RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 2 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
A.480
B.240
C.289
D.270
Answer: B.240
Explanation: 1/x - 1/20 = -1/24
x = 120
120 * 2 = 240
Answer: B
Question: A man sells a horse for Rs.1400 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
A.2270
B.2990
C.1540
D.8600
Answer: C.1540
Explanation: CP = SP + 1CP = SP - g
1400 + x = 980 - 2x
3x = 420 => x = 140
CP = 1400 + 140 = 1540
Answer: C
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
A.176
B.500
C.278
D.270
Answer: B.500
Explanation: 70 = (P*4*7/2)/100
P = 500
Answer:B
Question: A train running at the speed of 90 km/hr crosses a pole in 9 sec. What is the length of the train?
A.298 m
B.225 m
C.208 m
D.988 m
Answer: B.225 m
Explanation: Speed = 90 * 5/18 =25/1 m/sec
Length of the train = speed * time = 25 * 9
= 225 m
Answer:B
Question: What is the probability of having 53 Fridays in an ordinary year
A.1/5
B.1/6
C.1/7
D.1/8
Answer: C.1/7
Explanation: 1/7 because 53 friday in ordinary year then 53*7=371 (53/371=1/7)
ANSWER:C
Question: Two whole numbers whose sum is 72 cannot be in the ratio
A.3 : 4
B.3 : 5
C.4 : 5
D.5 : 7
Answer: A.3 : 4
Explanation: Sol.
The sum of the ratio terms must divide 72. So, the ratio
cannot be 3 : 4.
Answer A
Question: What is the are of an equilateral triangle of side 16 cm?
A.66√3 cm2
B.74√3 cm2
C.64√3 cm2
D.64√5 cm2
Answer: D.64√5 cm2
Explanation: Area of an equilateral triangle = √3/4 S2
If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm2;
Answer:D
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length.
A.22
B.88
C.27
D.40
Answer: C.27
Explanation: Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
=500∗2/25=40seconds
Answer: C
Question: 3/8 of 168 * 15 / 5 + X = 549 / 9 + 275
A.147
B.149
C.268
D.2696
Answer: A.147
Explanation: Explanation:
Let 3/8 of 168 * 15 / 5 + X = 549 / 9 + 275
Then, 63 * 15 / 5 + X = 61 + 275
63 * 3 + X = 336
189 + X = 336
X = 147
ANSWER: A
Question: The rental charge for a car is 34 cents for the first 1/4 mile driven and 6 cents for every 1/5 mile driven over the initial 1/4 mile. If a man paid $1.24 in rental charges, how many miles did he drive?
A.2.5
B.3.00
C.3.25
D.3.75
Answer: C.3.25
Explanation: For first 0.25 miles 34 cents.
So the person is left with 1.24-0.34 = 0.9
So the person can travel next (90/6) times 1/5 miles
i.e 15 *1/5 miles = 3 miles.
SO total distance is 3 + 0.25 = 3.25 miles(C)
Question: In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?
A.4! x 9!
B.4! x 2!
C.4! x 5!
D.4! x 6!
Answer: C.4! x 5!
Explanation: Explanation:
The word EDUCATION is a 9 letter word, with none of the letters repeating.
The vowels occupy 3rd,5th,7th and 8th position in the word and the remaining 5 positions are occupied by consonants
As the relative position of the vowels and consonants in any arrangement should remain the same as in the word EDUCATION, the vowels can occupy only the afore mentioned 4 places and the consonants can occupy1st,2nd,4th,6th and 9th positions.
The 4 vowels can be arranged in the 3rd,5th,7th and 8th position in 4! Ways.
Similarly, the 5 consonants can be arranged in1st,2nd,4th,6th and 9th position in5! Ways.
Hence, the total number of ways = 4! × 5!
Answer: C) 4! x 5!
Question: The average of first 6 prime numbers is?
A.10.11
B.11.11
C.12.11
D.6.83
Answer: D.6.83
Explanation: Sum of 6 prime no. = 41
Average = 41/6 = 6.83
ANSWER: D
Question: A train passes a station platform in 50 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.177 m
B.176 m
C.450 m
D.187 m
Answer: C.450 m
Explanation: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 50 = 15
x + 300 = 750
x = 450 m.
Answer: C
Question: X, Y and Z can do a work in 6 , 9 and 10 days respectively. They completed the work and got Rs.775. What is the share of Y?
A.250
B.240
C.260
D.230
Answer: A.250
Explanation: The ratio of their working rates = 1/6 : 1/9 : 1/10 = 15 : 10 : 6.
Since, they work together, the share of y
= 10/31 * 775 = Rs.250
Answer: A
Question: If six persons sit in a row, then the probability that three particular persons are always together is?
A.1/6
B.1/3
C.1/5
D.1/1
Answer: C.1/5
Explanation: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
Answer: C
Question: A certain bus driver is paid a regular rate of $18 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $976 in total compensation, how many total hours did he work that week?
A.36
B.40
C.44
D.48
Answer: D.48
Explanation: For 40 hrs = 40*18=720
Excess = 976-720=252
For extra hours =.75(18)=13.5+18=31.5
Number of extra hrs =252/31.5=8
Total hrs =40+8=48
Answer D 48
Question: In a group of cows and chickens, the number of legs was 16 more than twice the number of heads. The number of cows was:
A.8
B.7
C.10
D.12
Answer: A.8
Explanation: Let the number of cows be x and their legs be 4x.
Let the number of chicken be y and their legs be 2x.
Total number of legs = 4x + 2y.
Total number of heads = x + y.
The number of legs was 16 more than twice the number of heads.
Therefore, 2 × (x + y) + 16 = 4x + 2y.
or, 2x + 2y + 16 = 4x + 2y.
or, 2x + 16 = 4x [subtracting 2y from both sides].
or, 16 = 4x – 2x [subtracting 2x from both sides].
or, 16 = 2x.
or, x = 8 [dividing by 2 on both sides].
Therefore, the number of cows = 7.
Correct Answer:A)8
Question: Calculate the cost of e yards of cloth given that the cost of f yards of said cloth is g rupees?
A.Rs.(e*f)
B.Rs.(g*f)
C.Rs.(eg/f)
D.Rs.(g/f)
Answer: C.Rs.(eg/f)
Explanation: Cost of f yards = Rs. g.
Cost of 1 yard = Rs.	g/f
Cost of e yards = Rs.(g/f)* e= Rs.(eg/f)
Answer is C.
Question: Calculate the area of a triangle, if the sides are 13 cm, 12 cm and 5 cm, what is its area?
A.36 cm2
B.35 cm2
C.30 cm2
D.32 cm2
Answer: C.30 cm2
Explanation: The triangle with sides 13 cm, 12 cm and 5 cm is right angled, where the hypotenuse is 13 cm.
Area of the triangle = 1/2 * 12 * 5 = 30 cm2
Answer: C
Question: There are 100 students in a class. If 14% are absent on a particular day, find the number of students present in the class.
A.43
B.36
C.86
D.129
Answer: C.86
Explanation: Number of students absent on a particular day = 14 % of 100
i.e., 14/100 × 100 = 14
Therefore, the number of students present = 100 - 14 = 86 students.
Answer:C
Question: If x/6 and x/15 are integers, then x must be divisible by -
A.12
B.18
C.30
D.45
Answer: C.30
Explanation: Factors of 6 2 and 3
factors of 15 are 3 and 5
So number is 2*3*5 = 30
ANSWER:C
Question: If 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 140 units?
A.50 hours
B.40 hours
C.17.5 hours
D.12 hours
Answer: C.17.5 hours
Explanation: Here, we're told that 5 machines can produce 20 units in 10 hours....
That means that EACH machine WORKS for 10 hours apiece. Since there are 5 machines (and we're meant to assume that each machine does the same amount of work), then the 5 machines equally created the 20 units.
20 units/5 machines = 4 units are made by each machine every 10 hours
Now that we know how long it takes each machine to make 4 units, we can break THIS down further if we choose to...
10 hours/4 units = 2.5 hours per unit when 1 machine is working.
The prompt asks us how long would it take 20 machines to produce 140 units.
If 20 machines each work for 2.5 hours, then we'll have 20 units. Since 140 units is '7 times' 20, we need '7 times' more TIME.
(2.5 hours)(7 times) = 17.5 hours
Final Answer:
[Reveal]Spoiler:
C
Question: In shop contains 500 articles each of a cost of $10. He sold them at a price of $16. If the shop keeper has a order of 200 articles, how much profit he will get?
A.A)200
B.B)2000
C.C)1500
D.D)1200
Answer: D.D)1200
Explanation: Total money after selling articles = 200*16 = 3200
cost price = 200*10 = 2000
profit = 1200
correct option is D
Question: There are 50 people in a certain community who belong to the local golf club, tennis club or both clubs. If 1 as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?
