divelab/Sys2Bench huggingface dataset:
Question: Find the unknown term 8,X,6,2,-4, -12
Options:
A)2
B)4
C)6
D)8
E)9
Rationale: 8,X,6,2,-4, -12
i guess each differ in d range of 2
8 - 8 = 0
8 - 6 = 2
6 - 2 = 4
2 - 6 = -4
-4 - 8 = -12
ANSWER:D
Answer: D
Question: A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?
Options:
A)3.34 sq m
B)3.37 sq m
C)3.84 sq m
D)7.34 sq m
E)3.24 sq m
Rationale: Area of the path = Area of the outer circle - Area of the inner circle
= ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2
= (a - b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16
= 3.34 sq m
Answer:A
Answer: A
Question: Q is a set of four distinct prime numbers. If the sum of the integers in Q is odd and the number x is a member of Q, then what is the least value that x can be?
Options:
A)2
B)3
C)4
D)5
E)7
Rationale: 2 + 3 + 5 + 7 = 17 ( sum is ODD)
Least number = 2
A
Answer: A
Question: In a lottery, there are 10 prizes and 10 blanks. A lottery is drawn at random. What is the probability of getting a prize?
Options:
A)1/10
B)2/5
C)2/7
D)5/7
E)1/2
Rationale: Solution
P(getting a prize)	= 10 / (10+10)
‹=› 10 / 20
‹=› 1 / 2.
Answer E
Answer: E
Question: A cat leaps 5 leaps for every 4 leaps of a dog, but 2 leaps of the dog are equal to 3 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?
Options:
A)5:6
B)3:2
C)4:8
D)1:2
E)7:8
Rationale: Given;
2 dog = 3 cat;
Or, dog/cat = 3/2;
Let cat's 1 leap = 2 meter and dogs 1 leap = 3 meter.
Then, ratio of speed of cat and dog = 2*5/3*4 = 5:6.''Answer: 5:6;
Answer: A
Question: If a man buys 50 fish for $150 and sold them for $2.5 dollars each determine his loss.
Options:
A)$ 35
B)$ 30
C)$ 25
D)$ 20
E)$ 38
Rationale: Cost of 50 fishes = $150
Sold each fish for $2.5
So he sold 50 fishes for $(50 × 2.5) = $125
Loss = $(150 – 125) = $25
Therefore, loss = $ 25.
Answer:C
Answer: C
Question: A cistern 2 meters wide and 4 meters long contains water up to a depth of 1 meter 25 cm. What is the total area of the wet surface?
Options:
A)49
B)87
C)23
D)66
E)19
Rationale: Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(lh + bh) + lb
= [2 (4 x 1.25 + 2 x 1.25) + 2 x 4]
= 23
The answer is C.
Answer: C
Question: An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point?
Options:
A)6 hrs 21 min
B)6 hrs 91 min
C)6 hrs 01 min
D)6 hrs 23 min
E)3 hrs 21 min
Rationale: Time taken to cover 600 km = 600/100 = 6 hrs.
Number of stoppages = 600/75 - 1 = 7
Total time of stoppages = 3 * 7 = 21 min
Hence, total time taken = 6 hrs 21 min.
Answer:A
Answer: A
Question: Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?
Options:
A)620 m
B)120 m
C)420 m
D)250 m
E)550 m
Rationale: C
420 m
Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = 60
=> 300 + LY = 60 (12) = 720
=> LY = 720 - 300 = 420 m
Length of the stationary train = 420 m
Answer: C
Question: Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 185 cms. What was the ratio of men to women?
Options:
A) 5:2
B) 5:1
C) 4:3
D) 2:1
E) 3:1
Rationale: We're given a few facts to work with:
1) The average height of the females is 170cm
2) The average height of the males is 185cm
3) The average of the GROUP is 180cm
We're asked for the RATIO of men to women.
W = number of Women
M = number of Men
(170W + 185M)/(W+M) = 180
170W + 185M = 180W + 180M
5M = 10W
M = 2W
M/W = 2/1
The ratio of men to women is 2 to 1.
D
Answer: D
Question: A boat running downstream covers a distance of 16 km in 4 hours while for covering the same distance upstream,it takes 8 hours.What is the speed of the boat in still water ?
Options:
A)3 km/hr
B)6 km/hr
C)8 km/hr
D)Data inadequate
E)None of these
Rationale: Solution
Rate downstream =(16/4) kmph = 4 kmph, Rate upstream =(16/8) = 2 kmph.
