Therefore, length of the platform = 10 m/s * 12 sec = 120 meters.
Choice A
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is
A.17/28
B.17/25
C.17/26
D.17/22
Answer: B.17/25
Explanation: :The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 = 17/25.
Answer:B
Question: Two trains of equal are running on parallel lines in the same direction at 48km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
A.50
B.88
C.60
D.55
Answer: C.60
Explanation: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 48 - 36 = 12 km/hr.
= 12 * 5/18 = 10/3 m/sec.
2x/36 = 10/3 => x = 60.
Answer:C
Question: If p/q = 3/11 , then 2p+q= ?
A.12
B.14
C.17
D.15
Answer: C.17
Explanation: let p=3, q=11 then 2*3+11=17
so 2p+q=17.
ANSWER:C
Question: If the integer n has exactly five positive divisors, including 1 and n, how many positive divisors does √n have?
A.6
B.5
C.2
D.3
Answer: D.3
Explanation: take the example of 16...
it has 3 positive divisors (1,2,4,8,16)
Now, take the example of 4...
it has only 3 divisors..
so D is the ans
Question: Find the value of x from the below equation? : x^2+5x+25 = 0
A.No answer
B.25
C.1
D.0
Answer: A.No answer
Explanation: a = 1, b = 5, c = 25
x1,2 = (-5 Â± âˆš(5^2 - 4Ã—1Ã—25)) / (2Ã—1) = (-5 Â± âˆš(25-100)) / 2 = (-5 Â± âˆš -75) / 2
No real roots
A
Question: P started from his house towards west. After walking a distance of 25 m. He turned to the right and walked 10 m. He then again turned to the right and walked 15 m. After this he is to turn right at 1350 and to cover 30 m. In which direction should he go?
A.West
B.South
C.South-west
D.South-East
Answer: D.South-East
Explanation: south east
ANSWER:D
Question: The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 47. What is a possible value for the mean of the distribution?
A.46
B.54
C.48
D.49
Answer: B.54
Explanation: The standard deviation ({SD}) = 2;
3 standard deviations below the mean is greater than 47:
{Mean} - 3*{SD} > 47;
{Mean} - 6 > 47;
{Mean} > 53.
Answer: B.
Question: Employees of a certain company are each to receive a unique 6-digit identification code consisting of the digits 0, 1, 2, 3, 4, and 5 such that no digit is used more than once in any given code. In valid codes, the second digit in the code is exactly twice the first digit. How many valid codes are there?
A.48
B.56
C.64
D.72
Answer: A.48
Explanation: There are 4! ways to make codes starting with 12.
There are 4! ways to make codes starting with 24.
The number of codes is 2*4! = 48.
The answer is A.
Question: An artist who needs to buy only paint and canvas finds that the cost of canvas has decreased by 40 percent and the cost of paint has decreased by 60 percent. If paint previously accounted for 4 times as much of the expense of painting as did canvas, by what percent did the total cost for paint and canvas decrease?
A.40%
B.44%
C.50%
D.56%
Answer: D.56%
Explanation: Paint:Canvas cost is 4:1.
So, paint accounts for 80% of cost and canvas accounts for 20%.
Canvas, after decrease by 40% will be (100-40)% of 20% => 60% of 20% => 12% of original
Paint, after decrease by 60% will be (100-60)% of 80% => 40% of 80% => 32% of original
New cost as a % of old cost = 32+12 = 44% of original.
So, overall cost saving = 100-44 = 56%
Therefore, (D)
Question: The average earning of amechanic for the first 4days of a week is Rs.11 and for the last four days is Rs.22. If heearns Rs.20 on the fourth day, his average earning forthe whole week is?
A.s. 14
B.s. 20
C.s. 30
D.s. 16
Answer: D.s. 16
Explanation: Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x 11 + 4 x 22 -20
= Rs. 112
âˆ´ Average earning = 112/ 7
= Rs. 16
D
Question: When a certain number X is divided by 72, the remainder is 19. What is the remainder when X is divided by 8?
A.3
B.2
C.4
D.1
Answer: A.3
Explanation: Let possible value of x is 91
least possible value of x/8 is 91/8 => 11 quotient with remainder 3
Thus answer is (A) 3
Question: In how many ways a President, VP and Water-boy can be selected from a group of 10 people.
A.10C3
B.10P3
C.240
D.360
Answer: B.10P3
Explanation: Solution:
We are selecting three different posts here, so order matters.
Thus, total ways of selecting a President, VP and Water-boy from a group of 10 people would be 10P3.
Answer: Option B
Question: A man traveled from the village to the post-office at the rate of 25 kmph and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post-office from the village ?
A.70 m
B.80 km
C.20 km
D.10 km
Answer: C.20 km
Explanation: Explanation:
Average speed = , here a=25 b=4
= 2x25x4/(25+4) = 200/29 km/hr.
Distance covered in 5 hours 48 minutes
= Speed x time = (200/29)x (29/5) Distance covered in 5 hours 48 minutes = 40kms.
Distance of the post office from the village = (40/2) = 20 km.
Answer: C
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 42 years, was replaced by a new person. Find the age of the new person?
A.18
B.56
C.12
D.17
Answer: C.12
Explanation: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average
= (P-3) 10(P-3)
= 10P - 42 + Q
=> Q = 12
Answer:C
Question: 600 x 223 + 600 x 77 = ?
A.180000
B.138800
C.658560
D.116740
Answer: A.180000
Explanation: =600 x (223+77) (by distributive law)
=600 x 300
=180000
Answer is A
Question: Find the ones digit of 73^352
A.1
B.5
C.6
D.7
Answer: A.1
Explanation: The units digit of 73^352 will be the same as the units digit of 3^352.
