Question 1
There are three brothers x,y and z. If z's age is as much more than y's as y's age is more than x's age, find by how much percentage y is older than x. Hints: Age of z is 20 and y is 5 years older than x.
a. 100% b. 50% c. 25% d. 75%
Answer : b. 50%
Solution.:
Let a,b and c be the ages of x,y and z respectively.
It is given that z's age is as much more than y's as y's age is more than x's age.
Writing the above statement in the form of an equation, we get
c - b = b - a ...(1)
It is given that age of z i.e c = 20
Substituting c = 20 in eq 1 we get,
20 - b = b - a
20 = 2b - a ...(2)
It is also given that y is 5 years older than x. This implies b - a = 5 or b = a + 5...(3)
Substitute b = a + 5 in eq 2 we get,
20 = 2a + 10 - a
20 = a + 10 or a = 10
Substitute a = 10 in eq 3 we get
b = 15
Percentage by which b is more than a is (b - a)/a x 100% = (15 - 10)/10 x 100 = 50%
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Question 2
John is 100% older than Johan. 20 years hence, John will be 50% older than Johan. Can you find their ages.
a. 30,20 b. 40,20 c. 60,40 d. 50,10
Answer : b. 40,20
Solution :
Let age of John be b.
Let age of Johan be a.
Currently John is 100% older than Johan. This implies b - a/a = 100%
Or (b - a)/a = 1 ( this is because, 100% = 100/100 = 1)
Or b - a = a
Or b = 2a ...(1)
20 years later ages of John and Johan will be b + 20 and a + 20 respectively
After 20 years John will be older by 50%
i.e (b + 20)-(a+20)/(a+20) = 50% = 1/2
(b - a)/ (a + 20) = 1/2
Or 2b - 2a = a + 20
Or 2b = 3a + 20 ...(2)
Substitute 1 in 2 we get
4a = 3a + 20 or a = 20.
Substitute a = 20 in eq 1 we get
b = 40
John's age is 40 and Johan's 20.
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Question 3
Let a,b and c be ages of three brothers. b's age is greater than the sum of ages of a and c. After 7 years, by how much percentage b will be more than the sum of ages of a and c ?
a. (b - a - c - 7) / (a + c + 14) x 100% b. (b - a - c + 7) / (a + c + 14) x 100% c. (b - a - c) / (a + c + 7) x 100% d. (b - a - c - 7) / (a + c + 7) x 100%
Answer : a. (b - a - c - 7) / (a + c + 14) x 100%
Solution :
Percentage by which b's age will be greater than sum of a's and c's ages after 7 years
= Age of b after 7 years - (sum of ages of a and c after 7 years)
------------------------------------------------------------------------------------ x 100%
sum of ages of a and c after 7 years
= b + 7 - (a + 7 + c + 7)
--------------------------------- x 100%
a + 7 + c + 7
= (b - a - c - 7) / (a + c + 14) x 100%
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Question 4
Suresh Raina and Gautam Gambhir after a scintillating IPL match decide to travel by cycle to their respective villages. Both of them start their journey travelling in opposite directions. Each of their speeds is 6 miles per hour. When they are at a distance of 50 miles, a housefly starts flying from Suresh Raina's cycle towards Gautam Gambhir at a relative speed of 17 miles per hour with respect to Raina's speed. What will be the time taken by housefly to reach Gambhir?
(a)15 hours (b)10 hours (c) 50 hours (d)25 hours
Answer : b)10 hours
Solution:
Since Raina and Gambhir are travelling in opposite directions, Gambhir's Relative speed with respect to Raina's = Speed of Raina + Speed of Gambhir = 6 + 6 = 12 miles per hour.
Now housefly starts from Raina's cycle and travels towards Gambhir's cycle at 17 miles per hour.
Relative speed of housefly with respect to Gambhir = Speed of housefly with respect to Raina - Speed of Gambhir with respect to Raina = 17 - 12 = 5 miles per hour
Time taken for housefly to reach Gambhir = Distance to catch up / Relative speed of housefly with respect to Gambhir = 50/5 = 10 hours.
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Question 5
Pinky and Ponky decided to have a car race. Initially Pinky was 20 miles behind Ponky’s car. Both of them took the race in the same direction along the same route. Pinky was travelling at a constant speed of 68 miles per hour, while Ponky was travelling at a constant speed of 60 miles per hour. How many hours will it take for Pinky to overtake and drive 8 miles ahead of Ponky?
