Jeff Drove Two Laps around a Track. Was his Average Speed Less than 60 GMAT Data Sufficiency

Question: Jeff drove two laps around a track. Was his average speed less than 60 miles per hour for the two laps?

(1) Jeff's average speed for the first lap was 20 miles per hour.
(2) Jeff's average speed for the second lap was 120 miles per hour.

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) Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: A

Solution and Explanation:
Approach Solution 1:

Let the distance of one lap equal dd Avg Speed for the initial lap = A
Average Speed on the second lap equals B

Therefore, the entire duration is d/A + d/B
Total time if the total average speed is 60 = 2d/60 = d/30

The query asks whether d/A + d/B > d/30. or is 1/A + 1/B less than 1/30?

(1) Jeff's first lap average speed was 20 miles per hour.
1/A = 1/20
Since 1/20 is already bigger than 1/30, the answer is yes.
1 is adequate

(2) During the second lap, Jeff's average speed was 120 miles per hour.
1/120 is less than 1/30, hence the value of A is required to establish if 1/A + 1/B > 1/30 .
Two is insufficient

A is the correct answer.

Approach Solution 2:

Assume the length of one lap = D
Time to complete the first lap = x
Time to complete the second lap = y

Two-lap average speed equals 2D/(x+y)

0 < 2D/(x+y) < 2(D/x)
since y > 0
or
0 < 2D/ (x+y) < 2( D/y)
...because x > 0

Statement 1: Jeff's average speed over the two laps is 2*20 < 60

sufficient

Statement 2: Jeff's average speed for the two laps is 2*120

Therefore, it can be fewer than 60 or larger than 60.

A is the correct answer.

“Jeff drove two laps around a track. Was his average speed less than 60” - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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