∴ Speed in still water =1/2(4+2) kmph = 3 kmph.
Answer A
Answer: A
Question: The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
Options:
A)288
B)267
C)200
D)4096
E)2771
Rationale: Principal = [4913 / (1 + 25/(4 * 100))3]
= 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096.
Answer: D
Answer: D
Question: A hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 24 kilometers per hour. The cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?
Options:
A)10
B)15
C)20
D)25
E)30
Rationale: In 5 minutes, the cyclist travels a distance of (5/60)*24 = 2 km.
The time it takes the hiker to complete this distance is 2/4 hours = 30 minutes
The cyclist needs to wait 30 - 5 = 25 minutes
The answer is D.
Answer: D
Question: On the coordinate plane , points P and O are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?
Options:
A) (1.5,1)
B) (2,-5)
C) (0,0)
D) (1,1.5)
E) (2,2)
Rationale: Although it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options.
One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord).
Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that PO is the diameter of the circle.
There can be a case when PO is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle.
If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y CORDINATE and mark the ans=D
Answer: D
Question: There are 8 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?
Options:
A)120
B)720
C)1,008
D)1,520
E)1,980
Rationale: Answer is E. Can somebody tell me what answer I may have found if I had added the 8C2 and 9C2 (28+36=64)?
I'm guessing that would've been the number of 2-member committees which had men and women separately. Is that right?
C
Answer: C
Question: A person decided to build a house in 100days. He employed 100men in the beginning and 100 more after 25 days and completed the construction in stipulated time. If he had not employed the additional men , how many days behind schedule would it have been finished?
Options:
A)7
B)5
C)2
D)3
E)1
Rationale: 200 men do the rest of the work in 100-25 = 75 days
100 men can do the rest of the work in 75*200/100 = 75days
Required number of days = 75-80 = 5 days
Answer is B
Answer: B
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1232 cm is?
Options:
A)A)15
B)B)10
C)C)14
D)D)12
E)E)11
Rationale: 2 * 22/7 * 14 * x = 1232 => x = 14
ANSWER:C
Answer: C
Question: If e>0, which of the following must be true?
Options:
A)1 < e
B)0 < e < 2
C)-1 < e < 1
D)-10 <e
E)1/100 < e
Rationale: All we know is that e is some positive number. Right away we can see that D must be true: if e is positive then it MUST be true that it's greater than -10. Still let's check each option.
A. 1 < e. We don't know whether the number is greater than 1, it could be a positive number less than or equal to 1. Discard.
B. 0 < e < 2. The same here: we don't know whether the number is less than 2, it could be more than or equal to 2. Discard.
C. -1 < e < 1. The same as A. Discard.
E. 1/100 <e. We don't know whether the number is greater than 1/100, it could be a positive number less than or equal to 1/100. Discard.
Answer: D.
Answer: D
Question: An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 7 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?
--
Options:
A)12
B)19
C)60
D)180
E)630
Rationale: 7C3 * 4C2 * 3C2 = 35*6*3 = 630.
Answer: E.
Answer: E
Question: If the average marks of three batches of 72, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is
Options:
A)54.48
B)54.68
C)54.6
D)54.23
E)None of these
Rationale: Explanation:
(72Ã—50)+(60Ã—55)+(45Ã—60) / 72+60+45
9600 / 177=54.23
Option D
Answer: D
Question: There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
Options:
A)12
B)16
C)19
D)13
E)17
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: D
Question: A candidate got 35% of the votes and lost to the rival by 2400 votes. How many votes were cast?
Options:
A)7700
B)8000
C)8300
D)8600
E)8900
Rationale: 35%-----------L
65%-----------W
------------------
30% = 2400
10% = 800
100% of the votes = 8000
Answer: B
Answer: B
Question: If 4 tic equals 3 tacs and 6 tacs equal 4 tocs, what is the ratio of one tic to one toc?
Options:
A)15/2
B)6/5
C)5/6
D)3/10
E)2/1
Rationale: 4Tic=3*Tac and 6*Tac=4*Toc;
24*Tic=18*Tac and 18*Tac=12*Toc --> 24*Tic=12*Toc --> Tic/Toc=24/12=2/1.
Answer: E.
Answer: E
Question: A hall is 15 meters long and 10 meters wide. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, what is the volume of the hall (in cubic meters)?
