RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In certain year in Country C, x sets of twins and y sets of triplets were born. If there were z total babies born in Country C in this year, and x and y were both greater than 0, which of the following represents the fraction T of all babies born who were NOT part of a set of twins or triplets?
A.z - 2x - 3y
B.(2x+3y)/z
C.(x+y)/z
D.1 - (2x+3y)/z
Answer: D.1 - (2x+3y)/z
Explanation: X set of twins implies 2x babies of twin category.
Y set of triplets means 3y babies of triplet category.
Let K be the babies other than twin or triplet category.
Total babies = z = 2x+3y+k.
or K=Z-(2x+3y)
=> Fraction of babies other than twin or triplet categories = K/Z = Z-(2x+3y)/Z.
T= 1- (2x+3y)/Z. Hence answer is D.
Question: Each writer for the local newspaper is paid as follows: a dollars for each of the first s stories each month, and a + b dollars for each story thereafter, where a > b. How many more dollars will a writer who submits s+ a stories in a month earn than a writer who submits s+ b stories?
A.(a – b)( a + b + s)
B.a – b
C.a^2 – b^2
D.s( a – b)
Answer: C.a^2 – b^2
Explanation: total earned for s+a stories =a + a(a+b)
total earned for s+b stories =a+ b(a+b)
difference = a+a(a+b) -a -b(a+b)
=(a+b)(a-b) =a^2-b^2
answer is C
Question: In a race of 600 metres, A can beat B by 60 metres and in a race of 500 metres, B can beat C by 50 metres. By how many metres will A beat C in a race of 400 metres?
A.76 metres
B.80 metres
C.70 metres
D.84 metres
Answer: A.76 metres
Explanation: A runs	B runs	C runs
600 metres race	600m	540 m
500 metres race	500 m	450m
Combing ratio A runs B runs C runs
300metres - 2700meters - 2430metres
Unitary A runs B runs C runs
Method 400mtres - 360 metres - 324 metres
? A beats C by 400-324 = 76 metres.
Answer: A.
Question: What is the rate percent when the simple interest on Rs.720 amount to Rs.180 in 4 Years?
A.6.25
B.7.25
C.8.25
D.9.25
Answer: A.6.25
Explanation: 180 = (720*4*R)/100
R = 6.25%
Answer: A
Question: In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 22 percent are juniors and 75 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students?
A.42
B.48
C.64
D.76
Answer: C.64
Explanation: 200 are sophomores.
The number of freshmen is 600 - 160 - 0.22(800) = 264
The answer is C.
Question: Given: b2 = ac and ax=by=cz.
Determine the value of y.
A.2xz/(x+z)
B.8xz/(x+z)
C.3xz/(x+z)
D.7xz/(x+z)
Answer: A.2xz/(x+z)
Explanation: Explanation:
No explanation is available for this question!
ANSWER: A
Question: A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo?
A.12
B.51
C.13
D.15
Answer: D.15
Explanation: Two students can be selected from 6 in 6C2 =15 ways.
Therefore, the teacher goes to the zoo 15 times.
Ans: D
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.10000?
A.3310
B.1879
C.2779
D.2672
Answer: A.3310
Explanation: A = 10000(11/10)^3
= 13310
= 10000
----------
3310
Answer: A
Question: If the average of 6x and 8y is greater than 100, and x is twice y, what is the least integer value of x ?
A.22
B.20
C.21
D.23
Answer: B.20
Explanation: Substitution can be used in the following way:
Always start with the equation: x = 2y. It is more straight forward to manage as compared to the inequality.
Substitute y = x/2, not the other way because you need to find the minimum value of x. So you can get rid of y.
Now go on to the inequality. So 8y = 8x/2 = 4x
Now average of 6x and 4x is greater than 100. Average of 6x and 4x is 5x. So,
5x > 100
x > 20
Answer : B
Question: What is the greatest value of positive integer x such that 2^x is a factor of 100^40?