(a)1.7 hours (b)2.0 hours (c)2.5 hours (d)3.0 hours (e) 3.5 hours
Answer : e) 3.5 hours
Solution:
It is to be understood from the problem, that Pinky has to travel 20 miles first to catch up Ponky. Then, he has to travel an additional 8 miles to be ahead of Ponky. Pinky has to travel a total of 28 extra miles relative to Ponky’s car.
Relative Speed of Pinky with respect to Ponky = 68 - 60 = 8 miles per hour.
Time taken for Pinky to cover 28 extra miles compared to that of Ponky = Extra Distance / Relative Speed of Pinky with respect to Ponky = 28/8 = 3.5 hours.
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Question 6
Eveson was working for a multinational company. The pressure of work in the company was too heavy due to seasonal sales. Eveson decided to go weekend trip with his wife for relaxation. Husband and wife decided that the proposed trip should not exceed 8 hours driving in a day. They decided to maintain the average Speed of forward journey to 40 mph. Due to traffic on Sundays the return journey average speed can only be at 30 mph. How far the couple can select a picnic spot?
(a)142 Miles (b)200 Miles (c)137 Miles (d)220 Miles
Answer : c)137 Miles
Solution:
If x and y are the speeds corresponding to forward and return journeys, then average speed of the entire journey can be found using the formula : 2xy / x+y
In our case the rate for onward journey is given as 40 mph and rate for return journey is given as 30 mph
Hence average speed = 2x40x30 / 40+30 = 2400 / 70 = 240 / 7 mph
Total Travel Time is 8 hours. So total distance the couple can plan = Average Speed x Affordable Total Time = 240 / 7 x 8 =1920 / 7 = 274 miles (approximately)
Since 274 miles should be the total distance that can be covered including forward and return journeys, the picnic spot has to be at 274 / 2 = 137 miles approximately.
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Question 7
Rambabu is driving a Honda Unicorn Power bike at 80 km per hour. However being sugar patient, Rambabu could not travel continuously. He takes small breaks each of 2 minutes for every 15 minute of his drive. How much distance Rambabu will cover in 90 minutes?
a)118Km b)89Km c)112Km d) 104km
Answer : d) 104km
Solution:
For every 15 minutes he takes a rest for 2 minute.
Hence for 90 minutes of drive he would require 12 minutes of rest. In effect he will be traveling for 90 - 12 = 78 minutes.
For 60 minutes he covers 80 Km.
For 1 minute he would cover 80/60 Km.
For 78 minutes he would cover (80/60)78 = 104 Km
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Question 8
Priya was presented with new brand watch, as marriage anniversary gift by her husband. She observed, that the two hands of the new watch coincide every 64 minutes. She was trying to calculate, how many minutes the watch will lose per day. Can you guide Priya?
(a)32 8/11 (b)36 5/11 (c) 90 minutes (d) 96 minutes
Answer : a)32 8/11
Solution:
55 min spaces are gained by minute hand (with respect to hour hand) in 60 min. (In 60 minutes, hour hand will move 5 spaces while the minute hand will move 60 spaces. In effect the space gain of minute hand with respect to hour hand will be 60 - 5 = 55 minutes.)
In 60 min it will gain ,
60/55 x60 =65 5/11 min.
But minute hand of Priya's watch gains only 64 minutes (it is slow than normal)
Actual loss=65 5/11 -64 =1 5/11 = 16/11min
In 64 min. the loss is 16/11 min
In 24 hours the loss is = (16/11 x1/64 x24 x60)min =32 8/11 minutes.
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Question 9
It was 4’o clock in the evening. Shilu was staring at the new watch that was presented by her Dad two day's ago. She was trying to measure the exact time between 4 and 5’o clock during which the hands of the watch point in opposite directions forming a straight line. What would be that time?
(a) 45 minutes past 4 (b)40 minutes past 4 (c) 50 4/11 minutes past 4
(d)54 6/11 minutes past 4.
Answer : d)54 6/11 minutes past 4.
