Data Sufficiency

BTGModeratorVI wrote: ↑

Sun Apr 05, 2020 9:01 am

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.

Answer: B
Source: GMATPrep practice test

Target question: How long did it take to travel 400km
To find the travel time, we need to know the average speed traveled.
Let x = the average speed traveled.

REPHRASED target question: What is the value of x?

Statement 1: The car traveled the first 200 km in 2.5 hrs
No info about the 2nd half of the trip, so we can't determine the overall average speed (aka x).
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: If the car’s average speed had been 20 km/h faster, it would have traveled the 400 km in 1 hour less time.
Let's start with a word equation:
(travel time at x km/h) - 1 = (travel time at x+20 km/h)
Since time = distance/speed, we can now write:
(400/x) - 1 = 400/(x+20)

IMPORTANT: At this point, we need only determine whether this equation will yield 1 or 2 valid values of x. If it yields only 1 valid value, then statement 2 is sufficient. If it yields 2 valid values, then statement 2 is not sufficient.

Rewrite as: (400-x)/x = 400/(x+20)
Cross multiply: (400)(x) = (400-x)(x+20)
Simplify: 400x = 8000 + 380x - x²
Rewrite: x² + 20x - 8000 = 0
Factor: (x + 100)(x - 80) = 0
So, x = -100 or 80
Since x cannot be negative, it must be the case that x = 80
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent