Practice GMAT Data Sufficiency Question

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Police suspected that motorists on a stretch of I-75 often exceeded the speed limit yet avoided being caught through the use of radar detectors and jammers. Officer Johnson of the State Police recently pulled over a driver on I-75 and accused him of breaking the 50 mile-per-hour speed limit. Is Officer Johnson’s assertion correct?

Officer Johnson noted that the driver had traveled 30 miles from point A to point B on I-75.
Officer Johnson noted that it took the driver 30 minutes to travel from point A to point B on I-75.

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

The basic equation necessary for solving this problem is:
Distance = Rate*Time
D = RT
If Officer Johnson can prove that R, the driver’s average rate or speed, exceeded 50 miles-per-hour, Officer Johnson can prove that the driver broke the speed limit. We must be able to find R in order to definitively answer the question of whether Officer Johnson’s assertion is correct.
Evaluate Statement (1) alone.
1. Statement (1) indicates that D = 30 miles. Without information about T or R, we cannot find the value of R and, as a result, we cannot prove or disprove Officer Johnson's claim.
2. Statement (1) alone is NOT SUFFICIENT.
Evaluate Statement (2) alone.
1. Statement (2) indicates that T = 30 minutes. Without information about D or R, we cannot find the value of R and, as a result, we cannot prove or disprove Officer Johnson's claim.
2. Statement (2) alone is NOT SUFFICIENT.
Evaluate Statements (1) and (2) together.
1. From Statement 1: D = 30 miles
2. From Statement 2: T = 30 minutes
3. Putting the information together, we can construct the following algebraic equation:
  D = RT
  30mil = R(30min)
  R = 1mil/1min = one mile per minute
  R = One mile per minute * 60 minutes per hour = 60 miles per hour.
4. Since we have a value for R, we can definitively judge the veracity of Office Johnson's claim.
5. Statements (1) and (2), when taken together, are SUFFICIENT.
Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, but Statements (1) and (2) when taken together are SUFFICIENT, answer C is correct.

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