# LR - Mathematical Reasoning - Previous Year CAT/MBA Questions

You can practice all previous year OMET questions from the topic LR - Mathematical Reasoning. This will help you understand the type of questions asked in OMET. It would be best if you clear your concepts before you practice previous year OMET questions.

**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.

**XAT 2019 QADI | LR - Mathematical Reasoning**

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

**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:

**XAT 2019 QADI | LR - Mathematical Reasoning**

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

**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:

**XAT 2019 QADI | LR - Mathematical Reasoning**

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

**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.

**XAT 2012 QA | LR - Mathematical Reasoning**

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

**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 1.

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.

**XAT 2012 QA | LR - Mathematical Reasoning**

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

**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 4.

Workspace:

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