LR - Directions - Previous Year CAT/MBA Questions

The best way to prepare for LR - Directions is by going through the previous year LR - Directions XAT questions. Here we bring you all previous year LR - Directions XAT questions along with detailed solutions.

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It would be best if you clear your concepts before you practice previous year LR - Directions XAT questions.

1. XAT 2015 QA | LR - Directions XAT Question

Devanand’s house is 50 km West of Pradeep’s house. On Sunday morning, at 10 a.m., they leave their respective houses.

Under which of the following scenarios, the minimum distance between the two would be 40 km?
Scenario I: Devanand walks East at a constant speed of 3 km per hour and Pradeep walks South at a constant speed of 4 km per hour.
Scenario II: Devanand walks South at a constant speed of 3 km per hour and Pradeep walks East at a constant speed of 4 km per hour.
Scenario III: Devanand walks West at a constant speed of 4 km per hour and Pradeep walks East at a constant speed of 3 km per hour.

(a)
Scenario I only
(b)
Scenario II only
(c)
Scenario III only
(d)
Scenario I and II
(e)
None of the above

2. XAT 2012 QA | LR - Directions XAT Question

Shyam, a fertilizer salesman, sells directly to farmers. He visits two villages A and B. Shyam starts from A, and travels 50 meters to the East, then 50 meters North-East at exactly 45° to his earlier direction, and then another 50 meters East to reach village B. If the shortest distance between villages A and B is in the form of $a \sqrt{b + \sqrt{c}}$ meters, find the value of a + b + c.

(a)
52
(b)
54
(c)
58
(d)
59
(e)
None of the above

Answer: Option E

Text Explanation :

Total distance travelled by Shyam is;

$50 + 50 + \frac{50}{\sqrt{2}}$ km towards east, and $\frac{50}{\sqrt{2}}$ km towards north

Hence, smallest distance, say d, between village A and Village B is;

$d = \sqrt{({(100 + 25 \sqrt{2})}^{2} + {(25 \sqrt{2})}^{2})}$

Hence, $d^{2} = {(100 + 25 \sqrt{2})}^{2} + {(25 \sqrt{2})}^{2} = a^{2} (b + \sqrt{c})$

But, ${(100 + 25 \sqrt{2})}^{2} + {(25 \sqrt{2})}^{2} = 2500 (5 + 2 \sqrt{2})$

$= 2500 (5 + \sqrt{8})$

Hence, a² = 2500, b = 5 and c = 8

Hence, a + b + c = 50 + 5 + 8 = 63

Hence, option (e).

LR - Directions - Previous Year CAT/MBA Questions

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