divelab/Sys2Bench huggingface dataset:
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Options:
A)7 sec
B)6 sec
C)4 sec
D)2 sec
E)1 sec
Rationale: Speed of train relative to man = (60 + 6) km/hr
= 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [110 * 3/55] sec
= 6 sec
Answer: B
Answer: B
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.
A
Answer: A
Question: Last year a certain bond price with a face value of 5000 yielded 5% of its face value in interest. If that interest was approx 6.5 of the bond's selling price approx what was the bond's selling price?
Options:
A)4063
B)3846
C)5351
D)6000
E)6154
Rationale: Interest = 0.05*5000 = 0.065*selling price --> selling price = 0.05*5000/0.065 --> selling price = ~3,846
Answer: B.
Answer: B
Question: In what time will two trains cross each other completely, which are running on the same parallel lines in opposite directions, each train running with a speed of 90 kmph being 160 m and 140 m in length respectively?
Options:
A)5.6 sec
B)6.2 sec
C)6.0 sec
D)7.2 sec
E)6.8 sec
Rationale: D = 160m + 140m = 300m * 1/1000 = 0.3 kms
RS = 90 + 90 = 180 kmph
T = (0.3/180) * 3600 = 6.0 sec
ANSWER:C
Answer: C
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%?
Options:
A)Rs.429
B)Rs.480
C)Rs.429
D)Rs.427
E)Rs.482
Rationale: 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
Answer: B
Question: The jogging track in a sports complex is 1000 meters in circumference. Deepak and his wife start from the same point and walk in opposite directions at 20 km/hr and 12 km/hr respectively. They will meet for the first time in?
Options:
A)32min
B)40min
C)35min
D)25min
E)20min
Rationale: Clearly, the two will meet when they are 1000 m apart
To be 20+12 = 32 km apart, they take 1 hour
To be 1000 m apart, they take 32 * 1000/1000 = 32 min.
Answer is A
Answer: A
Question: What is 5/8 as a percent
Options:
A)62.5 %
B)63 %
C)63.5 %
D)64.5 %
E)65%
Rationale: 5/8 as a percent =(5 / 8 ) x100
= 0.625 x 100
=62.5%
answer : A i.e. 62.5 %
Answer: A
Question: Which one of the following can't be the square of natural number ?
Options:
A)30976
B)75625
C)28561
D)143642
E)235685
Rationale: Answer: Option D
The square of a natural number nerver ends in 2.
143642 is not the square of natural number.
Answer: D
Question: If 4x + y = 8 and y − 3x = 7, then what is the value of x + 2y?
Options:
A)1/7
B)3
C)15
D)52/7
E)60/7
Rationale: 4x + y = 8
−3x + y = 7
Adding both the equations --> x + 2y = 15
Answer: C
Answer: C
Question: At a certain university, 68% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?
Options:
A)25
B)37.5
C)55
D)62.5
E)75
Rationale: total women = 68%
total men = 40%
total tenured = 70% (both men and women)
therefore, women tenured + women professors + men tenured = 90%
men tenured = 22%
but question wants to know the percent of men that are tenured
22%/40% = 55%
C
Answer: C
Question: The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 25%. By approximately what percent would the output now have to be decreased in order to restore the original output?
Options:
A)20%
B)24%
C)30%
D)27%
E)79%
Rationale: The original output increases by 10% and then 25%.
Total % change = a + b + ab/100
Total % change = 10 + 25 + 10*25/100 = 37.5%
Now, you want to change it to 0, so,
0 = 37.5 + x + 37.5x/100
x = -37.5(100)/137.5 = 27% approximately
Answer is D
Answer: D
Question: 7^9 - 7^2 is approximation of which of the following?
Options:
A)7^9
B)9^8
C)9^9
D)9^11
E)9^10
Rationale: => Since 9^2 is a small number compared to 7^9, it can be disregarded. Thus, 7^9-7^2=7^9 is derived and the answer is A.
