RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct?
A.10 min past 7pm on wednesday
B.20 min past 7pm on wednesday
C.20 min past 9pm on wednesday
D.26 min past 7pm on wednesday
Answer: B.20 min past 7pm on wednesday
Explanation: This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours.
To show the correct time, it has to gain 5 min.
So the correct time will be shown on wednesday at 7:20 PM
Answer: B
Question: Pipes A and B can fill a tank in 10 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in
A.1 13/17 hours
B.2 8/11 hours
C.3 9/17 hours
D.5 5/11 hours
Answer: D.5 5/11 hours
Explanation: Solution
Net part filled in 1 hour	= (1/10 + 1/6 -1/12)
= 11/60.
Therefore, the tank will be full in 60/11 hrs.	â€¹=â€º 5 5/11 hrs.
Answer D
Question: In 2005, 25 percent of the math department’s 60 students were female, and in 2007, 35 percent of the math department’s 65 students were female. What was the percent increase from 2005 to 2007 in the number of female students in the department?
A.15%
B.51.7%
C.62.5%
D.115%
Answer: B.51.7%
Explanation: Female students in 2005 = 25% of 60 = 15
Female students in 2007 = 35% of 65 = 22.75
Percentage increase = [(22.75- 15)/15] *100 % = 51.7%
Correct Option: B
Question: If b < 2 and 2x - 5b = 0, which of the following must be true?
A.x < 5
B.x < 2
C.x = 3
D.x < 3
Answer: A.x < 5
Explanation: 2x - 5b = 0
Therefore, 2x = 5b
As, b<2
2x < 5(2)
i.e x < 5
Answer : A
Question: The integer x is divisible by both 4 and 6. Which of the following must be an integer?
A.x/12
B.x/9
C.x/25
D.x/24
Answer: A.x/12
Explanation: Prime factorization of 4 = 2^2
Prime factorization of 6= 2*3
LCM of 4 and 6 = 2^2 * 3 = 12
Therefore x/12 must be an integer
Answer A
Question: IBM and KTC quote for a tender. On the tender opening day, IBM realizes that their quotations are in the ratio 7:4 and hence decreases its price during negotiations to make it Rs 1 Lakh lower than KTC's quoted price. KTC realizes that the final quotes of the two were in the ratio 3:4. What was the price at which IBM won the bid?
A.Rs. 7 lakh
B.Rs. 3 lakh
C.Rs. 4 lakh
D.Rs. 1.5 lakh
Answer: B.Rs. 3 lakh
Explanation: Explanation :
IBM initially quoted Rs 7x lakh. KTC quoted 4x lakh.
IBM's final quote = (4x−1) Lakh.
Thus, (4x−1)/4=3/4
i.e x=1.
Hence, IBM's bid winning price = Rs 3 Lakh.
Answer : B
Question: If 25% of a number is subtracted from a second number, the second number reduces to its four-sixth. What is the ratio of the first number to the second number ?
A.5:3
B.4:3
C.6:3
D.3:4
Answer: B.4:3
Explanation: Explanation:
Let the numbers be p & q
q-p/4 = 4q/6
=> q-4q/6 = p/4
=> 2q/6 = p/4
=> p/q = 4/3
Answer B
Question: A certain drink of type A is prepared by mixing 4 parts milk with 3 parts fruit juice. Another drink of type B is prepared by mixing 4 parts of fruit juice and 3 parts of milk. How many liters of fruit juice must be added to 63 liters of drink A to convert it to drink B?
A.7
B.14
C.21
D.28
Answer: C.21
Explanation: In 63 liters of drink A, there are 36 liters of milk and 27 liters of juice.
With 36 liters of milk, we need a total of 48 liters of juice to make drink B.
We need to add 21 liters of juice.
The answer is C.
Question: What is the next number of the following sequence
7, 0, 1, 8, 5, 12, 9, 26, 3, 2, 23, ?
A.28
B.29
C.30
D.31
Answer: A.28
Explanation: 7,0,1,8,5,12,9,26,3,2,23,X
(7,0,1,8),(5,12,9,26),(3,2,23,X)
7+0+1=8
5+12+9=26
3+2+23=X => X=28
ANSWER:A
Question: Meena wrote all the numbers from 1 to 69,999 inclusive. How many digits did she write in total?
