Data Sufficiency

GMAT Prep

How many hours did it take Helen to drive from her house to her parent's house?

1) Helen's average speed on this trip was 72 kilometers per hour
2) If Helen's average speed on this trip had been 8 kilometers per hour greater, it would have taken her 1 hour less.

OA C

AAPL wrote:GMAT Prep

How many hours did it take Helen to drive from her house to her parent's house?

1) Helen's average speed on this trip was 72 kilometers per hour
2) If Helen's average speed on this trip had been 8 kilometers per hour greater, it would have taken her 1 hour less.

Statement 1:
If d=72, then t = d/r = 72/72 = 1 hour.
If d=144, then t = 144/72 = 2 hours.
Since the time can be different values, INSUFFICIENT.

Statement 2:
Time and rate have a RECIPROCAL RELATIONSHIP:
If the time is cut in HALF, then the rate DOUBLES.
If the time DOUBLES, then the rate is cut in HALF.

Case 1: r = 72 mph
Here, 8mph faster = 72+8 = 80mph, yielding the following ratio:
(faster rate)/(slower rate) = 80/72 = 10/9.
Since rate and time have a reciprocal relationship, we get:
(faster time)/(slower time) = 9/10.
Implication:
Since the faster time is 9/10 of the actual time -- 1/10 less than the actual time -- the 1 hour saved at the faster time is equal to 1/10 of the actual time:
1 = (1/10)t
t = 10 hours.

Case 1: r = 16 mph
Here, 8mph faster = 16+8 = 24mph, yielding the following ratio:
(faster rate)/(slower rate) = 24/16 = 3/2.
Since rate and time have a reciprocal relationship, we get:
(faster time)/(slower time) = 2/3.
Implication:
Since the faster time is 2/3 of the actual time -- 1/3 less than the actual time -- the 1 hour saved at the faster time is equal to 1/3 of the actual time:
1 = (1/3)t
t = 3 hours.

Since the time can be different values, INSUFFICIENT.

Statements combined:
Only Case 1 satisfies both statements, with the result that t = 10 hours.
SUFFICIENT.

The correct answer is C.