A.1) 4
B.2) 7
C.3) 17
D.4) 21
Answer: A.1) 4
Explanation: x -> Golf Club
x -> Tennis Club
y -> both
x+x-y = 50
2x - y =50
multiples of 2 greater than 50
52
54-4=50
IMO (A)
Question: A customer pays 65 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
A.A)$50
B.B)$60
C.C)$70
D.D)$85
Answer: D.D)$85
Explanation: Let x be the original price.
x - 20 = 65
x - 20 + 20 = 65 + 20
x + 0 = 85
x = 85
correct answer is D)$85
Question: A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
A.1642
B.1640
C.1632
D.2789
Answer: B.1640
Explanation: (x*8*3)/100 = ((2665 - x)*3*5)/100
24x/100 = 39975/100 - 15x/100
39x = 39975 => x = 1025
Second sum = 2665 – 1025
=1640
Answer:B
Question: The average of six number is 3.95. The average of two of them is 3.4, while the average of the other two is 3.62. what is the average of the remaining two number ?
A.4.5
B.4.6
C.4.7
D.4.83
Answer: D.4.83
Explanation: solution:
Sum of the remaining two numbers = (3.95 × 6) - [(3.4 × 2) + (3.62 ×2)]
=23.70 -(6.8 + 7.24) = 23.70 - 14.04 = 9.66.
∴ Required average =9.66/2 = 4.83 Answer D
Question: A began business with Rs.27000 and was joined afterwards by B with Rs.54000. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
A.9
B.6
C.7
D.8
Answer: A.9
Explanation: 27*12 : 54*x = 2: 1
x = 3
12 -3 = 9
Answer: A
Question: Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 6w widgets.
A.4
B.36
C.8
D.10
Answer: B.36
Explanation: I am getting 12. E. Hope havent done any calculation errors..
approach..
let y=no. of days taken by Y to do w widgets. Then X will take y+2 days.
1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day)
Solving, we have y = 4
=>X takes 6 days to doing x widgets. So, he will take 36 days to doing 6w widgets.
Answer : B
Question: james works in a bakery. He made cookies that cost $2 and made $200. How many customer did he have?
A.200 customers
B.85 customers
C.250 customers
D.100customers
Answer: D.100customers
Explanation: A cookie costs $2 adding another one is $4. 200 divided by 3 is 50 x 2 is 100. He had 100 customers. The correct answer is D.
Question: The product of a and b is equal to 11 more than twice the sum of a and b. If b = 7, what is the value of b - a?
A.2
B.5
C.7
D.24
Answer: A.2
Explanation: Given: ab = 2(a + b) + 11 and b = 7
Hence 7a = 2a + 14 + 11
5a = 25, a = 5
(A potential trap. Do not get excited here. We need to find b - a, not a)
b - a = 7 - 5 = 2
Correct Option: A
Question: In year Y imported machine tools accounted for 20 percent of total machine-tools sales in the United States, and Japanese imports accounted for 40 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
A.15x
B.13x
C.12.5x
D.14x
Answer: C.12.5x
Explanation: Sales of imported tools = 20% of the total sales = 0.20*{total} = {total}/5;
Sales of Japanese tools = 40% of the sales of imported tools = 2/5*{total}/5 = 2{total}/25
Since the sales of of Japanese tools was x, then 2{total}/25 = x -->2{total} = 25 x
{total} = 25x/2 =12.5 x
Answer: C
Question: In how many ways can the integer 84 be expressed as a product of two different positive integers?
A.10
B.8
C.5
D.4
Answer: D.4
Explanation: 84=(2^2)*3*7
Since 84 is not a perfect square, no of ways=4
Answer D
Question: In measuring the sides of a rectangle, one side is taken 8% in excess, and the other 7% in deficit. Find the error percent in the area calculated from these measurements.
A.0.11%
B.0.7%
C.0.44%
D.0.6%
Answer: C.0.44%
Explanation: Let x and y be the sides of the rectangle. Then, Correct area = xy.
Calculated area = (27/25) x (40/43) y = (913/909 )(xy)
Error In measurement = (913/909)xy- xy = (4/909)xy
Error percentage = [(4/909)xy (1/xy)100] % = (11/25) % = 0.44%.
Answer is C.
Question: __2A
x__B
____
CC
In the multiplication problem above, A, B, and C represent distinct digits. If the sum of A and B is equal to 4.6, what is the value of C?
A.6
B.5.2
C.4
D.3
Answer: B.5.2
Explanation: If A+B=4.6
assuming A and B are positive then A*B<10 (they could be either 1,2,3,4)
therefore
A*B=C
2*B=C
A+B=4.6
Three simple equations - divide the 1st/2nd --> A=2 plug it the 3rd --> B=2.6 --> C=5.2 (ANSWER B)
Question: A train 420 m long, running with a speed of 63 km/hr will pass a tree in?
