RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A slot machine in a Las Vegas casino has an average profit of $600 for each 8-hour shift for the five days Sunday through Thursday, inclusive. If the average per-shift profit on Friday and Saturday is 25% greater than on the other days of the week and the slot machine is in operation every hour of every day, what is the total weekly profit that the casino makes from the slot machine?
A.a - 4500
B.b - 9000
C.c - 13,500
D.d - 15,500
Answer: C.c - 13,500
Explanation: Correct answer is C - 13500.
Total profit per weekday = $600 X 3 (shifts)= $1800
Total profit per week (apart from SaturdaySunday) = $1800 X 5 = $9000
Total profit per shift on weekends = $600 X 125/100 = $750
Total profit on weekends = $750 X 3 (shifts) X 2 (Saturday, Sunday) = $4500.
Hence the answer is - $4500 + $9000 = $13,500. (C)
Question: A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
A.81 km/hr
B.88 km/hr
C.62 km/hr
D.46 km/hr
Answer: A.81 km/hr
Explanation: Explanation:
Let x is the length of the train in meter and y is its speed in kmph
x/8.4 = (y-4.5)(10/36) ---(1)
x/8.5 = (y-5.4)(10/36) ---(2)
Dividing 1 by 2
8.5/8.4 = (y-4.5)/ (y-5.4)
=> 8.4y - 8.4 × 4.5 = 8.5y - 8.5×5.4
.1y = 8.5×5.4 - 8.4×4.5
=> .1y = 45.9-37.8 = 8.1
=> y = 81 km/hr
Answer: Option A
Question: Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was:
A.three times as much
B.twice as much
C.the same
D.half as much
Answer: B.twice as much
Explanation: Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.
We know that
Speed = Distance/Time.
Or, Time = Distance/Speed.
So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the old time was: twice as much.
correct answer B
Question: There are 32 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station?
A.1800
B.1820
C.1150
D.1122
Answer: D.1122
Explanation: The total number of stations= 34
From 34 Stations we have to choose any two stations and the direction of travel (Ernakulam to Chennai is different from Chennai to Ernakulam) in 34P2 ways.
34P2= 34*33= 1122
ANSWER:D
Question: There are two buildings P and Q. If 15 persons are sent from P to Q, then the number of persons in each building is the same. If 20 persons are sent from Q to P, then the number of persons in P is double the number of persons in Q. How many persons are there in building P?
A.110
B.100
C.120
D.140
Answer: C.120
Explanation: Let the number of persons in building P = p
and the number of persons in building Q = q
If 15 persons are sent from P to Q,
then the number of persons in each building is the same
=> p-15 = q+15
=> p - q = 30 ----(Equation 1)
If 20 persons are sent from Q to P,
then the number of persons in P is double the number of persons in Q
=> 2(q - 20) = (p + 20)
=> 2q - 40 = p + 20
=> 2q - p = 60 ----(Equation 2)
(Equation 1) + (Equation 2)=> q = 90
From Equation 1, p = 30 + q = 30 + 90 = 120
i.e., Building P has 120 persons
Answer is C.
Question: In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes W of the competition are possible?
A.18
B.20
C.54
D.84
Answer: D.84
Explanation: the ways the three teams can be selected is..
i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways..
ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60
total W=84 outcomes
D
Question: A man spends 1/5 of his salary on food, 1/10 of his salary on house rent and 3/5 of his salary on clothes. He still has $18000 left with him. Find his salary.
A.$180000
B.$280000
C.$380000
D.$480000
Answer: A.$180000
Explanation: Solution:
The expenditure incurred on each item is expressed as part of the total amount (salary), so it is an independent activity.
In general for independent activities
[1 – (x1/y1 + x2/y2 + x3/y3)] × Total amount = Balance amount
[1 – (1/5 + 1/10 + 3/5)] × Total salary = $18000
[1 – 9/10] × Total salary = $18000
Therefore total salary = $18000 × 10 = $180000
Answer A
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
A.3
B.5
C.6
D.7
Answer: A.3
Explanation: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer:A
Question: Bradley owns b video game cartridges. If Bradley’s total is one-third the total owned by Andrew and twice the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
A.(16/3)b
B.(17/4)b
C.(13/4)b
D.(9/2)b
Answer: D.(9/2)b
Explanation: Step 1: Categorize the problem
This problem is testing basic algebra and equations, with an extra layer of complexity by having variables in the answer choices.