A.278,889
B.308,889
C.338,889
D.368,889
Answer: C.338,889
Explanation: 1-9=>1*9 digits
10-99=>2*90=180 (numbers between 10-99 is 90 where each has 2 digits)
100-999=>3*900=2700
1000-9999=>4*9000 = 36,000
10000-69999=>5*60,000 = 300,000
The answer is 338,889
The answer is C.
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. What is the probability of having 3 man in committee ?
A.10/36
B.11/72
C.12/72
D.28/36
Answer: D.28/36
Explanation: We may have (3 men and 2 women) = (7C3 x 6C2) = 525
or (4 men and 1 woman) = (7C4 x 6C1) = 210
or (5 men only) = (7C5) = 21
Required ways = 756
Probability of having 3 man in committee = 525 / 756 =28/36
ans - D
Question: What is the ratio F of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
A.1/4
B.3/8
C.1/2
D.3/5
Answer: D.3/5
Explanation: Let X be the side of the cube. Therefore X^2*6= surface area.
the rectangle is the same other than length is 2X. The width and height are the same as the cube. 2*W*H+2*W*L+2*H*L= 2X^2+4X^2+4X^2= 10X^2.
6X^2/10X^2 = 3/5 F.
Answer = D
Question: 8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 81. How much wine did the cask hold originally?
A.18 litres
B.24 litres
C.32 litres
D.42 litres
Answer: B.24 litres
Explanation: Let the quantity of the wine in the cask originally be x litres.
Then, quantity of wine left in cask after 4 operations = x(1-8/x)^4 litres.
therefore, (x(1-8/x)^4)/x=16/81
=>(1-8/x)^4=(2/3)^4
=>x-8/x=2/3
=>3x-24=2x
=>x=24 litres.
ANSWER:B
Question: A box measuring 49 inches long by 42 inches wide by 14 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?
A.78
B.82
C.84
D.86
Answer: C.84
Explanation: least number of cubes will be required when the cubes that could fit in are biggest.
7 is the biggest number that could divide all three, 49, 42 and 14.
Thus side of cube must be 7, and total number of cubes = 49/7 * 42/7*14/7 = 84
Ans C.
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 10 sec. What is the length of the fast train?
A.27 7/6
B.27 7/5
C.27 7/2
D.500/9
Answer: D.500/9
Explanation: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 10= 500/9
= 27 7/9 m.
Answer:D
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?
A.270
B.277
C.187
D.257
Answer: A.270
Explanation: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 27 * 10 = 270 m.
The length of the faster train = 270 m.
Answer: A
Question: Set A: {1, 3, 4, 6, 9, 12, 15}
If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 3?
A.3/14
B.2/7
C.9/14
D.5/7
Answer: B.2/7
Explanation: Probability of an event = (# of favorable outcomes) / (total # of outcomes).
There are 5 numbers you can choose from (3, 6, 9, 12, 15) so that the sum to be divisible by 3 and there are total of 7 numbers so P=C35C37=27P=C53C73=27.
Answer: B.
Question: How many two digit numbers of distinct digits can be formed by using digits 3, 4, 5, 6,7 and 8 such that the numbers are divisible by 9?
A.3
B.4
C.5
D.6
Answer: B.4
Explanation: CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9
Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition
If sum of Digits = 9, No. = 36, 45, 54, 63 --- 4 Cases
Answer: option B
Question: A train 150 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post?
A.11 s
B.10 s
C.7 s
D.12 s
Answer: B.10 s
Explanation: We know from the formula Time = Distance/ Speed
Thus, Time = 150/ 54 x 5/18
or, Time = 10 sec.
ANSWER:B
Question: A car runs at the speed of 60 km per hour when not serviced and runs at 80 kmph when serviced. After servicing the car covers a certain distance in 4 hours. How much time will the car take to cover the same distance when not serviced?