A.36 sec
B.16 sec
C.17 sec
D.88 sec
Answer: A.36 sec
Explanation: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 420 * 2/35 = 36 sec
Answer:A
Question: If a square mirror has a 20-inch diagonal, what is the approximate perimeter T of the mirror, in inches?
A. 40
B. 60
C. 80
D. 100
Answer: B. 60
Explanation: if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other.
And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter T must be less than 80, so we can eliminate answer choice C, D and E.
so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A.
Now we are left with is B
Question: In a T.V. factory, an average of 60TVs are produced per day for the fist 25days of the months. A few workers fellill for the next five daysreducing the daily avg for the month to58 sets/day . The average production per day for day last 5days is ?
A.35
B.39
C.48
D.50
Answer: C.48
Explanation: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 60
= 240
∴ Average for last 5 days = 240 / 5
= 48
C
Question: Factory X's bulbs work for over 5000 hours in 78% of cases, whereas factory Y's bulbs work for over 5000 hours in 65% of cases. It is known that factory X supplies 90% of the total bulbs available. What is the chance that a purchased bulb will work for longer than 5000 hours?
A.76.4%
B.76.7%
C.77.4%
D.75%
Answer: B.76.7%
Explanation: For X, 90% of 78% will work.
For Y, 10% of 65% will work. *10% is the rest of the bulb supply in the market.
So, the probability that a purchased bulb will work is:
0.90(0.78) = .702
0.10(0.65) = 0.065
The combined probability then is 70.2 + 6.5 = 76.7%
ANS B
Question: Positive Integer A gives the remainder of 32 when divided by another positive Integer B. If A/B = 147.64, what is the value of B?
A.96
B.75
C.48
D.50
Answer: D.50
Explanation: .64 of B = Remainder
.64 of B = 32
B = (32 *100) / 64= 50.
D
Question: There are three motor's are available in the office,namely P,Q,& R.Its power consumption is different.Ratio of the power consumption of 3 different motor's 3:4:5.Total power consumption of 3 motor's are 1250 units.Then find out the power consumption of motor R?
A.655.50 UNITS
B.258.54 UNITS
C.566.29 UNITS
D.520.84 UNITS
Answer: D.520.84 UNITS
Explanation: Ratio of the power consumption of 3 different motor's 3+4+5=12.
Power consumption of motor R= 5/12*1250 = 520.84 UNIT Answer: D
Question: There is a total of 90 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/3 and the probability that it will be green is 1/5. What is the probability that the marble will be either red or blue?
A.1/3
B.3/5
C.7/15
D.11/30
Answer: C.7/15
Explanation: P(red or blue) = 1 - P(white) - P(green) = 15/15 - 5/15 - 3/15 = 7/15
The answer is C.
Question: A can finish a work in 18days and B can do the same work in half the time taken by A. Then, working together what part of the same work they can finish in a day?
A.1/2
B.1/3
C.1/6
D.2/5
Answer: C.1/6
Explanation: 1days work of A+B = (18+9)/18*9 = 1/6
Answer is C
Question: The perimeter of one face of a cube is 24 cm. Its volume will be:
A.216cm3
B.400cm3
C.250cm3
D.625cm3
Answer: A.216cm3
Explanation: Explanation:
Edge of cude = 24/4 = 6 cm
Volume = a*a*a = 6*6*6 = 216 cm cube
Option A
Question: There is a single elimination checkers tournament, meaning when one player loses, they are out of the tournament. There are 50 players in the tournament, how many games are played?
A.49
B.25
C.20
D.10
Answer: A.49
Explanation: A
The number of games always adds up to one less than the number of players in a single elimination tournament. You may calculate it any way. Therefore, 49 games were played.
Question: Ram professes to sell his goods at the cost price but he made use of 850 grms instead of a kg, what is the gain percent?
A. 11%
A.11 1/9%
B.11 1/8%
C.17.65%
D.11 5/9%
Answer: C.17.65%
Explanation: 850 --- 150
100 --- ? => 17.65%
Answer:C
Question: In a city, the streets are aligned in a grid, where the east-west roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The north-south roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 8th Rd and 7th Ave in the shortest possible time, how many different routes could he take?
A.150
B.180
C.210
D.240
Answer: C.210
Explanation: Bills needs to walk 6 blocks north and 4 blocks east.
One possible solution is NNNNNNEEEE.
There are 10C6 = 210 possible solutions.