Answer: A
Question: Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 42 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast?
Options:
A)10%
B)12%
C)14%
D)17%
E)20%
Rationale: Let me try a simpler one.
Lets assume that candidate got 42% votes and total votes is 100.
Candidate won = 42
Remaining = 58
To get 50%, candidate requires 8 votes from 100 which is 8% and 8 votes from 58.
8/58 = .137 = 13.7%
Which is approx 14%. Hence the answer is C.
Answer: C
Question: If a real number x is chosen at random in the interval [0,4] and a real number y is chosen at random in the interval [0,6], what is the probability that x < y?
Options:
A)2/5
B)3/5
C)2/3
D)3/10
E)7/10
Rationale: Since x is in [0,4] and y is in [0,6] we can draw a rectangle in the coordinate plane with vertices (0, 0), (4, 0), (0, 6), and (4, 6).
The points above the line y=x satisfy x < y.
The part of the rectangle below y=x has an area of 8.
The whole rectangle has an area of 24.
P(x < y) = (24-8)/24 = 16/24 = 2/3
The answer is C.
Answer: C
Question: Mike, Jim and Bob are all professional fisherman. Mike can catch 30 fish in one hour, Jim can catch twice as much and Bob can catch 50% more than Jim. If the three started to fish together and after 40 minutes Mike and Bob left, how many fish did the three fishermen catch in one hour?
Options:
A)110
B)120
C)140
D)130
E)112
Rationale: All of them catch fishes in relation to number 30....
2/3*30+2*30+2*1.5*30*2/3=140
Answer is C
Answer: C
Question: A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 135 km downstream
Options:
A)5 hours
B)4 hours
C)3 hours
D)2 hours
E)None of these
Rationale: Explanation :
Speed of the boat in still water = 22 km/hr
speed of the stream = 5 km/hr
Speed downstream = (22+5) = 27 km/hr
Distance travelled downstream = 135 km
Time taken = distance/speed = 135/27 = 5 hours. Answer : Option A
Answer: A
Question: A tradesman by means of his false balance defrauds to the extent of 26%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Options:
A)58.76%
B)49.89%
C)84.67%
D)24.65%
E)45%
Rationale: g% = 26 + 26 + (26*26)/100
= 58.76%
Answer: A
Answer: A
Question: At a conference table, 5 employees gather around a table. One of the employees is the manager and he sits at the head of the table. Two of the employees sit on either side of the table. How many different seating arrangements can be made with these five employees?
Options:
A)5
B)10
C)24
D)32
E)120
Rationale: Head's sit is fixed. Now 4 people is left with 4 seats.
4 people can sit on 4 seats in 4! ways or 24 ways.
Ans is C
Answer: C
Question: How many positive four-digit integers do not contain any digits other than 1 or 0 and are such that the sum of the first two digits equals the sum of the last two digits?
Options:
A)3
B)4
C)8
D)10
E)12
Rationale: The sum of the first two (last two) digits cannot be 0 because 0000 is not a four-digit integer. If the sum of the first two digits is 1, two variants are possible: 1001 and 1010 (we have to remember that 0 cannot be the first digit). If the sum of the first two digits is 2, one variant is possible: 1111. In all, there are three numbers that satisfy the given conditions: 1001, 1010, and 1111.
Answer: A
Answer: A
Question: Find the area of region enclosed by | x | + | y | = 3
Options:
A)18
B)11
C)28
D)26
E)91
Rationale: We have to consider separately the form of the function w.r.t to where x, y lies.
x >0, y >0, x + y = 3
x > 0, y < 0, x - y = 3
x < 0, y >0, x - y = - 3
x < 0, y < 0, x + y = - 3
After having drawn the above 4 lines on the graph, the graph looks like aboe
Now the area of the graph = 4 right angle triangles.
