#2 from cracking the gmat 2009 bin 2

Total number of laps = x
Average time per lap = 51 seconds
Total time taken to run(I assume) x laps = 51x

After the lap of 39 seconds
Total number of laps = x+1
Total time taken to run(I assume) x+1 laps = 51x + 39
Average time per lap = Total time taken to run(I assume) x+1 laps/Total number of laps
= (51x + 39)/(x+1) = 49 seconds
=> 51x + 39 = 49x + 49
=> 2x = 10
=> x = 5 answer B

redng wrote:2. For the past x laps around the track, Steven's average time per lap was 51 seconds. If a lap of 39 seconds would reduce his average time per lap to 49 seconds, what is the value of x?

• (A) 2
  (B) 5
  (C) 6
  (D) 10
  (E) 12

answer: B

I don't even know how to approach this. Thanks!

We can plug in the answers, which represent the x number of laps.

Answer choice C: 6 laps
Time for the first 6 laps = 6*51 = 306.
Average time for all 7 laps = (306+39)/7 = 345/7 = 49 2/7.
Incorrect: the average time must be 49.
In order to reduce the average time just a bit more -- to 49 seconds per lap -- the time spent on the faster lap must be a slightly higher fraction of the total amount of time.
Here is the reasoning: If there are FEWER original laps, then the one additional faster lap will have a GREATER impact on the average.
Thus, the original number of laps must be just a bit less than 6.

The correct answer is B.

Answer choice B: 5 laps
Time for the first 5 laps = 5*51 = 255.
Average time for all 6 laps = (255+39)/6 = 294/6 = 49.
Success!