Solution:
At 4’o clock the hands are 20 minutes apart.To form a straight line in opposite direction the hands must be in 30 minutes apart. To accomplish this the minute hand have to close up the 20 minutes separation and after crossing the hour hand it has to gain 30 minute separation. In total minute hand will have to gain 20 + 30 = 50 minutes spaces apart.
55 min spaces are gained in 60 min. (In 60 minutes, hour hand will move 5 spaces while the minute hand will move 60 spaces. In effect the space gain of minute hand with respect to hour hand will be 60 - 5 = 55 minutes.)
50 min spaces can be gained in 60/55 x50 = 54 6/11 minutes.
Hence the answer is 54 6/11 minutes past 4
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Question 10
The famous church in the city of Kumbakonnam has a big clock tower and is said to be over 300 years old. Every Monday 10.00 A M the clock is set by Antony, doing service in the church. The Clock loses 6 mins every hour. What will be the actual time when the faulty clock shows 3 P.M on Friday?
(a) 4 A.M (b) 3.16 P.M. (c) 4.54 A.M. (d) 3 A.M
Answer : c) 4.54 A.M
Solution:
Total hours from Monday 10.00 AM to Friday 3.00 PM =101 HOURS
The clock loses 6 minutes every hour. In 101 hours it will lose 101 x 6 =606 minutes. ie 10 hours 06 minutes.
To find the actual time, calculate 10 hours 6 min backwards from Friday 3.00 PM which is 4 .54 AM
Hence the actual time would be 4 .54 AM when clock shows 3.00 PM on Friday.
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Question 11
Brilliant software company, Chennai has been doing an excellent business in the last four years. The company went on a recruitment spree from among the engineering colleges in and around Chennai. They recruited people from ECE, CSE, IT streams. All programmers are of equal respect. They receive equal salaries and perform equal load of work. Suppose 15 such programmers take 15 minutes to write 15 lines of code in total. How long will it take for 84 programmers to write 84 lines of code in total?
a) 84 minutes b)15 minutes c) 27 minutes d) 30 minutes
Answer : b) 15 minutes
Solution :
For such problems where efficiency of the workers are alike, we can use the below equation :
P1 x M1 / L1 = P2 x M2 / L2 ...(1)
In the above formula, P1 and P2 represent number of programmers in I and II scenarios respectively ; M1 and M2 minutes required for completion of work in I and II scenarios respectively and L1 and L2 represent number of lines of code in I and II scenarios respectively.
Given values : P1 = 15, L1 = 15, M1 = 15, P2 = 84, L2 = 84. We have to find M2
Applying given values in equation 1 we get,
15 X 15 / 15 = 84 X M2 / 84
Simplifying we get, M2 = 15 minutes which is our answer.
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Question 12
One of the leading software companies recruited boys and girls from different engineering colleges.They were given training in software program writing for three weeks in the company’s fully equiped modern training centre.All of the employees developed similar skills , abilities and were paid equal salary. How many programmers would be required to write 48 lines of code in twice the time that would be consumed 12 programmers to write 12 lines of code ?
a) 12 b)24 c)15 d)10
Answer : b) 24 programmers
Solution :
Given Values : L1 = 48, P2 = 12 and L2 = 12
Also from question it is clear that time taken in scenario 1 will be twice that in scenario 2.
Therefore, M1 = 2M2
Substituting the values in our familiar equation (ref solution for question 1)
P1 X 2M2 / 48 = 12 X M2 / 12
P1/24 = 1
Or P1 = 24 programmers.
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Question 13
M/s. Compaware software systems had a revenue of US $ 747 million during the last year. It was in 34th position among the leading software companies. The company wanted to improve its business position and ranking and hence recruited 600 programmers afresh and gave them intensive training in software code line writing. After the training was completed all the programmers attain similar level of expertise in writing of software code lines and hence they were paid similar salary. Supposing 108 programmers can write 108 lines of software code in 108 minutes, 72 programmers will write how many lines of software code in 72 minutes?
a) 108 b) 60 c) 72 d) 48
Answer : d) 48
Solution :
Given Values : P1 = 108, M1 = 108, L1 = 108, P2 = 72, M2 = 72
Applying these values in our familiar equation (ref solution of question 1) we get :
108 X 108 / 108 = 72 x 72 / L2
L2 = 72 x 72 / 108 = 48 lines
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Question 14
Somayaji Rao, retired Sub-Inspector of Police, Nandyal, Kurnool District, Andhra Pradesh has three grand children.The age of the eldest grand child is four times the age of youngest grand child. It is also seen that the second grand child’s age is half of the eldest grand child.The sum of the ages of all three grand children is 48.What is the age of eldest grand child?
a) 48 b) 24 c) 12 d) 30
Answer : b) 24
Solution :
Let the age of youngest grand child be X. Middle grand child age be Y and eldest grand child be Z years.