Options:
A)600
B)700
C)800
D)900
E)1000
Rationale: 2HL + 2HW = 2LW
H = LW / (L+W)
Volume = LWH = (LW)^2 / (L+W) = 900
The answer is D.
Answer: D
Question: A heap of coconuts is divided into groups of 2, 5 and 7 and each time one coconut is left over. The least number of Coconuts in the heap is?
A. 31 B. 41 C. 51 D. 61
Options:
A)A)31
B)B)41
C)C)51
D)D)61
E)E)71
Rationale: LCM = 70
=> 70 + 1 = 71
ANSWER:E
Answer: E
Question: 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last?
Options:
A)13
B)15
C)16
D)18
E)21
Rationale: Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days
So fodder will be available for (60 + 8 + 12) = 80 cows c 24x60 .0 .
for-^—=18 days.
D
Answer: D
Question: Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many W miles will Tom drive before Karen wins the bet?
Options:
A)15
B)18
C)21
D)24
E)27
Rationale: Let K and T be the speeds of Karen and Tom respectively.
t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles.
Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours
Thus the distance traveled by Tom when Karen is 4 miles ahead of him W: T*(t+4/60) = 45 (7/15+4/60) = 24 miles. D is the correct answer.
Answer: D
Question: What is the 50th digit to the right of the decimal point in the decimal form of 48/88?
Options:
A)6
B)7
C)9
D)11
E)4
Rationale: We have to use some long division. This long division allows us to get 48/88 in decimal form, which is 0.545454… where “54” is repeating.
We can see that the 1st, 3rd, 5th digit to the right of the decimal point is a 5 and that the 2nd, 4th, 6th digit to the right of the decimal point is a 4. In other words, each odd-positioned digit is a 5, and each even-positioned digit is a 4.
Then about the 50 digit to the right of the decimal point and we see that 50 is even, we know that the 50th digit is a 4.
Answer E.
Answer: E
Question: In how many ways can a supermarket manager display 5 brands of cereals in 3 spaces on a shelf?
Options:
A)120
B)30
C)60
D)40
E)20
Rationale: This is asking for the number of permutations, since we don't want repetitions. The number of ways is:
5P3 = 60
Ans- C
Answer: C
Question: A relay has a series of 5 circuits in a line. The even-numbered circuits are control circuits; the odd are buffer circuits. If both a control circuit and the buffer circuit immediately following it both fail in that order, then the relay fails. The probability of circuit one failing is 3/8; circuit two, 3/8; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?
Options:
A)9/80
B)3/10
C)303/800
D)35/80
E)497/800
Rationale: The relay fails when "2 and 3 fail" or "4 and 5 fail".
P(2 and 3 fail) = (3/8)*(3/10) = 9/80
P(4 and 5 fail) = (3/4)*(2/5) = 3/10
Both these cases include the cases in which all 4 circuits fail. So we need to subtract that probability once out of the sum.
P(2, 3, 4 and 5 fail) = (9/80)*(3/10) = 27/800
P(Relay fails) = 9/80 + 3/10 - 27/800 = 303/800
Answer (C)
Answer: C
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options:
A)150 m
B)175 m
C)120 m
D)145 m
E)165 m
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec
Length of the train= (Speed x Time) = (50/3 * 9) m = 150 m.
Answer: A
Answer: A
Question: Rose is two years older than Bruce who is twice as old as Chris. If the total of the age of Rose, Bruce and Chris be 42 years, then how old is Bruce ?
Options:
A)7 years
B)16 years
C)12 years
D)13 years
E)14 years
Rationale: Let Chris's age be x years. Then, Bruce's age = 2x years.Rose's age = (2x + 2) years.
(2x + 2) + 2x + x = 42
5x = 40
x = 8
Hence, Bruce's age = 2*8 = 16 years.
Answer : B
Answer: B
Question: The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly eight elements each?
Options:
A)27
B)18
C)16
D)8
E)9
Rationale: nC2 = 36
=> n*(n-1)/2 = 36 , by middle term factor
=> n = 9
nC3 = 9C8 = 9
So, Answer is E.
Answer: E
Question: A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 4 minutes?
Options:
A)150 m
B)200 m
C)170 m
D)133 m
E)250 m
Rationale: Relative speed of the thief and policeman = 11 - 10 = 1 km/hr.
