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need help with RTD problem

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need help with RTD problem

by queenisabella » Sat Feb 25, 2012 7:25 pm
Data Sufficiency Question

How much time did it take a certain car to travel 400 kilometers?
(1) The car traveled the first 200 kilometers in 2.5 hours.
(2) If the car's average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hour less time than it did.

OA is B.

[Mod Edit: Moving the post to the DS Forum]
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by neelgandham » Sat Feb 25, 2012 9:54 pm
How much time did it take a certain car to travel 400 kilometers?
(1) The car traveled the first 200 kilometers in 2.5 hours.
Since we don't know the time taken by the car to travel the next 200kms, statement I is insufficient to answer the question
(2) If the car's average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hour less time than it did.
Let Sa be the Average speed of the Car
Let Ta be the time taken to travel 400 Kms.
Sa*Ta = Distance travelled = 400kms
If the average speed of the car = Sa+20, then the car would take Ta-1 hours to travel 400kms

Since distance travelled is equal Sa*Ta = (Sa+20)*(Ta-1)
=> 20Ta-Sa-20 = 0
We already know that Sa*Ta = 400, So, Sa = 400/Ta. Replacing the value of Sa with 400/Ta in the above equation, we get

20Ta - (400/Ta) - 20 = 0
20Ta*Ta - 400 - 20Ta = 0
Ta*Ta - Ta - 20 = 0
Ta*Ta - 5Ta + 4Ta - 20 = 0
(Ta+4)*(Ta-5) = 0. Since time is always positive, Ta = 5kms/Hours. Sufficient to answer the question.

IMO B
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by Anurag@Gurome » Sun Feb 26, 2012 11:01 pm
queenisabella wrote:Data Sufficiency Question

How much time did it take a certain car to travel 400 kilometers?
(1) The car traveled the first 200 kilometers in 2.5 hours.
(2) If the car's average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hour less time than it did.

OA is B.

[Mod Edit: Moving the post to the DS Forum]
Distance, D = 400 kms
Let time taken = Y and the speed = S

(1) The car traveled the first 200 kilometers in 2.5 hours.
This statement only gives the time for first 200 kms but there is no info about the remaining 200 kms; NOT sufficient.

(2) If the car's average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hour less time than it did.

S = 400/T
(S + 20) = 400/(T - 1)
400/T + 20 = 400/(T - 1), which can be solve for T; SUFFICIENT.

The correct answer is B.
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