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GMAT - Data Sufficiency -

S E 3 months ago Data Sufficiency |

Data Sufficiency

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 hours less time than it did

Statement 1 - The car traveled the first 200 kilometers in 2.5 hours

Insufficient because the speed of the car may change between 200 and 400 km

 

Statement 2 -

Assume the average speed of the car for 400 kms be s and time taken be t

s = 400/t    (Since speed = distance / time) ... (1)

When time = t - 1, speed = s+20

s + 20 = 400 / (t - 1)

from equation (1)

400/t  + 20 = 400 / (t - 1)

400 (t - 1) + 20 t (t - 1) = 400 t

400t - 400 + 20t2 - 20t = 400t

20t2 - 20t - 400 = 0

t2 - t - 20 = 0

t2 - 5t + 4t - 20 = 0

t (t - 5) + 4 (t - 5) = 0

(t - 5) (t + 4) = 0

t = - 5 or t = 4 hours

t = -5 is not possible hence

t = 4 hours

Sufficient.

 

 

Hello, how did you get 20 in the initial formula?