Given Z = 4X ...(1)
Also Z = 2Y ...(2)
From 1 and 2 we get, 4X = 2Y
Or Y = 2X
In terms of X the age of three grand children = X, 2 X , 4 X
It is given that the sum of the ages of all the three grand children = 48
X + 2X + 4 X = 48
X = 6
So youngest grand child's age = 6
Eldest grand child age = 4 X = 4 x 6 = 24 years
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Question 15
Four years ago, the age of Kamalhasan was three times the age of his daughter.The total of the ages of Kamalhasan and his daughter after four years will be 64 years.What is the present age of Kamalhasan?
a)40 years b)36 years c)60 years d) none of these.
Answer : a) 40 years
Solution :
Let the age of Kamalhasan before four years be K and that of his daughter be D
Four years ago K = 3 D ...(1)
If four years ago Kamalhasan's age was K, today his age will be K +4, after 4 years his age will be K + 4 + 4
If four years ago daughter's age was D, today her age will be D + 4, after 4 years her age will be D + 4 + 4
Four years afterwards the sum of the ages of the two will be 64 years.
So (K + 4 + 4 ) + (D + 4+ 4) = 64
But from eq 1, we know that K = 3D. Therefore above equation becomes
(3D + 4 + 4 ) + (D + 4+ 4) = 64
4 D + 16 = 64
4D = 64 -16 = 48
D = 12
So Kamalhasan’s present age = K + 4 = 3D + 4 = (3 x 12) + 4 = 40 years
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Question 16
Brahmananda Sastri is grand father of three sons of his son. Nelson one of his grand son is three times older than another grand son Thompson. His third grand son James is not in station.He is studying in a school Ootacamund. Nelson’s age after three years will be six times the age of Thompson one year ago.What is the present age of Nelson?
a)6 b)12 c)9 d)15
Answer : c) 9
Solution :
The name of grand father and details about the third grand son are all time consumers.Candidates should be alert to read and consider only what is required to answer the question.
Let the present age of Nelson be N and the present age of Thompson be T
Then N = 3 T ...(1)
Nelson’s age after three years will be six times the age of Thompson one year ago. Formulating this in the form of equation we get,
N + 3 = 6 (T-1)
Substituting for N as 3 T (from 1) we get
3 T + 3 = 6 T – 6
3 + 6 = 6 T - 3 T = 3 T
9 = 3 T
3 = T
So Nelson’s age is 3 T = 3 x 3 = 9 years.
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Question 17
The ratio of the ages of Mohanapriya and Kulandaivelu is 3 : 4.Four years earlier the ratio was 5: 7.Find the present age of Kulandaivelu.
a) 32 b) 24 c) 36 d) 40
Answer : a) 32
Solution :
Let the ages of Mohanapriya and Kulandaivelu be 3 x and 4 x respectively
Four years earlier the ratio was 5: 7
(3x - 4) / (4x – 4) = 5/7
Cross multiplying
20x - 20 = 21 x - 28
-20 + 28 = 21x - 20 x
+8 = x
Kulandaivelu’s age = 4x = 4 x 8 = 32 years
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Question 18
Sneha is engaged. Her Fiance is one amongst Abdul, John, King and Vimal. Sneha either speaks truth or lies. One of four men always speaks truth while others may or may not speak the truth. Now based on the below statements, can you find the Fiance ?
1) Abdul says "Sneha always speaks truth".
2) King says "Sneha always lies".
3) Vimal says "Sneha always speaks truth but only to him".
4) John says "The only truth speaking person amongst Vimal and John is Sneha's Fiance"
a) Abdul b) King c) Vimal d) John.
Answer : d) John
Solution :
From the question, we know clearly that Sneha can speak either Truth or Lies.
But as per statement (1) Abul says "Sneha always speaks truth". Hence this statement cannot be true. Hence our inference is that Abdul always lies.