Area of the right angle triangle = 12×3×3=9212×3×3=92
Area of the entire region = 92×492×4 = 18 units
Answer:A
Answer: A
Question: The mean of four integers W will not change if all the integers are multiplied by any constant. What is always true about this set of numbers?
I. The mean of the set is 0
II. The sum of the largest member and the smallest member of the set is 0
III. The set contains both positive and negative integers
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I, II, and III
Rationale: If we consider a set {1,2,3,4}, when multiplied with a constant we take that constant as 1 and multiply resulting set will contain the same numbers as the original. so how can the answer be I only.....A
Answer: A
Question: Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?
Options:
A)1/3
B)1/9
C)1/4
D)1/2
E)1/6
Rationale: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8.Answer: A
Answer: A
Question: All the faces of cubes are painted with red colour.It is then cut into 64 equal small cubes.Find How many small cubes have no faces coloured ?
Options:
A)24
B)8
C)16
D)0
E)4
Rationale: There are 64 small cubes,Hence one side side of the big cube is 3√64=4 cm
Number of small cubes having only one faces coloured = (x - 2)^3
Here, x = side of big cube / side of small cube
x = 4 /1
x = 4
Required number = (4 -2)^3
= 8
Answer :B
Answer: B
Question: In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs.157300 was their profit, how much amount did B receive?
Options:
A)48400
B)48000
C)48100
D)48500
E)48600
Rationale: Assume that investment of C =x
Then, investment of A =2x
Investment of B =4x/3
A:B:C =2x:(4x)/3:x
=2:4/3:1=6:4:3
B's share =157300×4/(6+4+3)
=157300×4/13=12100×4=48400
Answer is A.
Answer: A
Question: The profits of QRS company rose 10% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June?
Options:
A)15%
B)32%
C)40%
D)62%
E)80%
Rationale: We need multipliers.
multiplier for a 10% increases = 1 + 0.10 = 1.1
multiplier for a 20% decreases = 1 – 0.20 = 0.8
multiplier for a 50% increases = 1 + 0.50 = 1.5
Now, multiply these. First, multiply (0.8) and (1.5), using the doubling & halving trick. Half of 0.80 is 0.40, and twice 1.5 is 3
(0.8)*(1.5) = (0.4)*(3) = 1.2
Now, multiply this by 1.1
1.2*1.1 = 1.32
Thus, the three percent changes combined produce a 32% increase. Answer = (B).
Answer: B
Question: For what values of 'k' will the pair of equations 3x + 4y = 12 and kx + 12y = 30 NOT have a unique solution?
Options:
A)12
B)9
C)3
D)7.5
E)2.5
Rationale: Explanatory Answer
Condition for Unique Solution to Linear Equations
A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point.
i.e., if the two lines are neither parallel nor coincident.
Essentially, the slopes of the two lines should be different.
What does that translate into?
ax + by + c = 0 and dx + ey + g = 0 will intersect at one point if their slopes are different.
Express both the equations in the standardized y = mx + c format, where 'm' is the slope of the line and 'c' is the y-intercept.
ax + by + c = 0 can be written as y = −abx−ca−abx−ca
And dx + ey + g = 0 can be written as y = −dex−ge−dex−ge
Slope of the first line is −ab−ab and that of the second line is −de−de
For a unique solution, the slopes of the lines should be different.
∴ −ab≠−de−ab≠−de
Or ad≠bead≠be
Condition for the equations to NOT have a unique solution
The slopes should be equal
Or ad=bead=be
Apply the condition in the given equations to find k
In the question given above, a = 3, b = 4, d = k and e = 12.
Therefore, 3k=4123k=412
Or 'k' should be equal to 9 for the pair of equations to NOT have a unique solution.
When k = 9, the system of equations will represent a pair of parallel lines (their y-intercepts are different). So, there will be NO solution.
Answer B
Answer: B
Question: If two positive numbers are in the ratio 1/6 : 1/5, then by what percent is the second number more than the first?