A.80
B.90
C.95
D.105
Answer: A.80
Explanation: Put in simple words, we need to find the highest power of 2 in 100^40
100 = 2^2*5^2
Therefore 100^40 = (2^2*5^2)^40 = 2^80*5^80
Answer : A
Question: The area of an equilateral triangle is subtracted from its base, and the perimeter is then added to this total, the result is 4. What is the height of the equilateral triangle if its base is 2?
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: An eqilateral triangle means all sides are equal; therefore, base = side. The equation is; base - Area + Perimeter = b - A + P = b -1/2bh + 3b, and b = 2. So, 2 - 2/2h + 6 = 4, and 8 - h = 4.
By plugging in the answers we can test the answers quickly; then, 4 is the only possible answer.
Answer: C
Question: At noon, ship A is 100km west of ship B. Ship A is sailing east at 35 km/hr and ship B is sailing north at 25km/hr. How fast is the distance between the ships changing at 4.00pm.
A.35.21 km/hr.
B.36.21 km/hr.
C.37.21 km/hr.
D.39.21 km/hr.
Answer: B.36.21 km/hr.
Explanation: Let the position of ship B at noon be at the origin
=>ship A has x-coordinate = -100km and B has x-coordinate =0km
At 4.00 p.m., ship A is at x = -100+4*35=40km
and B is at x = 0 and y = 4 * 25 = 100 km
Distance between them at 4.00 p.m. = √[(100)^2 + (40)^2] = 20√(29) km
Distance between the ships,
s^2 = x^2 + y^2
=> 2s ds/dt = 2x dx/dt + 2y dy/dt
=> rate of change of distance between the ships, ds/dt
= (x dx/dt + y dy/dt) / s
= [40 * 35 + 100 * 25] / [20√(29)] km/hr
= (1400 + 2500) / [20√(29)] km/hr
= 195/√(29) km/hr
≈ 36.21 km/hr.
ANSWER:B
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 3 different boat to go and 4 flight to return. In how many ways, can the boy perform his journey?
A.20
B.40
C.18
D.12
Answer: D.12
Explanation: Ans.(D)
Sol. Number of choices to go by ship = 3 Number of choices to return by airline = 4 From, fundamental principle, total number of ways of performing the journey = 3 x 4 = 12 ways
Question: At 6′o a clock ticks 6 times. The time between first and last ticks is 30 seconds. How long does it tick at 12′o clock
A.47
B.76
C.28
D.66
Answer: D.66
Explanation: Explanation:
For ticking 6 times, there are 5 intervals.
Each interval has time duration of 30/5 = 6 secs
At 12 o'clock, there are 11 intervals,
So total time for 11 intervals = 11 × 6 = 66 secs.
Answer: D
Question: What should be the least number to be added to the 2496 number to make it divisible by 5?
A.12
B.17
C.18
D.4
Answer: D.4
Explanation: Answer : 4
Option : D
Question: The interest on a certain deposit at 4.5% p.a. is Rs. 202.50 in one year. How much will the additional interest in one year be on the same deposit at 5% p.a ?
A.Rs. 20.25
B.Rs. 22.50
C.Rs. 25
D.Rs. 42.75
Answer: B.Rs. 22.50
Explanation: Solution
S.I=Rs.202.50, R=4.5%, T= 1 Year
principal = Rs (100*202.50 / 4.5*1)= Rs.4500
Now P =Rs.4500, R =5%, T= 1 year
S.I=(4500*5*1/100)= Rs.225
Different in interest = Rs. ( 225- 202.50)= Rs.22.50
Answer B
Question: Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $396 per week. How much does she earn in dollars per hour?
A.11
B.10
C.9
D.8
Answer: A.11
Explanation: Let Sheila earn x dollars per hour
So, on Monday, Wednesday and Friday , she earns 8x each
And, on Tuesday and Thursday, she earns 6x each
In total , over the week she should earn, 3(8x) + 2(6x) = 36x
She earns $396 per week
36x =396
x =11
Correct Option : A
Question: A girl has exactly 6 quarters, 7 dimes, and 10 nickels in her pocket. If she withdraws a number of these coins at random, how many coins would she have to withdraw to ensure that she has at least a 50 percent chance of withdrawing at least one quarter?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: When the probability of NOT drawing a quarter is 50% or less, then the probability of drawing a quarter is at least 50%.