As per statement (2) King says "Sneha always lies". Again this statement is false as Sneha can speak either Truth or Lies. Hence we can infer that King always lies.
On statement (3) Vimal says "Sneha always speaks truth but only to him". But there is no evidence / proof for this claim on data in question. Hence we can safely consider that Vimal also lies always.
In question it is clearly given that one of four men always speaks truth while others may or may not speak the truth. Since we have concluded Abdul, King and Vimal always lie, John should be the only truth speaking man.
According to statement (4) John says that "The only truth speaking person amongst Vimal and John is Sneha's Fiance". Since John is found to speak truth always, this particular statement from John should be absolutely True.
Also we have found earlier that Vimal always lies. Hence the truth speaking person John has to be the Fiance.
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Question 19
Three men Ravi, Ram, Rahul and two women Rekha and Padma were seated next to each other (not in order given) in a meeting. The arrangement was that the person who speaks definitely the truth will occupy the first position and the person who speaks definite lie always will be the last. The middle three positions will be filled by people whose statements may be truth or may be false. Can you find the correct arrangement from the options based on the statements below :
1) Padma says the probability of her occupying the 4th place is lesser than the probability of her occupying 1st place.
2) Rahul says that "Padma lies always when calculating probability"
3) Rekha says "Ram is the tallest of the 5 people"
3) Ravi says "He will be leaving early provided Rahul is a truth speaking person"
4) Ram says "He does not know probability"
a) Rahul - Ravi - Rekha - Ram - Padma b) Ravi - Rahul - Rekha - Ram - Padma
c) Rekha - Rahul - Ravi - Padma - Ram d) Rahul - Ravi - Ram - Padma -Rekha
Answer : a) Rahul - Ravi - Rekha - Ram - Padma
Solution :
Though the question looks bit difficult it is actually a simple question provided you can quickly extract out only required data and ignore irrelevant details.
All the options have different combinations for 1st and last positions. This means, if you are smart enough to find the person who always speaks truth and the person who always speaks lies, it is more than enough to answer the question.
According to statement I, Padma says that the probability of her occupying the 4th place is lesser than the probability of her occupying 1st place. But this cannot be true. This is because probability of Padma to occupy any given position is 1/5 . (1/5 is the probability of Padma to occupy any given position be it 1st or 2nd or 3rd or 4th or 5th positions). Therefore we can safely conclude that Padma is definitely lying.
According to statement 2, Rahul says "Padma lies always when calculating probability". This is a definite truth based on our conclusion in previous paragraph. We can safely conclude that Rahul speaks definitely the truth.
From the above two paragraphs, we can say that 1st position will be occupied by Rahul (as he speaks definite truth) and the last position will be occupied by Padma (as she speaks definite lies). Only option that has this combination is option a) and hence the answer.
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Question 20
Mylapore Times a local free newspaper conducted a test for students studying in corporation schools falling within the jurisdiction of Chennai. The test was aimed at ascertaining the level of mathematics knowledge among the school students. The following question was given :
“How many numbers are there between 133 to 294 both included, which are divisible by 7?”
a) 23 b) 24 c) 26 d) none of these.
Answer : b) 24.
Solution :
In this problem both the boundary numbers 133 and 294 are divisible by 7. Also the boundary numbers are inclusive for calculation. In such scenarios solving is very simple.
Quotient 1 (when upper boundary number is divided by the divisor, in our case 7) : When 294 is divided by 7 we get 42. (1)
Quotient 2 (when lower boundary number is divided by the divisor, in our case 7) : When 133 is divided by 7 we get 19.(2)
Answer can be obtained using the formula, Quotient 1 - Quotient 2 + 1 = 42 - 19 + 1 = 24
42 - 19 = 23 + 1 = 24
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Question 21
Porur Times is a newspaper which is distributed free to residents in and near Porur. It carries advertisement on different aspects such as rental, real estate, tuition, business deals etc. Porur Times gave a puzzle and wanted answers to be emailed to them within a day. The question read as under:
“How many three digit numbers can be formed using the digits 1,2,3,4,5 (but with repetition) that are divisible by 4?”
a) 12 b) 20 c) 60 d) 10
Answer : b) 20
Solution :
To solve this problem, we are going to utilize the simple rule that for a number to be divisible by 4, its last two digits must be divisible by 4.
