Question: A thief steals a car at 2.30 p.m. and drives it at 60 km/h. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/h. When will he overtake the thief?

(A) 4.30 p.m.
(B) 4.45 p.m.
(C) 5 p.m.
(D) 5.15 p.m.
(E) 5.20 p.m.

“A thief steals a car at 2.30 p.m. and drives it at 60 km/h”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. GMAT quant helps to test the content and logical skills of the candidates. The candidates must know the basic knowledge of calculations in order to solve the GMAT Problem Solving questions. The mathematical problems of the GMAT Quant topic in the problem-solving part can be solved by the candidates with better qualitative skills.

Solution and Explanation:

Approach Solution 1:

The problem statement informs that:

Given:

• A thief steals a car at 2.30 p.m. and drives it at a speed of 60 km/h
• The theft is found at 3 p.m. and the owner departs in another car at 75 km/h

Find out:

• When the owner will overtake the thief?

The thief steals the car at 2:30 p.m. and the owner departs in another car at 3 p.m.
Hence, there is a 30 minutes gap between the distance covered by the thief and the owner.
Distance covered by the thief in 30 minutes (that is ½ hour) = the product of speed and time = 60 * ½ = 30 km
Speed of the owner’s car = 75km/h
Therefore, the relative speed of the owner will be = (75 - 60) = 15 km/h

Time taken by the owner to cover the distance of 30 km is = Distance/ relative spee
= 30/15 = 2 hours.

Therefore, the time taken by the owner to overtake the thief is = 3.00 p.m + 2 hours = 5.00 PM

Hence, C is the correct answer.

Correct Answer: C

Approach Solution 2:

The problem statement discloses that:

Given:

• A thief drives a car at 2.30 p.m. at a speed of 60 km/h
• The owner departs in another car at 3 p.m. to catch the thief at a speed of 75 km/h

Find out:

• When does the owner catch the thief?

Let’s assume the time taken by the owner to overtake the thief is ‘t’ in hours. Therefore, the equation will be:

60(t + 1/2) = 75t
60t + 30 = 75t
30 = 15t
2 = t

Thus, we can say, that the owner takes 2 hours to overtake the thief.
Since the owner begins at 3 p.m., he will overtake the thief at 5 p.m.

Hence, C is the correct answer.

Correct Answer: C

Approach Solution 3:

The problem statement proclaims that:

Given:

• A thief drives a car at 2.30 p.m. at a rate of 60 km/h
• The owner begins at 3 p.m. to catch the thief at a speed of 75 km/h

Find out:

• The time the owner catches the thief

Let the thief is overtaken by the owner at x hours after 2:30 p.m.

Therefore, the distance that the thief covers in x hours = distance that the owner covered in (x-½) hours
Hence, we can say, 60x = 75 (x-½)
=> 15x = 75/2
=> x = 5/2 hours

Thus the thief is overtaken by the owner at 5 p.m.

Hence, C is the correct answer.

Correct Answer: C

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