P(not drawing a quarter with 2 coins) = 17/23 * 16/22 = 136/253 > 50%
P(not drawing a quarter with 3 coins) = 136/253 * 15/21 = 680/1771 < 50%
The answer is C.
Question: A room 11 m 47 cm long and 7m 77 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
A.636
B.640
C.647
D.651
Answer: D.651
Explanation: Explanation:
Area of the room = (1147 x 777) cm2.
Size of largest square tile = H.C.F. of 1147 cm and 777 cm = 37 cm.
Area of 1 tile = (37 x 37) cm2.
Number of tiles required =(1147×777)/(37×37)=651
Answer: Option D
Question: The area of the floor of a room is 20 m2 that of a longer wall 15 m2 and of the shorter wall 12 m2, find the edge of the new cube?
A.50 m^3
B.60 m^3
C.70 m^3
D.80 m^3
Answer: B.60 m^3
Explanation: Explanation:
lb = 20 ; lh = 15 ; fh = 12
(lbh)2 = 20 * 15 * 12 => lbh = 60 m^3
B)
Question: A 300 m long train crosses a platform in 48 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
A.500
B.350
C.828
D.277
Answer: A.500
Explanation: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/489 = 50/3
3x + 900 = 2400 => x = 500 m.
Answer: A
Question: A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint T, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
A.2
B.2 1/2
C.3
D.3 1/2
Answer: B.2 1/2
Explanation: Given W:B = 3:5
That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture.
But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio,
1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce
0.75: 1.25 gives 1+1.5 =2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure
0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable.
So correct ans is 2.5 gallons. B
Question: A man can row upstream at 25 kmph and downstream at 45 kmph, and then find the speed of the man in still water?
A.65
B.86
C.35
D.78
Answer: C.35
Explanation: US = 25
DS = 45
M = (45 + 25)/2
= 35
Answer: C
Question: A mixture contains alcohol and water in the ratio 2:5. If 10liters of water is added to the mixture, the ratio becomes 2:7. Find the quality of alcohol in the given mixture.
A.5
B.10
C.15
D.20
Answer: B.10
Explanation: Let the quantity of alcohol and water be 2x and 5x
2x/(5x+10) = 2/7
20x = 4(3x+5)
x=5
Quantity of alcohol = 2*5 = 10liters.
Answer is B
Question: A person crosses a 650 m long street in 5 minutes. What is his speed in km per hour?
A.5.2 km/hr.
B.8.2 km/hr.
C.7.8 km/hr.
D.3.2 km/hr.
Answer: C.7.8 km/hr.
Explanation: C
7.8 km/hr.
Speed=(600/5 * 60) m/sec
= 2.16 m/sec.
Converting m/sec to km/hr
=(2*18/5) km/hr
= 7.8 km/hr.
Question: A train is 360 meter long is running at a speed of 72 km/hour. In what time will it pass a bridge of 140 meter length?
A.11 seconds
B.38 seconds
C.40 seconds
D.25 seconds
Answer: D.25 seconds
Explanation: Speed = 72 Km/hr = 72*(5/18) m/sec = 20 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/20) = 25 seconds
Answer: D
Question: What is the product of all the prime factors of 16?
A.108
B.18
C.9
D.6
Answer: D.6
Explanation: The factors of 16 :
factors are 1,2,4.8,16 Ans - 2*2*2*2 = 16
Answer : D
Question: The surface of a cube is 24sq cm. Find its volume?
A.8
B.5
C.7
D.3
Answer: A.8
Explanation: 6a2 = 24
a = 2 => a3 = 8cc
Answer: A
Question: Laura can paint 1/x of a certain room in 20 minutes. What fraction E of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?
A.1/(3x)
B.3x/(x-3)
C.(x – 3)/(3x)
D.x/(x-3)
Answer: C.(x – 3)/(3x)
Explanation: Options with variables are often done by plugging in numbers.