Using digits present in 1,2,3,4,5 the two digit combination's that are divisible by 4 include
12, 24, 32, 44
Now placing any of the digits from 1,2,3,4,5 before the 2 digit numbers that we arrived in previous step, we can actually find the total number of 3 digit numbers formed from 1,2,3,4,5 that are divisible by 4.
They are,
112, 124, 132, 144
212, 224, 232, 244
312, 324, 332, 344
412, 424, 432, 444
512, 524, 532, 544
Therefore there are 20 numbers which is our answer.
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Question 22
Kumaresh attended a placement examination online and the following question was posed to him:
“ The difference between the squares of two consecutive odd integers is always divisible by" which of the following:
a) 6 b) 8 c) 7 d) 3
Answer : b) 8
Solution:
Let the two consecutive odd integers be (2x + 1) and (2x + 3).
Then, (2x + 3)2 - (2x +1)2
4x2 + 12x + 9 - 4x2 - 4x -1 = 8x + 8 = 8(x +1).
Now for any value of x, 8(x +1). is divisible by 8. Therefore, answer is 8.
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Question 24
For the IPL 5 cricket matches Mr. Bala Josiar has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams X and Y, Bala Josiar picks X with the same probability as X's chances of winning. Let's assume such rumors to be true and that in a match between Rajasthan Royals and Chennai Super Kings, Chennai Super Kings the stronger team seems to have a probability of 3/4 of winning the game. What is the probability that Bala Josiar will correctly pick the winner of the Rajasthan Royals–Chennai Super Kings game?
a) 7/ 16 b) 9/16 c) 3/4 d) 10/16
Answer : d) 10/16
Solution :
Probability that CSK wins = 3/4
Probability that RR wins = 1 - Probability that CSK wins = 1 - 3/4 = 1/4
Probability of picking a winner = Probability of picking RR x Probability that RR wins + Probability of picking CSK x Probability that CSK wins
Bala Josiar picks with the same probability of a team’s chance of winning. This means, Probability of picking RR = Probability that RR wins and Probability of picking CSK = Probability that CSK wins
Therefore, Probability of picking a winner = (Probability that CSK wins)2 + (Probability that RR wins)2
= ( 3/4 )2 + (1/4)2
= 9/16 + 1/16
= (9 + 1) / 16
= 10/16
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Question 25
Mr. Randor Guy, the famous astrologer staying at Anna Nagar, Chennai has been able to predict the winner of each Hockey match with amazing success. It is told in the sports circle that in a match between two teams A and B, Mr. Randor Guy picks A team with the same probability as A’s chances of winning. But he seems to be incapable of predicting a tie. Let us assume such rumors to be true and that in a match between Pakistan and India, India the stronger team has a probability of 2/3 of winning the game. Based on past data it is also estimated that the probability of match getting tied is 1/9. What is the probability that Randor Guy will correctly pick the winner of the Pakistan-India game?
a) 4/9 b) 2/3 c) 52/81 d) none of these.
Answer : c) 52/81
Solution :
This question is very similar to the previous question, except the fact that there is a probability of tie as well.
Probability of India winning = 2/3
Probability of Pakistan winning = 1 - Probability of India winning - Probability of Tie
= 1 - 2/3 - 1/9 = 1 - 5/9 = 4/9
So probability of picking a winner = probability of picking Pakistan* Probability of Pakistan winning + probability of picking India* Probability of India winning + probability of picking a tie x probability of tie ....(1)
Randor Guy picks with the same probability of a team’s chance of winning.
Therefore, Probability of picking Pakistan = Probability of Pakistan winning, Probability of picking India = Probability of India winning. Also we know that he is unable to predict a tie. Therefore, probability of picking a Tie = 0.
Applying above in eq (1) we get,
probability of picking a winner = (Probability of Pakistan winning )2+(Probability of India winning)2+ 0 x probability of tie
= ( 4/9 * 4/9) + ( 2/3* 2/3) + 0
= 16/81 + 4/9
= (16 + 36) / 81
= 52/81
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Question 26
Om Navasakthi Astrologers , Chennai has been able to predict the winner of each football match with amazing success. It is told in the sports circle that in a match between two teams A and B, Om Navasakthi Astrologers picks A team with the same probability as B’s chances of winning and vice versa. Let us assume such rumors to be true and that in a match between Germany and Brazil, Brazil the stronger team has a probability of 4/7 of winning the game. What is the probability that Om Navasakthi Astrologers will correctly pick the winner of the Germany-Brazil game?
a) 24/49 b) 4/7 c) 18/49 d) none of these.