Distance covered in 6 minutes = 1/60 * 4 = 1/15 km = 67 m.
Distance between the thief and policeman = 200 - 67 = 133 m
D
Answer: D
Question: Find the compound interest on $800 for 1year at 10% p.a. if CI is component yearly?
Options:
A)$40
B)$400
C)$840
D)$800
E)$80
Rationale: A = P(1 + R/100)^T
= 800(1 + 10/100)^1
= 800*21/20
=$840
CI = A-P = 840-800 = $40
Answer is A
Answer: A
Question: Given the two equations 3x + 2y = 16 and 5x + 3y = 26, by how much does r exceed s?
Options:
A)3
B)4
C)5
D)1
E)2
Rationale: Solve by Simultaneous Equations.
My Answer is E.
x=4
y=2
Answer: E
Question: A can do a piece of work in 20 days, B can do a piece of work in 12 days,both are working together for 3 days after A left the job,then how many days B requires to complete the remaining work?
Options:
A)6 Days
B)5 Days
C)3 Days
D)7 Days
E)12 Days
Rationale: First take LCM of (20,12) = 60; Total work = 60; A's one day work = 60/20 =3; B's one day work =60/12 = 5; One day work of both A+B= 3+5 = 8; Total work completed in 3 days = 8*3=24; remaining work is = 60 - 24=36; remaining work completed by B in = 36/12= 3 days.Answer =C
Answer: C
Question: Klaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. Given these choices, how many candle + flower groupings can she select?
Options:
A)54
B)72
C)96
D)144
E)432
Rationale: Klaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement.2 candles from 4 candles: 4C2: 6
8 flowers from 9 flowers: 9C8 : 9
So total grouping
9*6= 54.
Answer is A.
Answer: A
Question: A group of medical interns at Bohemus Medical School want to go on dates. There are 7 girls and 7 guys. Assuming girls go on dates with guys, how many possible ways can these 14 medical interns date each other?
Options:
A)A)4640
B)B)4740
C)C)4840
D)D)4940
E)E)5040
Rationale: 1st girl can go with 7 guys
2nd girl can go with remaining 6
3rd girl can go with remaining 5 and so on
so the total ways are 7!= 5040
E should be the answer
Answer: E
Question: Betty worked for three straight hours on her homework questions. If she solved 120 questions in the third hour, which was five times as many as she solved in the second hour, and six times as many questions as she solved in the first hour, how many questions did she solve in total?
Options:
A)156
B)160
C)164
D)168
E)172
Rationale: In the first hour, Betty solved 120/6 = 20 questions.
In the second hour, Betty solved 120/5 = 24 questions.
In the third hour, Betty solved 120 questions.
The total is 20 + 24 + 120 = 164.
The answer is C.
Answer: C
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
Options:
A)153600 m^2
B)153660 m^2
C)153700 m^2
D)153800 m^2
E)153900 m^2
Rationale: Perimeter = Distance covered in 8 min. = 12000	x 8	m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m^2.
A
Answer: A
Question: Rs.280 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
Options:
A)210
B)266
C)120
D)299
E)267
Rationale: 4x 5x 6x
100 50 25
400x + 250x + 150x = 28000
x = 35
6x = 210
Answer: A
Answer: A
Question: A man can row at 6 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
Options:
A)2.4 km
B)2.6 km
C)2.9 km
D)4.4 km
E)5.6 km
Rationale: Explanation:
Speed in still water = 6 kmph
Speed of the current = 1 kmph
Speed downstream = (6+1) = 7 kmph
Speed upstream = (6-1) = 5 kmph
Let the required distance be x km
Total time taken = 1 hour
â‡’ x/7+x/5=1
â‡’5x+7x=35
â‡’12x=35
â‡’x=2.9 km
Answer: Option C
Answer: C
Question: 2x<5y<0 which of the following is the greatest?
Options:
A)6x+3y
B)-(2x+2y)
C)-x+4y
D)2x+6y
E)x-2y
Rationale: Plugging in -1 for both x and y we get
A. 6x+3y =-9
B. -(2x+2y) =4
C. -x+4y =-3
D. 2x+6y =-8
E. x-2y =1
Answer: B
Answer: B
Question: 85% of a number is added to 24, the result is the same number. Find the number?
Options:
A)150
B)140
C)130
D)160
E)170
Rationale: (85/100) * X + 24 = X
3X = 480
X = 160
ANSWER:D
Answer: D
Question: Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel four times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?