Both working together can paint the room in 1 hr so if their individual rates were equal, each would take 2 hours alone.
2 hours is 120 mins so in 20 mins each would complete E=120/20 = 1/6th of the room alone.
So if x = 6 (Laura completes 1/6th of the room in 20 mins), the correct option will give 1/6. (Joseph will also paint 1/6th of the room if their rates are same)
If you put x = 6 in the options, only option (C) will give 1/6
Answer (C)
Question: A dog taken four every five leaps of hare but three leaps of the dog is equal to four leaps of the hare. Compare speed?
A.16:15
B.17:15
C.18:15
D.19:15
Answer: A.16:15
Explanation: A dog taken four every five leaps of hare but three leaps of the dog is equal to four leaps of the hare.
For time duration, when a dog takes 12 steps , hare takes 15 steps
but 12 steps of dog = 12*4/3 = 16 steps of hare
so ratio of speed of dog to speed of hare = 16:15
ANSWER:A
Question: If x > 1, which of the following decreases as x decreases?
I.1/( x + x^2)
II. 1/(2x^2 − x)
III. (x + 1)
A.I only
B.II only
C.III only
D.I and II only
Answer: C.III only
Explanation: let x= 4 and 3 b old and new values
ST1: x= 4 -> 4+16 = 1/20
x=3-> 3+9 = 1/12 ...increased
ST2:x= 4-> 2*16-4 =1/ 28
x=3->2*9-3 = 1/15
Increased
St3: x=4-> 5
x=3->4
Ans: C
Question: Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer Q between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it?
A.Q=12
B.Q=15
C.Q=17
D.Q.18
Answer: D.Q.18
Explanation: Since we are concerned with integers between 1 and 20, write down the primes till 40.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
(you should be very comfortable with the first few primes... )
2, 3, 5, 7, 11,12, 13, 17, 19, 23, 29, 31, 37 - Three pairs (11,13), (7,17), (5, 19)
2, 3, 5, 7, 11, 13,15,17, 19, 23, 29, 31, 37 - Three pairs (13, 17), (11, 19), (7, 23)
2, 3, 5, 7, 11, 13,17, 19, 23, 29, 31, 37 - Three pairs (11, 23), (5, 29), (3, 31)
2, 3, 5, 7, 11, 13, 17,18,19, 23, 29, 31, 37 - Four pairs (17, 19), (13, 23), (7, 29), (5, 31)
2, 3, 5, 7, 11, 13, 17, 19,20,23, 29, 31, 37 - definitely cannot be more than 4 since there are only 4 primes more than 20. So must be less than 4 pairs. Ignore.
Answer (D).
Question: A man sells a horse for Rs.620 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.227
B.299
C.740
D.860
Answer: C.740
Explanation: CP = SP + 1CP = SP - g
620 + x = 980 - 2x
3x = 360 => x = 120
CP = 620+ 120= 740
Answer: C
Question: Logan buys 100 shares of par value Rs. 30 each, of a company, which pays an annual dividend of 12% at such a price that he gets 10% on his investment. Find the market value of a share.
A.2
B.4
C.5
D.36
Answer: D.36
Explanation: Face value of each share = Rs.30
Total dividend received by Logan = 100Ã—30Ã—12/100 = Rs.360
Let market value of 100 shares = Rs.x
xÃ—10/100=360
x = 3600
ie, Market value of 100 shares = Rs.3600
Hence, Market value of each share = Rs.36
Answer is D.
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
A.33 1/7 %
B.33 8/3 %
C.33 1/3 %
D.33 1/8 %
Answer: C.33 1/3 %
Explanation: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Answer: C
Question: In a race, the speeds of A and B are in the ratio 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is?
A.1 hr
B.2 hr
C.1.5 hr
D.2.5 hr
Answer: B.2 hr
Explanation: Explanation :
Ratio of speeds = 3:4Distance remaining constant, the ratio of time taken = 4:3A takes 0.5 hours more than BHence time taken by A=4×0.5= 2 hour
Answer : B
Question: From the sale of sleeping bags, a retailer made a gross profit of 15% of the wholesale cost. If each sleeping bag was sold for $28, what was the wholesale cost per bag?