Step 2: Think like the test maker
What is the key detail or key details in the problem? The key detail to immediately recognize is that the problem gives you Andrew and Charlie’s totals in relation to Bradley’s total rather than giving you Bradley’s total in relation to the other two; and then the problem asks you to solve the problem in terms of b. This means that you have to relate Andrew and Charlie’s values in relation to Bradley’s total. The test maker is attempting to force you to structure the problem in the opposite way that most people are used to structuring information. By gaining this insight, it makes it easier to solve the problem.
Step 3: Solve the problem
b = Bradley’s total
3b = Andrew’s total
(1/2)b = Charlie’s total
Add each total
b + 3b+ (1/2)b = 4b + (1/2)b = (16/4)b + (1/2)b = (9/2)b
Therefore,choose D.
Question: If a - b = 2 and a2 + b2 = 25, find the value of ab.
A.A)10.5
B.B)12
C.C)15
D.D)18
Answer: A.A)10.5
Explanation: Explanation:
2ab = (a2 + b2) - (a - b)2
= 25 - 4 = 21
ab =10.5
Answer: A
Question: If the complement of a certain angle is two times the measure of that certain angle, then what is the measure of that certain angle?
A.45°
B.30°
C.22.5°
D.18°
Answer: B.30°
Explanation: Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.
The original angle is x, so the complement is 2x, and together, these add up to 90 degrees.
x + 2x = 90
3x = 90
x = 30°
Answer = (B)
Question: If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in
A.2 days
B.1 day
C.3 days
D.5 days
Answer: B.1 day
Explanation: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.
B)
Question: If the sum of 1/3 and 22/99 is converted to a decimal, what is the 3000th digit to the right of the decimal place?
A.2
B.3
C.5
D.8
Answer: C.5
Explanation: 1/3 +22/99 = 5/9=0.555555555...
hence, the 3000th digit would also be 5
Ans: C
Question: Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king?
A.1/11
B.2/13
C.4/13
D.3/17
Answer: C.4/13
Explanation: Here, n(S) = 52
There are 13 cards of diamond (including one king) and there are 3 more kings.
Let E = event of getting a diamond or a king.
Then, n(E) = (13 + 3) = 16
P (E) = 16 / 52 = 4/13
C
Question: If x and y are integers such that (x+1)^2 is less than or equal to 16 and (y-1)^2 is less than 64, what is the sum of the maximum possible value of xy and the minimum possible value of xy?
A. -16
B. -10
C. 0
D. 14
Answer: B. -10
Explanation: (x+1)^2 <= 16
x <= 3
x >= -5
(y-1)^2< 64
y < 9
y > -7
Max possible value of xy is -5 × -6 = 30
minimum possible value of xy is -5 × 8 = -40
-40 + 30 = -10
Answer : B
Question: If points A and B are (10-5) units apart, which of the following can have only one possible value?
I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB
A.I only
B.II only
C.III only
D.I and II only
Answer: A.I only
Explanation: I. The area of a square region with side AB --> side=AB=(10-5) or 5 --> the area of a square is 5^2=25, so only one possible value;
II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter;
III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12).
Answer: A.
Question: The banker's discount on a sum of money for 1 1/2 years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is:
A.10%
B.13%
C.12%
D.15%
Answer: C.12%
Explanation: B.D. for 3/2 years	= Rs. 558.
B.D. for 2 years
= Rs.(558 x 2/3 x 2)
= Rs. 744
T.D. for 2 years = Rs. 600.
Therefore, Sum = B.D. x T.D./B.D. - T.D
= Rs. (744 x 600/144	)= Rs. 3100.
Thus, Rs. 744 is S.I. on Rs. 3100 for 2 years.
Therefore, Rate =(100 x 744/3100 x 2)%
= 12%
Answer is C
Question: If two projectiles are launched at the same moment from 1998 km apart and travel directly towards each other at 444 km per hour and 555 km per hour respectively, how many minutes will it take for them to meet?
A.90
B.100
C.110
D.120
Answer: D.120
Explanation: The projectiles travel a total of 999 km per hour.
The time to meet is 1998/999=2 hours = 120 minutes
The answer is D.
Question: A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 35 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell?
A.525.
B.412.
C.432.
D.502.
Answer: A.525.
