divelab/Sys2Bench huggingface dataset:
Question: A pipe fills a pool in 3.5 hours. If the flow of water is changed so that the pipe's rate is halved, then how long will it take for the pipe to fill 2/3 of the pool?
Options:
A)4 hours and 40 minutes
B)3 hours and 10 minutes
C)2 hours and 20 minutes
D)7 hours
E)2/21 hours
Rationale: A pipe takes 3.5 hrs to fill the tank. So when rate is reduced to half it will take 7 hrs to fill the tank.
so time time taken to fill 2/3rd tank capacity is given by
7*2/3=4 hrs 40min
ANSWER:A
Answer: A
Question: A train 200 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options:
A)987
B)271
C)72
D)27
E)36
Rationale: Length = Speed * time
Speed = L/T
S = 200/20
S = 10 M/Sec
Speed= 10*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 36 Kmph
Answer:E
Answer: E
Question: A certain sum of money amounts to Rs 1008 in 2 years and to Rs 1164 in 3 years. Find the sum and the rate of interest.
Options:
A)14%
B)13%
C)12%
D)19%
E)None of these
Rationale: Explanation:
S.I. for 1 ½ years = Rs (1164 - 1008) = Rs 156 .
S.I. for 2 years = Rs (156 x x 2)= Rs 208.
Principal = Rs (1008 - 208) = Rs 800.
Now, P = 800, T= 2 and S.I. = 208.
Rate = (100 x S.I.) / (P x T) = [ (100 x 208)/(800 x 2)]% = 13%
Answer: B
Answer: B
Question: If abc = b^3 , which of the following must be true?
I. ac = b^2
II. b = 0
III. ac = 1/2
Options:
A)II&III
B)III
C)II
D)I
E)none
Rationale: E
Answer: E
Question: A Train requires 10 seconds to pass a pole while it requires 30 seconds to cross a stationary train which is 600 mtrs long. Find the speed of the train.
Options:
A)110 kmph
B)120 kmph
C)108 kmph
D)100 kmph
E)98 kmph
Rationale: In 10s the train crosses the pole and in 30 sec the train crosses one more stationary train
In 20 sec the train travels a distance of 600 mtrs
Speed = 600/20 = 30 m/s = 30 (3600/1000) = 30 * 18/5 = 108 kmph
Answer: C
Answer: C
Question: The radius of a wheel is 14.6 cm. What is the distance covered by the wheel in making 100 resolutions?
Options:
A)754 m
B)704 m
C)90.524 m
D)706 m
E)91.688 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 100 resolutions.
= 100* 2 * 22/7 * 14.6 = 9168.8 cm
= 91.688 m
Answer:E
Answer: E
Question: By investing in 1623% stock at 64, one earns Rs. 1600. The investment made is
Options:
A)s. 9600
B)s. 7500
C)s. 5640
D)s. 6144
E)s. 6760
Rationale: Explanation :
Market Value = Rs.64
Face Value is not given and hence take it as Rs.100
16 2/3% of the face value = 50/3
ie, to earn 50/3, investment = Rs.64
Hence, to earn Rs.1600, investment needed = 64×3×1600/50=6144
Answer : Option D
Answer: D
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
Options:
A)520
B)620
C)820
D)740
E)720
Rationale: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]
Required speed = (1200 x	3/5) km/hr = 720 km/hr
Answer E) 720 Km/hr
Answer: E
Question: Praveen starts business with Rs.3500 and after 5 months, Hari joins with Praveen as his partner. After a year, the profit is divided in the ratio 2 : 3. What is Hari’s contribution in the capital?
Options:
A)Rs.7500
B)Rs.8000
C)Rs.8500
D)Rs.9000
E)Rs.6000
Rationale: Let Hari’s capital be Rs. x. Then, 3500 * 12/7x = 2/3
=> 14x = 126000
=> x = 9000.
ANSWER:D
Answer: D
Question: Which of the following values is the greatest
Options:
A)a) 11% of 89
B)b) 22% of 78
C)c) 33% of 67
D)d) 55% of 56
E)e) 55% of 45
Rationale: Are you sure that you checked the answer key correctly? I just signed up forVeritas(haven't started yet, not until March) but I have access to the materials and the answer key I'm looking at says D
Answer: D
Question: The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8400. If his salary for the month of May is Rs.6500, find his salary for the month of January?