Answer : a) 24/49
Solution:
This is similar to earlier questions except the fact that Astrologers pick A team with the same probability as B’s chances of winning and pick B team with the same probability as A's chances of winning.
Probability of Brazil winning = 4/7.
Therefore, Probability of Germany winning = 1 - 4/7 = 3/7
So probability of picking a winner = probability of picking Brazil*Probability of Brazil winning + probability of picking Germany * Probability of Germany winning ....(1)
Astrologers pick A team with the same probability as B’s chances of winning and pick B team with the same probability as A's chances of winning.
Therefore, Probability of Brazil winning = probability of picking Germany and Probability of Germany winning = probability of picking Brazil
Applying this in eq (1) we get
probability of picking a winner = ( 3/7 * 4/7) + ( 4/7* 3/7)
= 12/49 + 12/49
= 24/49
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Question 27
A Maruti Swift car started from Chennai towards Mumbai at 7 am. A Tata Indigo car newly purchased started from Chennai at 10 am towards Mumbai and the second vehicle was able to cross the first vehicle at 6 pm on the same day. If Tata Indigo was running at an average speed of 80 km per hour what would have been the speed of Maruti Swift car?
a) 64.24 km/hour b) 59.12 km/hour c) 58.18 km/hour d) 65.42 km/hour
Answer : c) 58.18 km/hour
Solution :
Tata Indigo car had taken 8 hours to cross Maruti Swift running at 80 km/hour.
Distance covered by Tata Indigo in 8 hours = 80 x 8 = 640 km
This distance has been covered by Maruti Swift in 11 hours (as it started at 7 am and was crossed by Tata Indigo at 6 pm)
So average speed of Maruti Swift - 640 /11 = 58.18 km/hour
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Question 28
An Ashok Leyland Truck started from Ennore factory towards Kolkata at 6 am and it was running at an average speed of 60 km per hour. Another Tata Truck started from Ennore at 8.30 am and crossed the Ashok Leyland at 4.30 pm. What is the average speed of Tata Truck?
a) 78.75 km/hour b) 74.75 km/hour c) 72.50 km/hour d) 76.85 km/hour
Answer : a) 78.75 km/hour
Solution :
Ashok Leyland has run 10 ½ hours before the trucks met at an average speed of 60 km/hour
Distance covered by Ashok Leyland - 60 x 10 ½ = 630 km
This distance has been covered by Tata Truck in 8 hours (as it started at 8.30 am and crossed the other truck at 4.30 pm)
Average speed of Tata Truck = 630 / 8 = 78.75 km/hour
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Question 29
A Tata Indica car started from Hyderabad towards Madurai at 5.30 am and travelled at an average speed of 50 km/hour. An Innova car started at 8.30 am from Hyderabad again towards same destination at an average speed of 66 2/3 km/hour. At what time Innova will cross the Tata Indica Car?
a) 4.30 pm b) 5.30 pm c) 3.30 pm d) 6.40 pm
Answer : b) 5.30 pm
Solution :
Tata Indica starts at 5.30 which is 3 hours before Innova started. Therefore it has run for 3 hours at 50 Km/hr speed. Hence Tata Indica car has run 50 x 3 = 150 km by the time Innova starts.
The relative speed of Innova car = Innova Speed - Indica Speed = 66 2/3 - 50 = 16 2/3 km/hour
(Note: To calculate relative speed we are subtracting Indica's speed from Innova's speed as they travel in same direction. If they were travelling in opposite directions we would had added the speeds.)
Innova will take Distance/Relative Speed = (150) / (16 2/3) = 9 hours.
So Innova will cross Tata Indica 9 hours after 8.30 am i.e at 5.30 pm
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Question 30
Mr. Kohli had a doubt regarding a situation and he approached Mahendra for clarification. The question read as under:--
One of four people –two men Raman and Krishnan and two women, Sonam and Kala -- were murdered.
Hint : Raman's sister is Krishnan's wife and vice versa.