Explanation: Pastry is divided in 35 customers equally. So,total number of pastry must be a multiple of 35
Only option A satisfies the condition, and hence is the answer
Question: Worker A takes 8 hours to do a job. Worker B takes 6 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
A.20/9
B.40/9
C.50/9
D.24/7
Answer: D.24/7
Explanation: one day work of A = 1/8
one day work of B = 1/6
so one day work of A and B together = 1/8 + 1/6 = 7/24
so total days required = 24/7
ANSWER:D
Question: If the average (arithmetic mean) of (2a+16) and (3a-8) is 84, what is the value of a?
A.25
B.30
C.28
D.32
Answer: D.32
Explanation: ((2a+16) + (3a-8)) / 2 = (5a+8)/2 = 84
a= 32
The answer is D.
Question: Consider a quarter of a circle of radius 20. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.
A.20*(sqr2 -1)
B.8*(sqr3 -1)
C.4*(sqr7 - 1)
D.12* (sqr7 -1)
Answer: A.20*(sqr2 -1)
Explanation: I got 20/(sqr2 +1) and just forgot to multiply by (sqr2 -1).
Answer A
Question: If k^3 is divisible by 120, what is the least possible value of integer k?
A.12
B.30
C.60
D.90
Answer: B.30
Explanation: 120 = 2^3*3*5
Therefore k must include at least 2 * 3 * 5 = 30.
The answer is B.
Question: x is the product of each integer from 1 to 25, inclusive and y=100^k, where k is an integer . What is the greatest value of k for which y is a factor of x?
A.5
B.4
C.3
D.6
Answer: C.3
Explanation: The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula:
n5+n52+n53+...+n5k, where k must be chosen such that 5k≤n
x = 1*2*3....*25 = 25!
No. of trailing zeros in 25! = 25/5 + 25/5^2 = 6
100^k = 10^2k → k = 6/2 = 3
C
Question: If n is a positive integer, which of the following expressions must be even?
A.(n − 1)( n + 1)
B.(n − 4)( n + 1)
C.(n − 2)( n + 6)
D.(n − 5)( n + 1)
Answer: B.(n − 4)( n + 1)
Explanation: Whether n is even or odd, (n-4)(n+1) will have one odd factor and one even factor.
The product will be even.
The answer is B.
Question: 30 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 3:2. How many liters of Liquid Q must be added to make the ratio 3:4?
A.8
B.10
C.12
D.14
Answer: C.12
Explanation: Let x be the amount of liquid Q to be added.
(2/5)*30 + x = (4/7)*(30+x)
420 + 35x = 600 + 20x
15x = 180
x = 12
The answer is C.
Question: The speed at which a man can row a boat in still water is 21 kmph. If he rows downstream, where the speed of current is 5 kmph, what time will he take to cover 90 metres?
A.23.46
B.27.46
C.28.46
D.12.46
Answer: D.12.46
Explanation: Speed of the boat downstream = 21 + 5 = 26 kmph= 26 * 5/18 = 7.22 m/sHence time taken to cover 90 m = 90/7.22= 12.46 seconds.Answer:D
Question: The simple interest at z% for z years will be $z on a sum of
A.$ (1000)/z
B.$(100)z^2
C.$ z
D.$ (100)/z
Answer: D.$ (100)/z
Explanation: Principal =$(100*z)/(z*z)=$(100/z).
Answer is D
Question: The ratio of two quantities is 3 to 5. If each of the quantities is increased by 6, what is the ratio of these two new quantities?
A.It cannot be determined from the information given.
B.5/9
C.12/13
D.15/14
Answer: A.It cannot be determined from the information given.
Explanation: let the actual ratio be 3k/5k, increase numerator and denominator by 6 => 3k+6/5k+6
Until the value of k is unknown we can not determine the actual ratio.
OR
let the actual be 3/4. After increasing 6 => 9/10
let the actual be 6/8. After increasing 6 => 12/14
Therefore without actual quantities we cannot determine the actual ratio.
Answer : A
Question: A box contains 4 red chips and 4 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?
A.1/2
B.4/7
C.7/12
D.2/3
Answer: B.4/7
Explanation: Total selection ways: 8C2=8!/4!4!=28
Selecting one blue chip out of two: 4C1=4!/1!3!=4
Selecting one red chip out of four: 4C1=4!/1!3!=4
Thus, (4C1*4C1)/8C2=(4*4)/28=16/28=4/7=B
Question: For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.2?