Options:
A)2177
B)2876
C)4900
D)2981
E)2711
Rationale: Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May = 4 * 8400 = 33600 ----(2)
(2)-(1) i.e. May - Jan = 1600
Salary of May is Rs.6500
Salary of January = Rs.4900.Answer: C
Answer: C
Question: A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 4 inches wide on each side, the total area would have been (M + 108) square inches. What is the perimeter of the photograph, in inches?
Options:
A)34
B)36
C)16
D)40
E)42
Rationale: Let Length and Breadth of photograph be L and B respectively.
Perimeter is given by 2*(L+b) -----(1)
According to the question:
(L+2)(B+2) = m ----(2)
and
(L+8)(B+8) = m + 108 ---------> (L+8)(B+8) - 108 = m ------(3)
Equating (2) and (3)
(L+2)(B+2) = (L+8)(B+8) - 108
LB + 2L + 2B + 4 = LB + 8L + 8B +64 -108
Simplify
6L + 6B = 48 ------> 2(L+B) = 16 (Check eq (1))
Answer is C
Answer: C
Question: A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.40 per kg. What will be his gain percent?
Options:
A)8 1/7 %
B)2 1/3 %
C)6 2/3 %
D)8 1/8 %
E)8 1/9 %
Rationale: C.P. of 1 kg = 420/70 = Rs. 6
S.P. of 1 kg = Rs. 6.40
Gain % = 0.40/6 * 100 = 20/3
= 6 2/3 %
Answer:C
Answer: C
Question: At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?
Options:
A)60%
B)80%
C)100%
D)120%
E)140%
Rationale: Explanation:
A B C D
90 100 80 100
A D
90 ----- 100
360 ------ ? = 400
500 ------ 400
100 ------- ? => 80%
B)
Answer: B
Question: Which is better investment: 11% stock at 143 or 9 3/4% stock at 117?
Options:
A)11% stock at 143
B)9 3/4% stock at 117
C)Both are equally good
D)Cannot be compared, as the total amount of investment is not given
E)None
Rationale: Let investment in each case be Rs. (143 x 117).
Income in 1st case = Rs.11 x 143 x 117/143	= Rs. 1287.
Income in 2nd case = Rs.39 x 143 x 117/(4*117)	= Rs. 1394.25
Clearly, 9 3/4% stock at 117 is better.
ANSWER:B
Answer: B
Question: Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?
Options:
A)3 4/9 days
B)8 4/9 days
C)9 3/8 days
D)6 3/8 days
E)none of these
Rationale: 1/15 + 1/25 = 8/75
75/8 = 9 3/8 days
ANSWER:C
Answer: C
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18000. A's share is?
Options:
A)6029
B)6299
C)6000
D)6018
E)60012
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 18000 = 6000
Answer:C
Answer: C
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 7 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
Options:
A)s.4538
B)s.6342
C)s.4518
D)s.4530
E)s.4517
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 7 = Rs.6342
Answer: B
Answer: B
Question: What is the probability that you will get a sum of 8 when you throw three dice simultaneously?
Options:
A)21/6^3.
B)23/6^3.
C)25/6^3.
D)27/6^3.
E)29/6^3.
Rationale: This sum of 8 can occur in the following cases:
1-1-6 --> 3!/2!=3 ways;
1-2-5 --> 3!=6 ways;
1-3-4 --> 3!=6 ways;
2-2-4 --> 3!/2!=3 ways;
2-3-3 --> 3!/2!=3 ways.
Total of 3+6+6+3+3=21 ways.
Now, since the total number of outcomes is 6^3, then the probability is 21/6^3.
ANSWER:A
Answer: A
Question: In a certain code language, “ORANGE” is written as “NTETOO”. How would “BLACK” be written in that language ?
Options:
A)ANEIS
B)UGDII
C)GIKHK
D)HOUH
E)AHKSS
Rationale: Explanation:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
letter position
ANSWER: A
Answer: A
Question: If 50% of x equals the sum of y and 20, then what is the value of x–2y?