A.6 hours 12 minutes
B.5 hours 33 minutes
C.8 hours 15 minutes
D.7 hours 12 minutes
Answer: B.5 hours 33 minutes
Explanation: Explanation :
Time = 80*4 / 60 = 5 hours 33 mins
Answer â€“ B
Question: The price of the jewel, passing through three hands, rises on the whole by 56%. If the first and the second sellers 20% and 25% profit respectively find the percentage profit earned by the third seller.
A.20
B.4
C.5
D.2
Answer: B.4
Explanation: Let the original price of the jewel be $ p and let the profit earned by the third seller be x% Then, (100+x)% of 125% of 120% of P =156% Of P ((100+X)/100*125/100*120/100*P)=(156/100*P)
==> (100+X)=(156*100*100)/(125*120)=104=>X=4%
Answer B)
Question: . A car covers a distance of 390 km in 4 hours. Find its speed?
A.104
B.55
C.66
D.98
Answer: D.98
Explanation: 390/4 = 98 kmph
Answer: D
Question: If 40% of (x-y) = 20% of (x+y), then what percent of x is y?
A.50.5%
B.44.4%
C.22.2%
D.33.3%
Answer: D.33.3%
Explanation: 40% of (x-y) = 20% of (x+y)
40/100 (x-y) = 20/100 (x+y)
x = 3y
Required percentage = y/x *100 = y/3y * 100 = 33.3%
Answer is D
Question: Set X consists of all two-digit primes and set Y consists of all positive even multiples of 5 less than 100. If the two sets are combined into one, what will be the range of the new set?
A. 87
B. 89
C. 90
D. 92
Answer: A. 87
Explanation: Set X = {11, 13, 17,............., 83, 89, 97}
Set Y = {10, 20, 30,..............., 70, 80, 90}
Combining two sets, say Set Z
Set Z = { 10,11, 13, 17, 20,30,..................., 70, 80, 83, 89, 90, 97}
Range = Max Value - Min Value
Range (Z) = 97 - 10 = 87
OA A is the answer.
Question: Prints a page 60 pg per min .If the printed for 1 hours except 10 min.Where there
was an paper jam,how many page did it print
A.10,880
B.12,880
C.3,000
D.8,880
Answer: C.3,000
Explanation: 60 pages ------->1 min
1 hrs except 10 mints means=1*60=60-10=50 mints
i.e.,50*60=3,000 pages printed.
ANSWER:C
Question: The probability is 1/2 that a certain coin turns up heads on any given toss. If the coin is tossed six times, what is the probability that the coin turns up tails on at least one of the tosses?
A.15/16
B.21/32
C.31/32
D.63/64
Answer: D.63/64
Explanation: P(6 heads)= 1/2*1/2*1/2*1/2*1/2*1/2=1/64.
P(at least one tail)=1-1/64=63/64.
The answer is D.
Question: A batsman in his 15th inning makes a score of 75 and their by increasing his average by 3. What is his average after the 15th inning?
A.31
B.32
C.33
D.34
Answer: C.33
Explanation: 14x + 75 = 15(x + 3)
x = 30 + 3 = 33
Answer:C
Question: Which of the following equations represents a line that is perpendicular to the line described by the equation 2x + 3y = 12?
A.4x + 2y = 5
B.5x + y = 7
C.3x - 2y = 8
D.4x - 3y = 9
Answer: C.3x - 2y = 8
Explanation: Perpendicular lines have slopes which are negative reciprocals of each other.
The line 2x + 3y = 12 in slope-intercept form is y = -(2/3)x + 4
The slope of this line is -2/3.
The slope of a perpendicular line is 3/2.
3x - 2y = 8 in slope-intercept form is y = (3/2)x - 4
The answer is C.
Question: Manoj, Nayan and Ajit together started a software company. It was agreed that Manoj would invest Rs. 6500 for 6 months, Nayan, Rs. 8400 for 5 months and Ajit Rs. 10,000 for 3 months. Manoj wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of Nayan in the profit ?