A.12.6.
B.14.4.
C.15.8.
D.16.2.
Answer: D.16.2.
Explanation: [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.2
= 6*0 + 2*7.2 + 8 - 6.2
= 0 +14.4 +1.8
16.2
Answer D
Question: the price of a commodity(in rupees per kilogram) is 100+0.1n, on the nthvday of 2007(n=1,2,,,,,100), and then remains constant. On the other hand, the price of another commodity is 89+0.15n on the nth day of 2007(n=1,2,,,,,,365). On which date in 2007, will the price of these twocommodities be equal????
A.11th may
B.12th may
C.20th may
D.22th may
Answer: C.20th may
Explanation: price of both the commodity cannot be same within 100days( by puttng n=100 in both the price)
price of 1st commodity after 100 days =100+0.1*100= 110
day on which 2nd commodity becomes equal to 1st= 89+0.15n=110
n=140
140th day of 2007 is 20th may
ANSWER:C
Question: At 3.40, the hour hand and the minute hand of a clock form an angle of
A.120°
B.125°
C.130°
D.135°
Answer: B.125°
Explanation: Solution
Angle traced by hour hand in 17/2 hrs	= (360/12x17/2 )°
= 255.
Angle traced by min hand in 30 min	= (360/60x30)°
= 180.
Required angle	= (255 - 180)°
=75°
Answer B
Question: The average age of 15 students of a class is 14 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is?
A.3years
B.4years
C.5years
D.6years
Answer: B.4years
Explanation: Age of the 15th student
=[15 * 14 - (14 * 5 + 16 * 9)]
= (210 - 214) = 4 years.
Answer:B
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is?
A.11 years
B.16 years
C.33 years
D.14 years
Answer: A.11 years
Explanation: Age of the 15th student
=[15 * 15 - (14 * 5 + 16 * 9)]
= (225 - 214) = 11 years.
Answer:A
Question: A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:
A.3 : 1
B.1 : 3
C.1 : 2
D.2 : 1
Answer: A.3 : 1
Explanation: Explanation :
Let speed upstream = x
Then, speed downstream = 2x
Speed in still water = (2x + x)/2 = 3x/2
Speed of the stream = (2x − x)/2 = x/2
Speed in still water : Speed of the stream = (3x/2) (2x/2) = 3 : 1. Answer : Option A
Question: Two numbers are in the ratio of 1 : 2. If 6 be added to both, their ratio changes to 3 : 5. The greater number is
A.20
B.24
C.28
D.32
Answer: B.24
Explanation: Let the ratio be X : Y,
Given X/Y = 1/2 ,
(X + 6)/(Y + 6) = 3/5
=> X = 12
And Y = 24
ANSWER:B
Question: On flipping 3 coins together what is the outcomes for at least two tail?
A.1/7
B.3/8
C.3/11
D.4/13
Answer: B.3/8
Explanation: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Favorable outcomes for at least two heads
= favorable outcomes for exactly two heads and favorable outcomes for more than two heads
= {TTH, HTT, TTT}
3/8
B
Question: If x is 20 percent more than y and y is 60 percent less than z, then x is what percent of z?
A.500%
B.48%
C.500/3%
D.125%
Answer: B.48%
Explanation: Z = 100 ; Y = 40 so X = 48
X as % of Z = 48/100 * 100 => 48%
Answer will be (B)
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is:
A.500
B.277
C.222
D.297
Answer: A.500
Explanation: Explanation:
110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/112 = Rs. 500
Answer:A
Question: A ladder 18 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 6 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip?
A.12.5
B.15
C.18
D.19
Answer: A.12.5
Explanation: 18^2-6^2=288
it means that the height is equal to 16.9.
since the top of the ladder slips down 4 feet, then the height of the wall =16.9-4=12.9
the bottom =sqrt(18^2-12.9^2)=sqrt(324-166.41)=12.5
ans is A
Question: For her customer feedback score, Jess wants to average at or above an 8.0 rating. For the month of June, she received the following scores: 7, 8, 8, 7, 9, 9, 6, 7, 8 and 7. By what percent did she fall short of her goal?
A. 4%
B. 5%
C. 8%
D. 10%
Answer: B. 5%
Explanation: Expected minimum rating = 8
Deviation from the expected minimum rating = (-1 + 0 + 0 - 1 + 1 + 1 - 2 - 1 + 0 - 1)/10 = -4/10 = -0.4
Current rating is 0.4 less than 8.