Options:
A)20
B)40
C)60
D)80
E)90
Rationale: Explanation :
Given, 50% of x equals the sum of y and 20.
=>(50/100)×x=y+20.
=>x/2=y+20.
=>x=2y+40.
=>x–2y= 40.
Answer : B
Answer: B
Question: The speed at which a man can row a boat in still water is 6.5 kmph. If he rows downstream, where the speed of current is 2.5 kmph, what time will he take to cover 90 metres?
Options:
A)90 seconds
B)36seconds
C)26 seconds
D)18 seconds
E)6.5 seconds
Rationale: Speed of the boat downstream = 6.5 + 2.5
= 9 kmph
= 9 * 5/18 = 2.5 m/s
Hence time taken to cover 90m =90/2.5
= 36 seconds.
Answer:B
Answer: B
Question: If -4 < x < 7 and -5 < y < 3, which of the following specifies all the possible values of xy?
Options:
A)-42 < xy < 21
B)-42 < xy < 24
C)-28 < xy < 18
D)-24 < xy < 21
E)-35 < xy < 20
Rationale: The least value of xy is a bit more than 7*(-5)=-35 and the largest value of xy is a bit less than (-4)*(-5)=20.
Therefore -35 < xy < 20.
Answer: E.
Answer: E
Question: Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. The area of the space encosed by the four pieces is
Options:
A)12
B)28
C)42
D)72
E)11
Rationale: required area = 14*14 - (4 * 1/4 * 22/7 * 7 *7) sq cm
= 196 - 154
= 42 sq cm.
Answer: C
Answer: C
Question: When 28 is divided by the positive integer s, the remainder is 1. What is the sum of all the possible values of s for which this is true?
Options:
A)2
B)3
C)9
D)30
E)39
Rationale: The only possible values of the form 28=sp+1 are 3,9 or 27
The sum = 3+9+27 =39. E is the correct answer. We dont need to look for values >28 as all these values will leave a remainder of 28 and not 1.
Answer: E
Question: A man takes 3 hours 45 minutes to row a boat 10 km downstream of a river and 2 hours 30 minutes to cover a distance of 3 km upstream. Find the speed of the current.
Options:
A)1 km/hr
B)1/2 km/hr
C)3/4 km/hr
D)4 km/hr
E)None of these
Rationale: Explanation:
First of all, we know that
speed of current = 1/2(speed downstream - speed upstream) [important]
So we need to calculate speed downstream and speed upstream first.
Speed = Distance / Time [important]
Speed upstream =(10/3 3/4)km/hr
=8/3km/hr
Speed Downstream = (3/2 1/2)km/hr
=6/5km/hr
So speed of current = 1/2(8/3−6/5)
=3/4km/hr
Option C
Answer: C
Question: if At what time between 7 & 2 will the hands of a watch point in opposite directions?
Options:
A)50 4/11 min past 4
B)50 4/11 min past 1
C)50 4/81 min past 7
D)50 4/81 min past 2
E)50 4/11 min past 6
Rationale: At 4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30min. spaces apart.
Minute hand will have to gain 5 min. spaces.
55min spaces are gained in 60 min.
5 min. spaces are gained in (60/55 * 50) min. or 54 6/11 min.
Required time = 54 6/11 min. past 4.
Answer: Option 'A'
Answer: A
Question: A and B can do a piece of work in 7 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
Options:
A)33
B)878
C)30
D)88
E)11
Rationale: C = 1/5 – 1/6 = 1/30 => 30 days
Answer: C
Answer: C
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
Options:
A)12 m
B)25 m
C)127.5 m
D)32m
E)56m
Rationale: Explanation:
When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 = 127.5 m.
ANSWER C
Answer: C
Question: An urn contains 5 black and 3 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black?
Options:
A)1/5
B)3/7
C)5/14
D)3/5
E)2/7
Rationale: Let E and F denote respectively the events that first and second ball drawn
are black. We have to find P(E n F) or P (EF).
Now P(E) = P (black ball in first draw) = 5/8
Also given that the first ball drawn is black, i.e., event E has occurred, now there are 4 black balls and Eight white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.