3^1=3 --> the units digit is 3;
3^2=9 --> the units digit is 9;
3^3=27 --> the units digit is 7;
3^4=81 --> the units digit is 1;
3^5=243 --> the units digit is 3 AGAIN;
...
So, as you can see the units digit repeats in blocks of 4: {3, 9, 7, 1}, {3, 9, 7, 1}, ... Now, since 352=(multiple of 4)+0, since 3 is an odd number, the units digit of 3^352 will be 1.
Answer: A.
Question: In a class, 30% of the students offered English, 20% offered Hindi and 10% offered both. If a student is selected at random, what is the probability that he has offered English and Hindi
A.2/5
B.1/5
C.3/5
D.6/5
Answer: A.2/5
Explanation: P(E)=30/100,
P(H)=20/100
P(E and H)=10/100
P(E or H)=3/10+2/10-1/10
=2/5
ANSWER A
Question: A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 40 square feet of the wall, and no tiles overlap, what is the area of the entire wall?
A.160
B.220
C.360
D.440
Answer: B.220
Explanation: The number of jumbo tiles = x.
The number of regular tiles = 2x.
Assume the ratio of the dimensions of a regular tile is a:a --> area = a^2.
The dimensions of a jumbo tile is 3a:3a --> area = 9a^2.
The area of regular tiles = 2x*a^2 = 40.
The area of jumbo tiles = x*9a^2 = 4.5(2x*a^2 ) = 4.5*40 = 180.
Total area = 40 + 180 =220.
Answer: B.
Question: An IT company pays an average salary of $2000 for its 30 team leads and $5000 for it 2 managers. What is the average salary for the company?
A.$12,00
B.$4,000
C.$3,000
D.$2,187.50
Answer: D.$2,187.50
Explanation: Number of team leads is 30
Their average salary is $2000
Managers of the company are 2
Their average salary is $5000
Total salary of team leads is 30*20,00=$60,000
Total salary of the managers is 2*5000=$10,000
Total salary for the company is 60,000+10,000=70,000
Average salary for the company is 70,000/30+2=$2,187.50
Answer is D
Question: If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number S of integers that can be negative?
A.2
B.3
C.4
D.5
Answer: D.5
Explanation: Minimuum should be 1
Maximum should be 4:
1 out of a or b to make the multiplication negative
3 out of c, d, e or f to make the multiplication negative.
Negative+Negative<0
Answer:C
maximum will be 5..
you dont require both the multiplicatin to be negative for entire equation to be negative...
any one a or b can be negative to make ab negative and it can still be more(away from 0) than the multiplication of 4 other -ve numbers...
actually by writing minimum required as 1 out of 6,you are actually meaning S= 5 out of 6 also possible as you will see 5 or 1 will give you same equation..
ans D
Question: What is the greatest possible length which can be used to measure exactly the lengths 18 m, 40 m and 6 m 50cm?
A.20 cm
B.23 cm
C.25cm
D.10 cm
Answer: D.10 cm
Explanation: Required length = HCF of 1800 cm, 4000 cm, 650 cm = 50 cm
Answer is D
Question: A gym offers 11 levels of fitness classes, and in an attempt to reward those who progress toward higher levels of fitness it charges $50 less per course for each level of fitness. Jessica completed all 11 levels by taking one course at each level, and her total cost was $4675. What is the cost V for a course at the gym's highest level?
A.$175
B.$245
C.$425
D.$675
Answer: A.$175
Explanation: Let the cost of a course in level 1 = x
=> Cost of level 2 = x-(50*1)... and so on
=> cost of level 11 = x-(50*10) = x-500
=> Total cost V of 1 course in each of the 11 levels = x+(x-50)+(x-100)+.....+(x-500)
= 11x -50 (1+2+....+10)
= 11x - (50*55)
=> 11x-2750 = 4675
11x = 7425
x= 675
x-500=175
Answer A
Question: If X and Y are sets of integers, X # Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 8 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X # Y consists of how many integers?
A.6
B.14
C.22
D.30
Answer: B.14
Explanation: The number of integers that belong to set X ONLY is 8-6=2;
The number of integers that belong to set Y ONLY is 18-6=12;
The number of integers that belong to set X or set Y, but not both is 2+12=14.
Answer: B.
Question: In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a four. You pick a card from a full playing-card deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning?
A.1/48
B.5/16
C.11/16
D.11/12
Answer: C.11/16
Explanation: First lets get the overview
Event 1(A) = Flipping the quarter( Probability of both winning/loosing = 1/2)
Event 2(B) = Rolling a dice( Probability of winning = 1/6 ;Probability of loosing= 1 - 1\6 =5\6)
Event 3(C) = Drawing a card( SPADES) Probability of winning = 13/52=3/4 ;Probability of loosing= 1 - 3/4 =1/4)
So now as above we have three events A,BC.
1st method(This is lengthy method)
Possible cases in which it's a win( the highlighted green event is a win and red is loose.
1.ABC= 1/2*5/6*3/4
OR
2.ABC= 1/2*1/6*3/4
OR
3.ABC= 1/2*5/6*1/4
OR
4.ABC= 1/2*1/6*3/4
OR
5.ABC= 1/2*5/6*1/4
OR
6.ABC= 1/2*5/6*1/4
OR
7.ABC= 1/2*1/6*1/4
As we now OR means add
Adding up all of them we'll get the probability of winning ie 11/16
Answer : C