Percentage = (0.4/8)*100 = 5%
Answer: B
Question: he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg. What might be the weight of the new person ?
A.75 kg
B.95 kg
C.45 kg
D.85 kg
Answer: B.95 kg
Explanation: Explanation:
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (75 + 20) kg = 95 kg.
Answer: B
Question: A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
A.287m
B.278m
C.400m
D.228m
Answer: C.400m
Explanation: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 42
= 50/3
3(x + 300)
= 2100 è x
= 400m.
Answer:C
Question: Water boils at 212°F or 100°C and melts at 32°F or 0°C . If the temperature of the particular day is 35°C , it is equal to
A.40
B.80
C.95
D.100
Answer: C.95
Explanation: Let F and C denotes the temparature in Fahrenheit anid Celcsius respectively.
Then, (F - 32) /(212 - 32) = (C - 0)/(100 - 0), if c = 35, then F = 95.
C
Question: One night 40 percent of the female officers on a police force were on duty. If 240 officers were on duty that night and half of these were female officers, how many female officers were on the police force?
A.90
B.300
C.270
D.500
Answer: B.300
Explanation: Let total number of female officers in the police force = F
Total number of officers on duty on that night = 240
Number of female officers on duty on that night = 240/2 = 120
(40/100)*F = 120
=>F = 300
Answer B
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
A.70%
B.20%
C.60%
D.10%
Answer: B.20%
Explanation: Explanation:
900 ---- 180
100 ---- ? => 20%
Answer: B
Question: The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
A.48
B.12
C.75
D.28
Answer: C.75
Explanation: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 150 + P
C + M = 150
Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 150/2 = 75.
Option C
Question: If m and n are positive integers, and m=2n and k=9m, then -
A.k is a factor of m.
B.2m is a factor of k.
C.3m is a factor of k/2.
D.m/2 is a factor of k.
Answer: D.m/2 is a factor of k.
Explanation: m=2n --> m is even.
k=9m --> m is factor of k, thus m/2 = integer must also be a factor of k.
Answer: D.
Question: The average age of 40 students is 8 years. If the age of teacher is also included , then their average age increases by half a year. What is the age of the teacher?
A.45 years
B.48.5 years
C.28.5 years
D.26.5 years
Answer: C.28.5 years
Explanation: Total age of 40 students = 40*8 = 320
Let the age of the the teacher be x, Then (320+x)/41 = 8+1/2 =8 ½.
320+x =17/2*41 =697/2 = 348.5,
x =348.5-320 = 28.5
ANSWER:C
Question: In how many ways can a Chief Minister and a Vice Minister be elected from a team of 11 members?
A.110
B.121
C.132
D.144
Answer: A.110
Explanation: There are 11 choices for the Chief Minister.
Then there are 10 choices for the Vice Minister.
The total number of ways is 11*10 = 110.
The answer is A.
Question: Two cars namely A and B start simultaneously from a certain place at the speed of 40 kmph and 55 kmph, respectively.The car B reaches the destination 2 hours earlier than A. What is the distance between the starting point and destination?
A.8 hours 12 minutes
B.6 hours 15 minutes
C.7 hours 20 minutes
D.7 hours 12 minutes
Answer: C.7 hours 20 minutes
Explanation: Explanation :
Let the time taken by car A to reach destination is T hours
So, the time taken by car B to reach destination is (T – 2) hours.
S1T1 = S2T2
=> 40(T) = 55 (T – 2)
=> 40T = 55T -110
=> 15T = 110
T = 7 hours 20 minutes
Answer – C
Question: The length of a train and that of a platform are equal. If with a speed of 36 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
A.299
B.300
C.299
D.750
Answer: B.300
Explanation: Speed = [36 * 5/18] m/sec = 10 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 10 => x = 10 * 60 / 2 = 300
Answer: B
Question: When 22 is divided by the positive integer k, the remainder is 2, for how many different values of k is this true?
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: When 22 is divided by k, remainder is 2 i.e. there are 2 balls leftover after grouping. so k must be greater than 2.
It also means that 20 is completely divisible by k.
Factors of 20 are 1, 2, 4, 5, 10, 20
Out of these, k can be 4, 5, 10 and 20.
Answer (D)