Options:
A)70%
B)90%
C)60%
D)50%
E)20%
Rationale: Given ratio = 1/6 : 1/5 = 5 : 6
Let first number be 5x and the second number be 9x.
The second number is more than first number by 1x.
Required percentage = x/5x * 100 = 20%.
Answer:E
Answer: E
Question: Two trains of length 100 m and 200 m are 90 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
Options:
A)21/9 sec
B)32/3 sec
C)18/7 sec
D)32/3 sec
E)53/2 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 90/35 = 18/7 sec.
Answer:C
Answer: C
Question: If the annual increase in the population of a town is 10% and the present number of people is 14000, what will the population be in 2 years?
Options:
A)12100
B)15240
C)12456
D)16940
E)10002
Rationale: The required population is = 14000 (1 + 10/100)^2
= 14000 * 11/10 * 11/10
= 16940
Answer is D
Answer: D
Question: A reduction of 30% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
Options:
A)s.42
B)s.46
C)s.48
D)s.41
E)s.34
Rationale: 800*(25/100) = 240 ---- 5
? ---- 1 => Rs.48
Answer: C
Answer: C
Question: If a /2= b/3 = c/5, then the value of (a + b + c)/c is :
Options:
A)1/√5
B)√2
C)2
D)5
E)6
Rationale: a/2= b/3 = c/5 = k (say).
Then, a = 2k, b = 3k, c = 5k.
(a + b + c)/c = (2k + 3k + 5k)/5k
= 10k/5k
= 2.
ANSWER:C
Answer: C
Question: In how many of ways can 4 balls be placed in 5 tins if any number of balls can be placed in any tin?
Options:
A) 5C4
B) 5P4
C) 54
D) 4^5
E) 5^4
Rationale: Now, each of the 4 different balls has 5 choices (5 tins to go to), so total # of distribution is 5*5*5*5=5^4.
Answer: E.
Answer: E
Question: In how many ways Chief Minister and Minister be elected from a team of 12 members?
Options:
A)124
B)131
C)132
D)145
E)165
Rationale: To do this, if captain is elected first, then we have 12 ways of doing this.
For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 12*11 = 132 ways.
C
Answer: C
Question: When positive integer N is divided by positive integer J, the remainder is 26. If N/J = 150.40, what is value of J?
Options:
A)75
B)65
C)60
D)130
E)30
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 150.40
Here 150 the quotient.
Given that Remainder = 26
So, 150.40 = 150 + 26/J
So, J = 65
Answer: B
Answer: B
Question: The ratio between the radii of two spheres is 1:3. Find the ratio between their volumes?
Options:
A)1:28
B)1:27
C)1:22
D)1:21
E)1:29
Rationale: r1 : r2 = 1:3
r13 : r23 = 1:27
Answer: B
Answer: B
Question: The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 21 minutes is:
Options:
A)9.75
B)5.75
C)8.75
D)6.75
E)5.15
Rationale: Explanation:
Speed downstream = (20+5) kmph = 25 kmph
Distance travelled = (25*(21/60)) km = 8.75 km.
ANSWER:C
Answer: C
Question: The simple form of the ratio 4/3:2/5 is?
Options:
A)10:6
B)10:3
C)15:3
D)25:3
E)30:3
Rationale: 4/3 : 2/5 = 20:6 = 10:3
ANSWER:B
Answer: B
Question: During a sale, the price of a pair of shoes is marked down 15% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?
Options:
A)9%
B)10%
C)11%
D)18%
E)90%
Rationale: Assume the price = 100
Price during sale = 85
Price after sale = 100
Percent increase = 15/85*100 = 18% approx.
Correct Option: D
Answer: D
Question: The train 160 m long is running with a speed of 80 km/hr. In what time will it pass a man running in same direction with the speed of 8 km/hr.
Options:
A)16 seconds
B)8 seconds
C)15 seconds
D)6 seconds
E)28 seconds
Rationale: Man and train are running in same direction,
Relative Speed = 80 - 8 = 72 kmph. = (72 * 5)/18 = 20 m/sec
Length of the train = 160 m.