A.2330
B.2660
C.3000
D.none of the above
Answer: B.2660
Explanation: Explanation :
Manoj is a working member and for that, he receive 5% of the profit
= 5% of 7400 = 5*7400/100 = 370
Remaining amount = 7400-370 = 7030
Ratio of their investments = 6500*6 : 8400*5 : 10000*3
= 65*6 : 84*5 : 100*3 = 13*6 : 84 : 20*3 = 13*2 : 28 : 20
= 13 : 14 : 10
Share of Nayan in the profit = 7030 * (14/37) = 190*14 = 2660
Answer : B
Question: A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability R that the 2 apples selected will include the spoiled one?
A.a. 1/5
B.b. 3/10
C.c. 2/5
D.d. 1/2
Answer: C.c. 2/5
Explanation: there can be two ways in which one can select a spoiled apple and a good apple.
1. you pick the spoiled one first and the good one later..
Prob of picking bad one = 1/5 (one bad apple)
Prob of picking a good one from the remaining 4 good apples (4/4 =1)
therefore the total prob for case 1 = i/5 * 1 = 1/5
Total prob R= porb1 + prob2 = 1/5+1/5 = 2/5.C
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
A.15
B.66
C.18
D.16
Answer: A.15
Explanation: Explanation:
90 * 10/60 = 15 kmph
Answer:A
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.238
B.480
C.287
D.117
Answer: B.480
Explanation: 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: If a boat is rowed downstream for 200 km in 10 hours and upstream for 96 km in 12 hours, what is the speed of the boat and the river?
A.14 , 18
B.14 , 6
C.14 , 14
D.6 , 6
Answer: B.14 , 6
Explanation: Explanation:
If x: speed of boats man in still water
y: speed of the river
Downstream speed (Ds) = x + y
Upstream speed (Us) = x â€“ y
x = (Ds + Us) / 2
y = (Ds â€“ Us) / 2
In the above problem Ds = 20 ; Us = 8
x = (20 + 8) / 2 = 28/2 = 14 km/hr
y = (20 - 8) /2 = 12/2 = 6 km/hr
ANSWER: B
Question: On an order of 3 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of:
A.20%
B.25%
C.30%
D.35%
Answer: B.25%
Explanation: Clearly, the retailer gets 1 dozen out of 4 dozens free.
Equivalent discount = 1/4 * 100 = 25%.
Answer B) 25%
Question: Ajith and Rana walk around a circular course 115 km in circumference, starting together from the same
point. If they walk at speed of 4 and 5 kmph respectively, in the same direction, when will they meet ?
A.after 20 hours
B.after 115 hours
C.after 115 minutes
D.after 20 minutes
Answer: B.after 115 hours
Explanation: Rana is the faster person. He gains 1 km in 1 hour. So Rana will gain one complete round over
Ajith in 115 hours. i.e. they will meet after 115 hours.
Answer: B
Question: If a Ã— b = 2a - 3b + ab, then 4 Ã— 5 + 5 Ã— 4 is equal to :
A.31
B.32
C.43
D.45
Answer: A.31
Explanation: Explanation:
4 Ã— 5 + 5 Ã— 4 = (2 Ã— 4 - 3 Ã— 5 + 4 Ã— 5) + ( 2 Ã— 5 - 3 Ã— 4 + 5 Ã— 4)
= (8 -15 + 20 + 10 - 12 +20) = 31.
Answer: A
Question: If ab-a-b=265
bc-b-c=155
ac-c-a=150
then find a?
A.16
B.17
C.18
D.19
Answer: B.17
Explanation: (A-1)(B-1)=AB-A-B+1=265+1=266..(1)
(B-1)(C-1)=BC-B-C+1=155+1=156..(2)
(C-1)(A-1)=CA-C-A+1=150+1=151..(3)
(1)/(2) gives..(A-1)/(C-1)=266/156..(4)
(3)*(4) gives..(A-1)^2=257.47...A=17.04
Solving other equations..B=17.58 and C=10.4
ANSWER:B
Question: Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of Rs.12 per square metre.
A.1824
B.1854
C.1872
D.1888
Answer: C.1872
Explanation: Explanation:
Area of the carpet = Area of the room = (13 × 9) m2 = 117 m2.
Length of the carpet = (area/width) = 117 ×(4/3) m = 156 m.