That is P(F|E) = 4/7
By multiplication rule of probability, we have
P (E n F) = P(E) P(F|E)
= 5/8 × 4/7 = 5/14
C
Answer: C
Question: Set S consists of integers {4, 7, 10, 14, 15}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 50%. What is the value of integer n?
Options:
A)28
B)32
C)36
D)40
E)44
Rationale: The average of the numbers in set S is 10.
If we increase the mean by 50%, the new mean is 15.
Thus, on average, 5 numbers increase by 5.
Therefore n = 15+25 = 40
The answer is D.
Answer: D
Question: What is least possible value of |23 - 7y| is
Options:
A)0
B)1
C)2
D)5
E)9
Rationale: Since y can be ANY number, we can minimize the value of |23 - 7y| by setting 23 - y equal to zero
If 23 - 7y = 0, then 23 = 7y, which means y = 23/7
In other words, when y = 23/7, we find that |23 - 7y| = 0
Answer:A
Answer: A
Question: find the terms which do not contain 7 between 1000 and 9999
Options:
A)9000
B)8000
C)8500
D)8800
E)8900
Rationale: Total number of four digit numbers =9000 (i.e 1000 to 9999 )
We try to find the number of numbers not having digit 2 in them.
Now consider the units place it can be selected in 9 ways (i.e 0,1,2,3,4,5,6,8,9)
Tens place it can be selected in 9 ways (i.e 0,1,2,3,4,5,6,8,9)
Hundreds place it can be selected in 9 ways (i.e 0,1,2,3,4,5,6,8,9)
Thousands place can be selected in 8 ways (i.e 1,2,3,4,5,6,,8,9) here '0' cannot be taken
Total number of numbers not having digit 7 in it =9 x 9 x 9 x 8 =5832
Also,Total number of numbers having digit 7 in it = 9000-5832 =3168
ANSWER:A
Answer: A
Question: If the sum of six numbers is between 135 and 164, then the average (arithmetic mean) of the six numbers could be which of the following?
Options:
A)15.4.
B)20.5.
C)25.5.
D)31.25.
E)32.5.
Rationale: 135/6=22.5
164/6=27.33
Only C fits in between these two limits.
Answer: C
Answer: C
Question: When is |y-8| = 8-y?
Options:
A)y=0
B)y<0
C)y>8
D)y<8
E)y<=8
Rationale: When is |x-8| = 8-x?
Choice A: X=8, it is true but X cannot be always 8
Choice B: X=0, it is also true, but X cannot be always 0
Choice C: X>8, it is false, for e.g. X=6, then one side of equation is 2 and the other side is -2
Choice D: X<=8, this choice encapsulate Choice A, Choice B and for all other conditions and is true for above said equation. Hence the answer choice is E.
Answer: E
Question: Sum of the squares of three numbers is 522 and the sum of their products taken two at a time is 131. Find the sum?
Options:
A)20
B)22
C)25
D)27
E)28
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 522 + 2* 131
a + b + c = √784 = 28
E
Answer: E
Question: What number fits best in the missing place?
_	4	5	3	5
9	5	7	10	3
Options:
A)3
B)8
C)4
D)5
E)6
Rationale: C
4
5 = Five (four letters) => 4
7 = Seven (five letters) => 5
10 = Ten (three letters) => 3
3 = Three (five letters) => 5
Therefore, 9 = Nine (four letters) => 4.
Therefore the missing number is 4.
Answer: C
Question: A man rows his boat 84 km downstream and 48 km upstream, taking 2 hours each time. Find the speed of the stream?
Options:
A)6 kmph
B)5 kmph
C)9 kmph
D)8 kmph
E)1 kmph
Rationale: Speed downstream = d/t = 84/(2) = 42 kmph
Speed upstream = d/t = 48/(2) = 24 kmph
The speed of the stream = (42 - 24)/2 = 9 kmph
Answer:C
Answer: C
Question: How many of the positive factors of 25 , 150 and how many common factors are there in numbers?
Options:
A)2
B)4
C)3
D)5
E)1
Rationale: factors of 25 - 1, 5, 25
factors of 150 - 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Comparing both, we have three common factors of 25 and 150- 1,5,25
Answer(C)
Answer: C
Question: When n is divided by 12, the remainder is 2. What is the remainder when 4n is divided by 5?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Let n=2 (leaves a remainder of 2 when divided by 15)
4n = 4(2) =8, which leaves a remainder of 3 when divided by 5.