Time taken to pass the man = 160/20 = 8 seconds.
Answer: Option B
Answer: B
Question: In a college, 70 percent of students study math, 75 percent of students study English, 85 percent study French and 80 percent study German.
Can you find out the percentage of students who study all 4 subjects ?
Options:
A)12%
B)10%
C)16%
D)18%
E)19%
Rationale: B
10% of student study all four subjects.
Answer: B
Question: If the perimeter of a rectangular garden is 950 m, its length when its breadth is 100 m is?
Options:
A)338 m
B)778 m
C)375 m
D)276 m
E)971 m
Rationale: 2(l + 100)
= 950 => l
= 375 m
Answer:C
Answer: C
Question: A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 5 minutes. How much time will be take to cover a distance of 5 kilometres?
Options:
A)48 min.
B)50 min.
C)45 min.
D)55 min
E)None of these
Rationale: explanation
Rest time = Number of rest × Time for each rest
= 4 × 5 = 20 minutes
Total time to cover 5km
= (5⁄10 × 60)minutes + 20 minutes = 50 minutes
Answer B
Answer: B
Question: A caterer ordered 200 ice-cream bars and 200 sundaes. If the total price was $200.00 and the price of each ice-cream bar was $0.40, what was the price of each sundae?
Options:
A)$0.60
B)$0.80
C)$1.00
D)$1.20
E)$1.60
Rationale: Let price of a sundae = S
Price of ice cream bar = .4 $
200 * .4 + 200*S = 200
=> 200*S = 200
=> S =0.6
Answer A
Answer: A
Question: A card is drawn from a pack of 52 cards.The probability of getting a queen club or a king of heart?
Options:
A)3/26
B)1/26
C)4/26
D)6/26
E)10/26
Rationale: n(s)=52
Let e=event of getting a queen of club or a king of heart.
n(e)=2
P(e)=n(e)/n(s)
=2/52
=1/26
Option:B
Answer: B
Question: Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety of tea in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, what is the price of the third variety per kg ?
Options:
A)Rs.182.50
B)Rs.170.5
C)Rs.175.50
D)Rs.180
E)Rs.190
Rationale: Explanation:
Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed in the ratio 1 : 1
So their average price
=(126 + 135)/2=130.5
Hence let's consider that the mixture is formed by mixing two varieties of tea, one at Rs. 130.50 per kg and the other at Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. Now let's find out x
By rule of alligation,
(xâˆ’153):22.5=1:1
â‡’xâˆ’153=22.50
â‡’x=153+22.5=175.5
Answer IS C
Answer: C
Question: M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 3. Q is a subset of M consisting of 5 terms. Exactly 80% of the numbers in Q are located within 2 standard deviations from the average of M. Which of the following could Q be?
Options:
A){3, 4, 5, 10, 14}
B){4, 6, 7, 10, 12}
C){3, 5, 5, 10, 17}
D){1, 5, 7, 10, 18}
E){5, 6, 7, 10, 12}
Rationale: Exactly 80% of the numbers in Q, so 4 out of 5 numbers are from 10 - 2*{SD} = 4 to 10 + 2*{SD} = 16.
A. {3, 4,5, 10, 14} --> 4 numbers are in this range. Ok
B. {4,6, 7, 10, 12} --> all 5 numbers are in this range. Discard.
C. {3,5, 5, 10, 17} --> only 3 numbers are in this range. Discard.
D. {1,5, 7, 10, 18} --> only 3 numbers are in this range. Discard.
E. {5, 6, 7, 10, 12} --> all 5 numbers are in this range. Discard.
Answer: A.
Answer: A
Question: At a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint.Verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 35 liters of forest green to change it to Verdant green?