A.3.0
B.3.36
C.24.34
D.25.0
Answer: C.24.34
Explanation: Cost price * 1.15 = Selling price --> Cost price * 1.15 = $28 --> Cost price = $24.34.
Answer: C.
Question: A wildlife preserve is being planned for 4,000 rhinoceroses. The preserve is to contain a total of 10,000 acres of watering area, plus 100 acres of grazing area for each rhinoceros. If the number of rhinoceroses is expected to increase by 10 percent, how many thousand acres should the preserve have in order to provide for the increased population?
A. 450
B. 330
C. 320
D. 310
Answer: A. 450
Explanation: Number of rhinos = 4000
Watering area = 10,000 acres
Number of rhino to increase by 10 percent ,then number of rhino = 4400
Grazing area for a rhino = 100
Total grazing area for 4400 rhinos= 4400 * 100 = 4,40,000
Total area required for the wildlife preserve = 4,40,000 + 10,000 = 4,50,000 = 450 * 1000
Answer A
Question: How many cubes of 10cm edge can be put in a cubical box of 1m edge
A.3348
B.2888
C.1000
D.2877
Answer: C.1000
Explanation: Explanation:
number of cubes=(100x100x100)/(10x10x10)=1000
Answer: C) 1000
Question: In a group of 26 junior high school students, 7 take French, 10 take Spanish, and 4 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?
A.7
B.6
C.5
D.4
Answer: C.5
Explanation: C
5
Add 7 + 10 + 4 to get 21.
Then subtract 21 from the total students ⇒ 26 – 21 = 5.
Answer is C
Question: If 9a - b = 10b + 65 = -12b - 2a, what is the value of 11a + 11b?
A.-11
B.-5
C.0
D.5
Answer: C.0
Explanation: (i) 9a - 11b = 65
(ii) 2a + 22b = -65
Adding (i) and (ii):
11a + 11b = 0
The answer is C.
Question: 17 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
A.154
B.184
C.240
D.272
Answer: D.272
Explanation: 2*17C2 = 2*136 = 272
The answer is D.
Question: A and B runs around a circular track. A beats B by one round or 10 minutes. In this race, they had completed 4 rounds. If the race was only of one round, find the A's time over the course:
A.8.5 min
B.7.5 min
C.1.5 min
D.9.5 min
Answer: B.7.5 min
Explanation: Explanation:
B runs around the track in 10 min.
i.e , Speed of B = 10 min per round
A beats B by 1 round
Time taken by A to complete 4 rounds
= Time taken by B to complete 3 rounds
= 30 min
A's speed = 30/4 min per round
= 7.5 min per round
Hence, if the race is only of one round A's time over the course = 7 min 30 sec
Answer: B
Question: A graph may be defined as a set of points connected by lines called edges. Every edge connects a pair of points. Thus, a triangle is a graph of 3 edges and 3 points. The degree of a point is the number of edges connected to it. For, example, a triangle is a graph with 3 points of degree 2 each. Consider a graph with 12 points. It is possible to reach any point from any through sequence of edges. The number of edges 'e' in the graph must satisfy the condition
A.11 ≤ e ≤ 66
B.10 ≤ e ≤ 66
C.11 ≤ e ≤ 65
D.0 ≤ e ≤ 11
Answer: A.11 ≤ e ≤ 66
Explanation: Explanation :
The least number of edges will be when one point is connected to each of the other 11 points, giving a total of 11 lines. One can move from any point to any other point via the common point.
The maximum edges will be when a line exists between any two points. Two points can be selected from 12 points in 12C2 i.e. 66 lines.
Answer : A
Question: At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 350-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $200?
A.1,108
B.2,900
C.2,108
D.2,124
Answer: B.2,900
Explanation: We have $200 and we have to maximize the number of hot dogs that we can buy with this amount.
Let's try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money, which in this case is 350 for $22.95.