Therefore Cost of carpeting = (156 × 12) = Rs.1872
Answer: Option C
Question: How many cubes of 10cm edge can be put in a cubical box of 1m edge
A.10
B.100
C.1000
D.10000
Answer: C.1000
Explanation: number of cubes=(100x100x100)/(10x10x10)=1000 Answer: C
Question: A has 10000 chocolates.20% of the chocolates are Eaten.What percentage of the uneaten Chocolates must be eaten so that 3/2 of all chocolates are eaten?
A.39.25
B.37.25
C.37.26
D.38.21
Answer: B.37.25
Explanation: Number of chocolates=10,000
Currently Eaten=10,000*20/100=2000
Uneaten Chocolates=10000-2000=8000
2/3 of all chocolates=5000
The number of chocolates to be eaten to make 2/3 of all chocolates Eaten =5000-2000=3000
So now the question remains - 3000 is how much percentage of uneaten chocolates (8000)
= 3000 * 100 /8000
=37.5
Answer (B)
Question: A man walks from B to C, a distance of x miles, at 6 miles per hour and returns at 12 miles per hour. What is his average speed?
A.10 mph
B.9.6 mph
C.8.0 mph
D.8.4 mph
Answer: C.8.0 mph
Explanation: Total distance covered = 2x
Time taken12miles / hour = x/12 hrs
Time taken @ 6 miles / hour = x/6 hrs
Avg speed = 2x / (x/6 + x/12) = 8 mph
Ans is C
Question: A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to
contradict each other, narraƟng the same incident
A.30%
B.35%
C.40%
D.45%
Answer: B.35%
Explanation: Explanation:
Let A = Event that A speaks the truth
B = Event that B speaks the truth
Then P(A) = 75/100 = 3/4
P(B) = 80/100 = 4/5
P(A-lie) = 1-3/4 = 1/4
P(B-lie) = 1-4/5 = 1/5
Now
A and B contradict each other =
[A lies and B true] or [B true and B lies]
= P(A).P(B-lie) + P(A-lie).P(B)
[Please note that we are adding at the place of OR]
= (3/5*1/5) + (1/4*4/5) = 7/20
= (7/20 * 100) % = 35%
Answer: B
Question: ♠n denotes the number obtained when n is rounded to the nearest tenth. For example ♠4.31 = 4.3
♠2.423 - ♠3.421 =
A.1.05
B.1.04
C.-0.8
D.-1.0
Answer: C.-0.8
Explanation: ♠2.423 - ♠3.421
2.4 - 3.2 = -0.8
Answer : C
Question: In digging a pond 25 m * 10 m * 5 m the volumes of the soil extracted will be?
A.1750
B.1000
C.2866
D.2787
Answer: A.1750
Explanation: 25 * 10 * 5 = 1750
Answer: A
Question: A zeebra chases a tiger 5 hours after the tiger runs. zeebra takes 6 hours to reach the tiger. If the average speed of the zeebra is 55 kmph, what s the average speed of the tiger?
A.35kmph
B.32kmph
C.30kmph
D.31kmph
Answer: C.30kmph
Explanation: tiger take 11 hours and zeebra take 6 hours...then Distance chased by them is 55*6.so speed of tiger is (55*6)/11=30kmph.
ANSWER IS C
Question: The speed of a boat in upstream is 45 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?
A.70,10 kmph
B.67.5,22.5 kmph
C.70.5,70.5 kmph
D.78.6,10.25 kmph
Answer: B.67.5,22.5 kmph
Explanation: Speed of the boat in still water
= (45+90)/2
= 67.5 kmph. Speed of the stream
= (90-45)/2
= 22.5 kmph.
Answer:B
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
A.7m
B.6m
C.5m
D.2m
Answer: D.2m
Explanation: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer: D
Question: From January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 15 percent. The enrollment on January 1, 1993, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 1991 ?
A.38
B.39
C.40
D.41
Answer: B.39
Explanation: Soln:-
15x=45 --> 23/20*x=45 --> x=45*20/23=900/23=~39.
Answer: B.
Question: A team of 11 member is to be formed from a group of 5 men and 8 women. At most 3 men are allowed. How many combination are possible.