1) Raman’s sister argued exactly once with Sonam’s legal husband after the murder.
2) Krishnan’s sister argued twice with the victim’s legal spouse after the murder.
Help Mahendran identifying the victim?
a) Krishnan b) Raman c) Sonam d) none of these.
Answer : a) Krishnan.
Solution :
1) Raman’s sister argued exactly once with Sonam’s legal husband after the murder.
2) Krishnan’s sister argued twice with the victim’s legal spouse after the murder.
From both the statements, we can see that the victim has to be a MAN as both the sisters were involved in arguments after the murder.
To solve such problems, we will have to assume a Victim and check the possibility of all statements. If even one of the statements is logically impossible then our nearest assumption would be false.
1) Assume Raman is the victim.
1a) Assume Raman's Sister is Kala
(If Raman's Sister is Kala then Krishnan's sister has to be Sonam. Also Raman's wife has to be Sonam and Krishnan's wife has to be Kala.)
As per statement I, Kala would had argued with Raman after the murder. – Impossible. (But since we have assume Raman is the victim this is not possible.)
1b) Assume Raman's Sister is Sonam
(If Raman's Sister is Sonam, then Krishnan's Sister would be Kala, Raman's Wife would be Kala and Krishnan's wife would be Sonam)
As per statement I, Sonam would had argued with Krishnan after the murder. - Possible
As per statement II, Kala would had argued with Kala after the murder.- Impossible. (Kala cannot argue with herself)
2) Assume Krishnan is the victim.
2a) Assume Raman's Sister is Kala
(If Raman's Sister is Kala then Krishnan's sister has to be Sonam. Also Raman's wife has to be Sonam and Krishnan's wife has to be Kala.)
As per statement I, Kala would had argued with Raman after the murder. - Possible
As per statement II, Sonam would had argued twice with Kala after the murder. – Possible
All the statement hold good if Krishnan is the Victim provided Raman’s sister is Kala.
2b) Assume Raman's Sister is Sonam
(If Raman's Sister is Sonam, then Krishnan's Sister would be Kala, Raman's Wife would be Kala and Krishnan's wife would be Sonam)
As per statement I, Sonam would had argued with Krishnan after the murder. – Impossible (as we have assumed Krishnan is the victim)
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Question 31
Consider the below statements. One of the friends is lying while others are saying the truth. Find the person who is lying.
1) Ram says he is taller than both Ravi and Rahul
2) Raju says he is not taller than Ram and Ravi
3) Rahul says he is taller than Rajan and also adds he is neither taller nor shorter than Ravi
4) Rajan says he is taller than Ram
5) Ravi says he is taller than Rajan
a) Ravi b) Rajan c) Ram d) Rahul e) Raju
Answer : b) Rajan
Solution :
Based on the statements given, let us start arranging the people in order of their heights.
As per statement 1, Ram is taller than both Ravi and Rahul. Also from second part of statement 3, we can easily say that Rahul is equal in height to that of Ravi.
Arrangement : Ram, Ravi, Rahul
As per statement 2, Raju is shorter than both Ram and Ravi
Arrangement : Ram, Ravi, Rahul, Raju
As per statement 3, Rahul is taller than Rajan
Arrangement: Ram, Ravi, Rahul, Rajan, Raju (as of now we will assume Rajan is taller than Raju)
As per statement 4, Rajan is taller than Ram,
Here is the catch! Rajan is clearly shorter than Ram from statements 1 and 3. Now if we assume Rajan is speaking the truth then we will have to conclude both Ram and Rahul are lying. But the question clearly says only one of the friends is lying. Hence statement 4 is false and Rajan is lying.
(Additional Information : As a matter of fact, Ravi is also saying truth as his statement perfectly falls in line with the arrangement we made so far...)
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Question 32
Consider four brothers A,B,C,D. A is the eldest of all.
The immediately younger brother to A always plays with the youngest brother among all four.
D is the immediately elder brother to the youngest brother.
Find the brother who is immediately younger to A.
a) B b) C c) either B or C d) can’t be determined
Answer : c) either B or C
Solution :
It is given that A is the eldest of all and D is immediately elder to the youngest brother.
Hence one among B and C has to be the youngest and the other one has to be immediately younger to A. But data in question is insufficient to arrive at the right person amongst B and C.
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