Practice GMAT Data Sufficiency Question

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Peter can drive to work via the expressway or via the backroads, which is a less delay-prone route to work. What is the difference in the time Peter would spend driving to work via the expressway versus the backroads?

Peter always drives 60mph, regardless of which route he takes; it takes Peter an hour to drive round-trip to and from work using the backroads
If Peter travels to and from work on the expressway, he spends a total of 2/3 of an hour traveling

A)	Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)	Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)	BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)	EACH statement ALONE is sufficient.
E)	Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Correct Answer: C

Since this is a distance-rate-time problem, begin with the core equation:
Distance = Rate(Time)
Note that there are two distance equations, one for traveling the expressway and the other for traveling the backroads.
Distance_express = Rate_express(Time_express)
Distance_backroad = Rate_backroad(Time_backroad)
In order to answer the question, you need to find the value of:
Time_express - Time_backroad
Evaluate Statement (1) alone.
1. Statement (1) says Rate_express = Rate_backroad = 60 mph.
2. Statement (1) also says that 2(Time_backroad) = 1 hour
  (Time is multiplied by 2 because the statement gives the time "to drive round-trip to and from work.")
  Time_backroad = 1/2 hour.
3. Filling in all the information, you have the following:
  Distance_express = 60(Time_express)
  Distance_backroad = 60mph((1/2) hour) = 30 miles
4. Without information concerning the distance or time to travel on the expressway, you cannot solve for Time_express. Consequently, Statement (1) is NOT SUFFICIENT.
Evaluate Statement (2) alone.
1. Statement (2) says that 2(Distance_express) = Rate_express((2/3) of an hour)
  (Note that the distance is multiplied by two because Peter travels twice the distance when he goes "to and from work".)
  So, Time_express = 1/3 of an hour.
2. Fill in the information that is known:
  Distance_express = Rate_express(1/3 of an hour)
  Without any information about Time_backroad, you cannot determine Time_express - Time_backroad. Statement (2) is NOT SUFFICIENT.
Evaluate Statements (1) and (2) together.
1. Putting Statements (1) and (2) together, you know Time_backroad from Statement (1) and you know Time_express from Statement (2).
2. So, Time_express - Time_backroad = 1/3hour - 1/2hour or 20 minutes - 30 minutes = 10 minutes or 1/6 of an hour. Statements (1) and (2) together are SUFFICIENT.
Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is NOT SUFFICIENT yet Statements (1) and (2), when taken together, are SUFFICIENT, answer C is correct.

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