Options:
A)4
B)6
C)5
D)9
E)12
Rationale: W: the time for Wyane to do the job
S: the time for his son to do the job
We have 1/W + 1/S = 1/4 and W = 4S
Then we have 1/(4*S) + 1/S = 1/4 <=> 5/(4*S) = 1/4 <=> S = 5
ANS: C
Answer: C
Question: The banker’s discount of a certain sum of money is Rs. 72 and the true discount on the same sum for the same time is Rs. 60. The sum due is
Options:
A)210
B)280
C)360
D)450
E)None
Rationale: Sol.
Sum = B.D. * T.D. / B.D. - T.D. = Rs.[72 * 60 / 72 - 60] = Rs. [72 * 60 / 12] = Rs. 360.
Answer C
Answer: C
Question: In how many ways can an animal trainer arrange 5 lions and 4 tigers in a row so that no two lions are together?
Options:
A)2880
B)3000
C)3100
D)3200
E)3400
Rationale: They have to be arranged in the following way:
| L | T | L | T | L | T | L | T | L |
The 5 lions should be arranged in the 5 places marked 'L'.
This can be done in 5! ways.
The 4 tigers should be in the 4 places marked 'T'.
This can be done in 4! ways.
Therefore, the lions and the tigers can be arranged in 5!×4!=5!×4!= 2880 ways
Option is A
Answer: A
Question: On increasing the number of lines in a page by 60, they become 240. What is the % of increase in the no. of lines in the page?
Options:
A)33.3%
B)305
C)50%
D)55%
E)60%
Rationale: Explanation : Number of pages increased = 60
Now , the number of pages of book = 240
Number of pages of the books before increase = 240 – 60 = 180
% increase in the number of pages in the book = 60 /180
x 100% = 33.3%
A
Answer: A
Question: x and y are positive integers. If 1/x + 1/y < 2, which of the following must be true?
Options:
A)x + y > 4
B)xy>1
C)x/y + y/x < 1
D)(x - y)^2 > 0
E)None of the above
Rationale: since x and y are both +ive int, x*y>1... only exception being x=y=1 as it is not given they are different integers...
however it is given 1/x +1/y<2.. this cannot be true if x=y=1.... so one or both have to be > 1
ANSWER:B
Answer: B
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 26000, then the share of B is?
Options:
A)s.12028
B)s.12000
C)s.12003
D)s.12029
E)s.24029
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 26000
Share of B = 6/13 (26000) = Rs.12000
Answer: B
Answer: B
Question: Two trains of length 100 m and 200 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
Options:
A)18 sec
B)15 sec
C)21 sec
D)20 sec
E)19 sec
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5
= 20 mps.
Distance covered in passing each other
= 100 + 200 = 300 m.
The time required = d/s
= 300/20
= 15 sec.
Answer: B
Answer: B
Question: Mr. Smith calculated the average of 10 three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 39.6 The difference between the unit digit and hundreds digit of that number is :
Options:
A)2
B)4
C)5
D)6
E)7
Rationale: Since the average increased by 39.6 and there were a total of 10 numbers, it means the incorrect number was 39.6 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 396
99c - 99a = 99(c - a) = 396
99*4 = 99(c - a)
So c - a = 4
Answer (B)
Answer: B
Question: A train passes a platform in 32 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
Options:
A)180 meter
B)240 meter
C)200 meter
D)260 meter
E)None of these
Rationale: Explanation:
Speed of the train = 54 km/hr = (54×10)/32 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 32
=> 300+L = 15×32 =480
=> L = 480-300 = 180 meter
Answer: Option A
Answer: A
Question: A wooden cube whose edge length is 5 inches is composed of smaller cubes with edge lengths of one inch. The outside surface of the large cube is painted red and then it is split up into its smaller cubes. If one cube is randomly selected from the small cubes, what is the probability that the cube will have at least one red face?
Options:
A)70.6%
B)74.5%
C)78.4%
D)82.1%
E)86.9%
Rationale: There are a total of 5*5*5 = 125 cubes.
All the exterior cubes will have at least one face painted red.
The interior is formed by 3*3*3 = 27 cubes.
The number of cubes with at least one side painted red is 125 - 27 = 98 cubes
The probability that a cube has at least one side painted red is 98/125 which is 78.4%
The answer is C.
Answer: C