A.9
B.10
C.11
D.12
Answer: B.10
Explanation: At most 3 men means not more than 3,
Case 1 All women not possible
Case 2 10 women and 1men not possible
Case 3 9 women and 2 men not possible
Case 4 8 women and 3 men =5C3 * 8C8 = 10.
ANSWER:B
Question: A trader bought a car at 20% discount on its original price. He sold it at a 45% increase on the price he bought it. What percent of profit did he make on the original price?
A.A)10%
B.B)12%
C.C)16%
D.D)20%
Answer: C.C)16%
Explanation: Original price = 100
CP = 80
S = 80*(145/100) = 116
100 - 116 = 16%
C)
Question: The slant height of a cone is 12 cm and radius of the base is 4cm, find the curved surface of the cone.
A.33
B.88
C.48
D.77
Answer: C.48
Explanation: π * 12 * 4 = 48
Answer:C
Question: Two trains of length 400 m and 200 m are 200 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 36 kmph. After how much time will the trains meet?
A.8 sec
B.20/7 sec
C.33/7 sec
D.21/7 sec
Answer: A.8 sec
Explanation: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 36)*5/18 = 25 mps.
The time required = d/s = 200/25 = 8 sec.
Answer : A
Question: What is the greatest integer m for which the number 40!/14^m is an integer?
A.8
B.7
C.6
D.5
Answer: D.5
Explanation: 14^m = 2^m*7^m.
Let's figure out how many 7's are in the prime factorization of 40!
The multiples of 7 are: 7, 14, 21, 28, 35.
Thus 7^5 will divide 40! but 7^6 will not.
Clearly 2^5 will divide 40!
So m=5 is the largest possible integer.
The answer is D.
Question: If n = (33)^43 + (23)^33 what is the units digit of n?
A.0
B.2
C.4
D.6
Answer: D.6
Explanation: First of all, the units digit of (33)^23 is the same as that of 3^23 and the units digit of (23)^33 is the same as that of 3^33. So, we need to find the units digit of 3^23 + 3^33.
Next, the units digit of 3 in positive integer power repeats in blocks of four {3, 9, 7, 1}:
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!)
...
Thus:
The units digit of 3^23 is the same as the units digit of 3^3, so 7 (43 divided by the cyclicity of 4 gives the remainder of 3).
The units digit of 3^33 is the same as the units digit of 3^1, so 3 (33 divided by the cyclicity of 4 gives the remainder of 1).
Therefore the units digit of (33)^23 + (23)^33 is 3 + 3 = 6.
Answer: D.
Question: If n = 2×3×5×7×11×13×17, then which of the following statements must be true?
I. n2 is divisible by 600
II. n + 19 is divisible by 19
III. is even n+4 / 2 = even
IV . divisible by 35 only
A.I only
B.none and IV only
C.III only
D.I and III only
Answer: B.none and IV only
Explanation: n = 2×3×5×7×11×13×17 = 39270
I. not divisible by 600
II 39270+19=39289 not divisible by 19
III. 39270+4/2= odd= 19637
iv. divisible by 35
B
Question: The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
A.255
B.267
C.235
D.277
Answer: C.235
Explanation: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m.
Answer:C
Question: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 101 players took part in that tournament. How many matches were played?
A.90 matches
B.95 matches
C.99 matches
D.100 matches
Answer: D.100 matches
Explanation: D100 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 100 matches were played.
Question: A room is 18 meters long, 15 meters wide 12 meters in height. The longest possible rod which can be placed in the room is
A.25.28 meters
B.24.28 meters
C.23.28 meters
D.26.28 meters
Answer: A.25.28 meters
Explanation: Square root of 18^2+15^2+12^2...(Diognal) which is square root of 639 that lies 25<√639<26. Hence the answer should be A
Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train.
A.175 m
B.145 m
C.140 m
D.200 m
Answer: D.200 m
Explanation: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 12 = 200 meter
ANSWER: D
Question: A vendor bought 6 toffees for a rupee.How many for a rupee he must sell to gain 20%.
A.3
B.4
C.5
D.6
Answer: C.5
Explanation: SP=(100+20)*1/100=1.20
1.20 rupees=6 toffees
so for 1 rupee=6/1.2=5
ANSWER:C