Options:
A)1/3
B)2/3
C)4/3
D)35/3
E)10/3
Rationale: 35 liter of Forset green have 20 liter of blue and 15 liter of yellow
Suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is
Blue/yellow =20/(15+x) = ¾
45+3x=80 => x =35/3
Answer : D
Answer: D
Question: Which of these numbers is not divisible by 3?
Options:
A)339
B)342
C)552
D)1111
E)672
Rationale: One may answer this question using a calculator and test for divisibility by 3. However we can also test for divisibilty by adding the digits and if the result is divisible by3 then the number is divisible by 3.
3 + 3 + 9 = 15 , divisible by 3.
3 + 4 + 2 = 9 , divisible by 3.
5 + 5 + 2 = 12 , divisible by 3.
1 + 1 + 1 + 1 = 4 , not divisible by 3.
The number 1111 is not divisible by 3 the answer is D.
Answer: D
Question: If (t-8) is a factor of t^2-kt-40, then k=
Options:
A)16
B)1
C)2
D)6
E)14
Rationale: t^2-kt-48 = (t-8)(t+m) where m is any positive integer.
if 48/8 = 6, then we know as a matter of fact that:
m = +6
and thus k = 8-6 = 1
t^2-kt-m = (t-a)(t+m) where a>m
t^2+kt-m = (t-a)(t+m) where a<m
t^2-kt+m = (t-a)(t-m)
t^2+kt+m = (t+a)(t+m)
B
Answer: B
Question: A man buys a cycle for Rs. 1750 and sells it at a loss of 8%. What is the selling price of the cycle?
Options:
A)s. 1090
B)s. 1610
C)s. 1190
D)s. 1202
E)s. 1092
Rationale: S.P. = 92% of Rs. 1750 = Rs.	92	x 1750/100 = Rs. 1610
Answer: Option B
Answer: B
Question: A train passes a station platform in 42 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)123
B)166
C)240
D)157
E)330
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, (x + 300) / 42 = 15
x + 300 = 630
x = 330 m.
Answer: E
Answer: E
Question: The value of Underrot 72pi/9 + Underrot 4 is most nearly equal to which of the following integers? (Please refer to the picture below for the exact version of the question)
Options:
A)27
B)14
C)18
D)19
E)21
Rationale: Under root (72pi/9) ~ 25
Under root (4) = 2
Hence, 9+1 = 10 is the approx answer. A is the correct answer.
Answer: A
Question: A boy swims downstream 91 km and upstream 21 km taking 7 hours each time, what is the speed of the boy in still water?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: 91 --- 7 DS = 13
? ---- 1
21 ---- 7 US = 3
? ---- 1 M = ?
M = (13 + 3)/2 = 8
Answer:C
Answer: C
Question: Pipes A and B can fill a tank in 5 hours 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.
Options:
A)3 9/5
B)3 9/17
C)3 7/5
D)3 7/17
E)None of these
Rationale: Explanation:
Net part filled in 1 hour =(1/5 + 1/6 - 1/12)
=17/60hrs
=3 9/17
Answer is B
Answer: B
Question: If 1/(6 + 3/x) = 1, then x =
Options:
A)-3/5
B)1
C)1/3
D)-1/3
E)-3
Rationale: The expression 1/(6 + 3/x) = 1/x) should have been equal to something .
If 1/(6 + 3/x) = 1
=> x/(6x + 3) = 1
=> x = 6x + 3
=>-5x = 3
=>x = -3/5
Correct Option: A
Answer: A
Question: How many 7-letter words can be formed using the letters of the English alphabet that contain 2 different vowels and 5 different consonants?
Options:
A)4!*5c2 *21c2
B)4!*5c3 *21c2
C)5!*5c2 *21c2
D)7!*5c2 *21c5
E)6!*5c2 *21c2
Rationale: combination for 2 vowels out of 5 = 5c2 ways
combination for 5 consonants of 21 = 21c5 ways
Additionally the arrangement can be = 7!
total arrangements =7!*5c2 *21c5
D
Answer: D