Answer C
Answer: C
Question: A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is?
Options:
A)4pm
B)3pm
C)5pm
D)6pm
E)7pm
Rationale: Time from 7 am to 4.15 pm = 9 hrs 15 min = hrs
3 min. 5 sec. of this clock = 3 min. of the correct clock.
Now 3min.5sec. is hrs of this clock = 3 min.is hrs of the correct clock
hrs of clock = hrs of the correct clock.
= 9 hrs of the correct clock.
The correct time is 9 hrs after 7 am. i.e., 4 pm.
Answer: A
Answer: A
Question: The measure of the side of a square is quadrupled. If x represents the perimeter of the original square, what is the value of the new perimeter?
Options:
A)3x
B)4x
C)9x
D)12x
E)27x
Rationale: Original perimeter = x
Hence original side = x/4
New side = 4x/4
New perimeter = 4*4x/4 = 4x
Correct Option: B
Answer: B
Question: A train travels from Albany to Syracuse, a distance of 100 miles, at the average rate of 50 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 5 hours and 24 minutes. What was the average rate of speed of the train on the return trip to Albany?
Options:
A)31.25
B)30
C)32
D)34
E)36
Rationale: 50*T =100 THEREFORE T = 100/50 =2
ON RETURN SPEED * ( 5.4 -2) =100 THEREFORE T = 100/3.2 =31.25
A
Answer: A
Question: What is the present worth of Rs. 396 due in 2 years at 5% simple interest per annum?
Options:
A)128
B)277
C)120
D)360
E)371
Rationale: Let the present worth be Rs. x. Then,
S.I. = (396 - x)
(x * 5 * 2) / 100 = (396 - x)
10x = 39600 - 100x
110x = 39600 => x = 360.
Answer: D
Answer: D
Question: If x is less than y by 45% then y exceed x by:
Options:
A)33.33%
B)25%
C)81.81%
D)66.66%
E)None of these
Rationale: Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 25%)
=> 45/(100-45)*100
=81.81%
ANSWER:C
Answer: C
Question: Meg and Bob are among the 4 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?
Options:
A)12
B)30
C)60
D)90
E)120
Rationale: Total # of ways the race can be finished is 4!. In half of the cases Meg finishes ahead of Bob and in other half Bob finishes ahead of Meg. So, ways Meg to finish ahead of Bob is 4!/2=12.
Answer: A.
Answer: A
Question: If GAVE is coded as 4657 and BAT is coded as 229. How is GATE coded?
Options:
A)4697
B)4967
C)4976
D)7496
E)4796
Rationale: g-4 a-6 e-7 from the code gate
t - 9 from bat
ANSWER:A
Answer: A
Question: Last year the price per share of Stock N increased by x percent and the earnings per share of Stock N increased by y percent, where x is greater than y. By what percent did the ratio of price per share to earnings per share increase, in terms of x and y?
Options:
A)x/y%
B)(100+y) %
C)100*(x-y)%
D)100*(x-y)/(100+y) %
E)(x-y)/(100+y) %
Rationale: Let P = the old price per share; E = the old earning per share. Thus P/E is the price to earning ratio before the increases
After the increase the new price is: P*(1+x/100) and the new earning is: E*(1 +y/100)
The new P/E is: (1+x/100)P/(1+y/100)E
The Percent of P/E increase = (new P/E - P/E)/(P/E). Subsititute new P/E to the equation we have:
[(1+x/100)/(1+y/100)*P/E - P/E]/(P/E)*100%. Simplifly the expression and you should get the answer to be:
100*(x-y)/(100+y) %
Answer : D
Answer: D
Question: What is the sum of all three digit integers formed using the digits 1, 2, and 3 (repetition is allowed)
Options:
A)4443
B)5980
C)5992
D)5990
E)5994
Rationale: n = 3*3*3 = 27
<x> = (333 + 111) / 2 = 222
Sum = number of integers x average value
n * <x> = 27 * 222 = 5994
answer = E
Answer: E
Question: A trader mixes 26 kg of rice at Rs. 10 per kg with 30 kg of rice of other variety at Rs. 20 per kg and sells the mixture at Rs. 20 per kg. His profit percent is:
Options:
A)No profit, no loss
B)30.23%
C)8%
D)10%
E)None of these
Rationale: C.P. of 56 kg rice = Rs. (26 x10 + 30 x20) = Rs. (260 + 600) = Rs. 860
S.P. of 56 kg rice = Rs. (56 x 20) = Rs. 1120
Gain =260/860x100% = 30.23%
Answer: Option B
Answer: B
Question: Aram’s car was fined when he gave Joe and Peter a ride, so they decided to help Aram pay the fine. Joe paid $3 more than 1/4 of the fine and Peter paid $3 less than 1/3 of the fine, leaving pay $4 less than 1/2 the fine to complete the payment. What fraction of the fine did Aram pay?
