LR - Mathematical Reasoning - Previous Year CAT/MBA Questions
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Read the following scenario and answer the THREE questions that follow.
An examination had ten multiple choice questions; labelled Q1 to Q10 respectively. Each question had four answer options — A, B, C and D — of which one and only one was the correct answer. For each correct answer, the candidate obtained 1 mark. There were no negative marks for wrong answers. The answers chosen by six candidates named Om, Pavan, Qadir, Rakesh, Simranjeet and Tracey to each of the ten questions and the total marks obtained by each of them are shown in the table.
What is the correct answer for Q5?
- (a)
Not possible to determine uniquely
- (b)
A
- (c)
B
- (d)
C
- (e)
D
Answer: Option D
Text Explanation :
The correct answer for Q5 is C.
Workspace:
For which of these questions is D the correct answer?
- (a)
Both Q1 and Q9
- (b)
Both Q1 and Q8
- (c)
Q8
- (d)
Q1
- (e)
Q9
Answer: Option C
Text Explanation :
Q6 and Q8 have D as the correct answer.
Workspace:
Which of these questions witnessed the least number of the students answering correctly?
- (a)
Both Q3 and Q4
- (b)
Q4
- (c)
Q5
- (d)
Q10
- (e)
Q2
Answer: Option B
Text Explanation :
Of the different possibilities are ( 1, 6, 7), (1, 6, 9), (6, 7, 9), (1, 7, 9).
But the cases 6, 7, 9 fails because if he answered all three of them correctly then he must have answered 1 wrongly but since if 1 is answered wrong then all of 1, 6, 7, 9 are answered correctly by Simarjeet when
Simarjeet can answer actually a total of 3 questions only correctly hence this case fails.
Similarly if considered the cases ( 1, 6, 7) and (1, 6, 9) as the questions which were answered correctly. The cases fail because if they are answered correctly we cannot possibly have Pavan answering 5 questions correctly.
Hence the only possibility is he must have answered the questions :
( 1, 7, 9) correctly.
Hence the correct answers are:
Now drawing the table based on the answers marked by them
Simarjeet must have answered 1 question of the Q2, Q4, and Q6 correctly. Qadir must have answered the remaining two of them correctly.
If Simarjeet answered Q4 correctly and Q2, Q6 wrong the answers for Q2, Q4 and Q6 will be: B, B, and D
But if Q2 and Q4 are answered as B then Om must have scored 3 marks instead of2 and hence the case fails.
If Simarjeet answered Q6 correctly and Q2, Q4 wrong the answers for Q2, Q4 and Q6 will be: A, C, and C.
But Pavan cannot score 5 marks.
Hence Simarjeet must have answered Q2 correctly and answers for Q2, Q4, and Q6 will be :
(B, C, D).
Q4 was answered wrong by 5 members.
Workspace:
Answer the next 3 questions based on the information given below.
Given below is the time table for a trans-continental train that cuts across several time zones. All timings are in local time in the respective cities. The average speed of the train between any two cities is the same in both directions.
Which of the following pairs of cities are in the same time zone?
- (a)
Vaq and Sab
- (b)
No pair of cities are in the same time zone.
- (c)
Sab and Raz
- (d)
Sab and Raz
- (e)
Zut and Yag
Answer: Option E
Text Explanation :
When travelling between 2 cities in different time zones, the actual travelling time is the average of two time taken both ways between the cities when calculated on local basis.
Also, the time difference between the two cities is half of difference of time taken both ways between the cities when calculated on local basis.
Let’s take the example of journey between Vaq and Yag.
Time taken to go from Vaq to Yag, on local basis (11:55 pm to 10:50 am) = 10 hours 55 mins.
Time taken to go from Yag to Vaq, on local basis (7:50 am to 2:45 pm) = 6 hours 55 mins.
∴ The actual travelling time between Yag and Vaq is average of 10 hours 55 mins and 6 hours 55 mins i.e., 8 hours 55 mins.
Also, the time difference between the two cities is half of (10 hours 55 mins - 6 hours 55 mins) i.e., 2 hours.
Similarly, we can calculate the travelling time and time difference between all the cities.
From the table we can see that Zut and Yag are in the same time zone.
Hence, option (e).