For the sake of calculation, let's take $23. 23x8 gives 184 ,i.e. a total of 350x8 = 2800 hot dogs . We are left with ~$16. Similarly, let's use $3 for calculation. We can buy 5 20-pack hot dogs (3x5), a total of 20x5 = 100 hot dogs. So we have 2900 hot dogs.
2108 looks far-fetched (since we are not likely to be left with > $1.55). Hence, (b) 2900 (ANSWER B)
Question: A telecom service provider engages male and female operators for answering 1000 calls per day. A male operator can handle 40 calls per day whereas a female operator can handle 50 calls per day. The male and the female operators get a fixed wage of Rs. 250 and Rs. 300 per day respectively. In addition, a male operator gets Rs. 15 per call he answers and female operator gets Rs. 10 per call she answers. To minimize the total cost, how many male operators should the service provider employ assuming he has to employ more than 7 of the 12 female operators available for the job?
A.15
B.14
C.12
D.10
Answer: D.10
Explanation: Explanation :
There are two equations to be formed 40m + 50f = 1000.
250m + 300f + 40 x 15m + 50 x 10f = A.
850m + 8000f = A.
m and f are the number of males and females. A is the amount paid by the employer.
Then the possible value of f = 8,9,10,11,12.
Iif f= 8, M =15.
If f = 9,10,11 then m will not be an integer while f =12 then m will be 10.
By putting f = 8 and m=15 , A = 18800.
when f =12 and m= 10 then A = 18100.
Hence, the number of males is 10.
Answer : D
Question: A batsman makes a score of 100 runs in the 17th inning and thus increases his averages by 5. What is his average after 17th inning?
A.39
B.35
C.20
D.40.5
Answer: C.20
Explanation: let the average after 16th inning =x
then total run after 16th inning=16x
then total run after 17th inning=16x+100
then average run after 17th inning=(16x+100)/17
(16x+100)/17=x+5 = > 16x+100 = 17x+85 => x =15
x=15;
average after 17th inning =15+5=20
ANSWER:C
Question: Two trains are traveling on a collision course. If train A is traveling at a speed of 350 mph and train B is traveling 28% slower, how much time will it take the trains to collide if the initial distance between the two is 2107 miles?
A.Two hours and 30 minutes.
B.One hour and 10 minutes.
C.Two hours and 25 minutes.
D.Three hours and 5 minutes.
Answer: D.Three hours and 5 minutes.
Explanation: Answer is D. Three hours and 5 minutes.
Since they are racing towards each other, the speed is accumulative, ie. 350 mph + 350*0.72 = 602 (0.72 because the second train is 28% slower)
So time before collision is total distance / total speed = 2107/602 = 3 hours and 5 mins
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
A.1/5
B.2/47
C.3/8
D.12/455
Answer: D.12/455
Explanation: Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (Â²Câ‚)(â´Câ‚‚)/Â¹âµCâ‚ƒ
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455.
D
Question: The product of the prime numbers between 0 and 20 is closest to...
A.10^5
B.10^6
C.10^7
D.10^8
Answer: C.10^7
Explanation: Write out the primes 1 - 20
2 x 3 x 5 x 7 x 11 x 13 x 17 x 19
Round the numbers off in multiples of 5. Try to alternate rounding up and down
5 x 5 x 5 x 5 x 10 x 10 x 20 x 20
25 x 25 x 10 x 10 x 20 x 20
pull out 10 from each number
10^6 (2.5 x 2.5 x 2 x 2)
10^6 (5 x 4)
10^7 (2)
round off the 2.
answer is C
Question: Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 12 years more than the present age of Anand. Find the present age of Anand?
A.22
B.16
C.27
D.187
Answer: B.16
Explanation: Let the present ages of Anand and Bala be 'a' and 'b' respectively.
a - 10 = 1/3 (b - 10) --- (1)
b = a + 12
Substituting b = a + 12 in first equation,
a - 10 = 1/3 (a + 2) => 3a - 30 = a + 2
=> 2a = 32 => a = 16.
Answer:B