Options:
A)$13
B)$15
C)$20
D)$28
E)$48
Rationale: As given Aram' payment is [1][/2]*Fine -4
i.e Total Fine = 2 * (Sam's payment + 4)
Now, as everything looks integer, Fine should be able to divide by 4 and 3 . Because Joe's contribution has 1/4 of the fine and Peter's contribution has 1/3 of the fine
So, that leads me to following :
Options , Aram's pay , Total Fine (F) , F/4 , F/3
A) , 13 , 34 , No i.e 34/4 , No i.e 34/3
B) , 14 , 38 , No , No
C) , 20 , 48 , Yes Yes
,
No need to further go on as we have got F/4 and F/3 correct, just for confirmation we go further
D) , 28 , 64 , Yes , No
E) , 48 , 104 , Yes , No
Correct answer is C
Answer: C
Question: The number of sailors on a ship is 82% more than the number of officers. The ratio of sailors to officers would be
Options:
A)33:25
B)47:20
C)47:25
D)22:25
E)91:50
Rationale: Sailor = 1.82 * Officer
Sailor/Officer = 1.82/1 = 182/100 = 91/50
Answer will be E
Answer: E
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 40 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
Options:
A)10 sec
B)16 sec
C)13 sec
D)67 sec
E)8 sec
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 40
D = 40 * 100/18 = 2000/9
RS = 60 + 40 = 100 * 5/18
T = 2000/9 * 18/500 = 8 sec
Answer: E
Answer: E
Question: When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 6, the quotient is 3y and the remainder is 5. What is the value of 7y – x ?
Options:
A)2
B)1
C)0
D)-1
E)-2
Rationale: (1) x = 11y + 4
(2) 2x = 18y + 5
Let's subtract equation (1) from equation (2).
7y + 1 = x
7y - x = -1
The answer is D.
Answer: D
Question: A cycle is bought for Rs.900 and sold for Rs.1125, find the gain percent?
Options:
A)27%
B)20%
C)80%
D)30%
E)25%
Rationale: 900 ---- 225
100 ---- ? => 25%
Answer: E
Answer: E
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 6 years at 10% per annum is Rs.80 of money?
Options:
A)1000
B)1200
C)4800
D)3600
E)8400
Rationale: P = 80(100/10)6 => P = 1500
Answer: C
Answer: C
Question: A person crosses a 600 m long street in 5 minutes, What is his speed in km per hour?
Options:
A)4.3
B)7.2
C)2.3
D)3.2
E)1.1
Rationale: Explanation:
Speed = {\color{Blue} \left ( \frac{600}{5\times 60} \right )m/ sec =2m/ sec=\left ( 2\times \frac{18}{5} \right )km/hr=7.2km/hr}
Answer: B
Answer: B
Question: A train passes a station platform in 36 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)150 m
B)350 m
C)300 m
D)240 m
E)none
Rationale: Speed =(54 x5/18m/sec) = 15 m/sec.
Length of the train = (15 x 20)m =300 m.
Let the length of the platform be x metres.
Then,x + 300/36= 15
x + 300 = 540
x = 240 m
Answer: D
Answer: D
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 6 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Options:
A)26 km/hr
B)17 km/hr
C)90 km/hr
D)77 km/hr
E)46 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/6 = 3x => x = 25/2.
So, speed of the faster train = 50/2 = 50/2 * 18/5
= 90 km/hr.
Answer:C
Answer: C