Workspace:
What is the total time taken in minutes by the train to go from Zut to Raz?
- (a)
28 hours, 40 minutes
- (b)
22 hours, 40 minutes
- (c)
24 hours, 40 minutes
- (d)
20 hours, 40 minutes
- (e)
16 hours, 40 minutes
Answer: Option B
Text Explanation :
Consider the solution to first question of this set.
Journey time of train from Zut to Raz = 1 hour 45 mins + 8 hours 55 mins + 7 hours 50 mins + 3 hours 55 mins = 22 hours 25 mins.
Waiting time at stations Yag, Vaq and Sab = 5 + 5 + 5 = 15 mins.
Total travel time between Zut to Raz = 22 hours 25 mins + 15 mins = 22 hours 40 mins.
Hence, option (b).
Workspace:
What time is it at Yag when it is 12:00 noon at Sab?
- (a)
5:00 pm
- (b)
7:00 pm
- (c)
9:30 pm
- (d)
2:30 pm
- (e)
12:00 pm
Answer: Option A
Text Explanation :
Consider the solution to first question of this set.
Time difference between Yag and Sab = 2 + 3 = 5 hours..
∴ Yag is 5 hours ahead of Sab.
∴ If it is 12 noon at Sab, it will be 5 pm at Yag.
Hence, option (a).
Workspace:
Answer the following question based on the information given below.
Ramya, based in Shanpur, took her car for a 400 km trip to Rampur. She maintained a log of the odometer readings and the amount of petrol she purchased at different petrol pumps at different prices (given below). Her car already had 10 litres of petrol at the start of the journey, and she first purchased petrol at the start of the journey, as given in table below, and she had 5 litres remaining at the end of the journey.
What has been the mileage (in kilometers per litre) of her car over the entire trip?
- (a)
8.00
- (b)
8.50
- (c)
9.00
- (d)
9.50
- (e)
None of the above
Answer: Option A
Text Explanation :
Ramya has 10 litres petrol in her car to start with.
She purchased 20 litres, 15 litres and 10 litres on three occasions.
She was left with 5 litres in her car at the end of the journey.
Hence, she utilized (10 + 20 + 15 + 10 – 5) = 50 litres.
She travelled (800 – 400) = 400 km.
Hence, the mileage of Ramya’s car = 400/50 = 8 km/litre
Hence, option (a).
Workspace:
Answer the following question based on the information given below.
Ramya, based in Shanpur, took her car for a 400 km trip to Rampur. She maintained a log of the odometer readings and the amount of petrol she purchased at different petrol pumps at different prices (given below). Her car already had 10 litres of petrol at the start of the journey, and she first purchased petrol at the start of the journey, as given in table below, and she had 5 litres remaining at the end of the journey.
Her car’s tank-capacity is 35 litres. Petrol costs Rs. 45/- litre in Rampur. What is the minimum amount of money she would need for purchasing petrol for the return trip from Rampur to Shanpur, using the same route? Assume that the mileage of the car remains unchanged throughout the route, and she did not use her car to travel around in Rampur.
- (a)
1714
- (b)
1724
- (c)
1734
- (d)
1744
- (e)
Data insufficient to answer.
Answer: Option D
Text Explanation :
Ramya’s car already has 5 litres in the tank.
Her car’s tank capacity is 35 litres.
She can fill a maximum of 30 litres more.
The petrol cost in Rampur is Rs. 45/litre
As the cost of petrol is lower at all the succeeding petrol pumps that come on the way and hence, to minimize the cost, she will fill enough petrol to reach the first pump i.e 150 km.
She already has 5 litres using which she can travel 40 km.
Hence, to travel 110 km, she will need 110/8 = 13.75 litres at the rate of 45 per litre.
On reaching the first petrol pump in the reverse journey, she will fill up enough petrol to reach the second petrol pump as the cost of petrol in the second pump is less than the cost of the first pump.
This distance is 50 km.
Ramya needs 50/8 = 6.25 litres at the rate of Rs. 40/litre.
For the rest of the journey (200 km) she will need 200/8 = 25 litres at the rate of Rs. 35/litre.
Hence the total cost is (13.75 × 45 + 6.25 × 40 + 25 × 35) = 1743.75
Hence, option (d).
Workspace:
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