The answer is C.
Question: A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?
A.18
B.20
C.24
D.26
Answer: A.18
Explanation: Let the original side of the square be x.
(x-8)*(x-6) = 120 = 10*12
x = 18
The answer is A.
Question: 62467 × 9998 = ?
A.624545037
B.627745452
C.624545077
D.624545066
Answer: D.624545066
Explanation: D
624545066
62467 × 9998 = 62467 × (10000 - 2)
= 62467 × 10000 - 62467 × 2
= 624670000 - 124934
= 624545066
Question: A car travels 25 km an hour faster than a bus for a journey of 500 km. If the bus takes 10 hours more than the car, then the speeds of the bus and the car are
A.25 km/h and 40 km/h, respectively
B.25 km/h and 60 km/h, respectively
C.25 km/h and 50 km/h, respectively
D.25 km/h and 70 km/h, respectively
Answer: C.25 km/h and 50 km/h, respectively
Explanation: Let the speed of the bus be x km / h.
Then speed of the car = (x + 25) km / h
∴ 500/x=500/x+25+10
⇒ x2 + 25x – 1250 = 0 ⇒ x = 25
Thus, speed of the bus = 25 km/h
Speed of the car = 50 km/h
Answer C
Question: This topic is locked. If you want to discuss this question please re-post it in the respective forum.
If y ≠ 3 and 3r/y is a prime integer greater than 2, which of the following must be true?
I. r = y
II. y = 1
III. r and y are prime integers.
A. None
B. I only
C. II only
D. III only
Answer: A. None
Explanation: 3r/y and if r=y then ans is 3 and 3 is prime number, which is greater than 2. so ans must be B. Please post OA.
Question: In May Mrs Lee's earnings were 90 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?
A.92
B.35
C.64
D.46
Answer: A.92
Explanation: Lets say the Family Income is 100
In May, lee earned 90Family income is 10
In june, Lee earned 20% more than May, so it is (90+20*90/100 = 108)
Family Income is same 10
In June Lee's Income percent is 108*100/118 ~ 92
Ans is A
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 5 years at 50% per annum is Rs.200 of money?
A.1256
B.2000
C.3600
D.8400
Answer: B.2000
Explanation: P = 200(100/50)5 => P = 2000
Answer: B
Question: Three carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if two of the carpenters work together at their respective rates ?
A.11/15
B.3/5
C.11/30
D.47/90
Answer: D.47/90
Explanation: Farmer A, B, C, and D
A's rate: 1/3 job/hour
B's rate: 1/4 job/hour
C's rate: 1/5 job/hour
D's rate: 1/7 job/hour
By intuition we know that the three fastest farmers are A B and C.
As such
(1/3 + 1/4 + 1/5)*(2/3) = ?
47/90 or (D)
Question: A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
A.Rs. 45
B.Rs. 50
C.Rs. 55
D.Rs. 60
Answer: A.Rs. 45
Explanation: A : B : C = (10 x 7) : (12 x 5) : (15 x 3) = 70 : 60 : 45 = 14 : 12 : 9.
C's rent = Rs. (175 x9/35) = Rs. 45.
THE CORRECT ANSWER IS A.
Question: Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 1/2 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
A.2/5
B.1/3
C.4/13
D.8/29
Answer: A.2/5
Explanation: Now ultimately the speed of every machine is given with respect to Mach O.
So lets assume the speed of O, say 12 hrs to make x units (assuming 6 because we can see we will need to divide by 3 and 4
Mach O makes x units in 12 hrs
So, Mach N = 1/2 of O = 1/2*12 = 6 hrs to make x units
and Mach M = 3/4 of N = 3/4*6 = 6 hrs to make x units
No they are running simultaneously. Lets see how much each mach makes in 1 hr
Mach O = x/12 units
Mach N = x/6 units
Mach M = x/6 units
In 1 hr, together they make - x/12+x/6+x/6 = 5x/12
So what ratio of this has Mach N made?
(x/6) / (5x/12) = 2/5
Ans:A=2/5
Question: A polling company reports that there is a 80% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z?
A.10
B.16
C.6
D.4
Answer: B.16
Explanation: 80% - Candidate Elected
100%-60% = 40% - Candidate doesnotsigh Bill X
50% - Candidate randomly chooses between two bills.
These are multiplicative:
80% x 40% x 50%
0.8 x 0.4 x 0.5 = 0.16 = 16%
Answer (B)
Question: Find the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself?
A.6 years
B.7 years
C.9 years
D.4 years
Answer: D.4 years
Explanation: 4 years
Answer: D