Avg Problem

rem the basic avg formula
i.e avg = sum / n

here u r given a new avg 49 after the addition of one more value

so lets there were x laps... and avg time was 51 secs

51 = ( sum of x laps) / x

therefore: sum of x laps = 51 * x

now when we add 39 to this, avg changes to 49

hence (51x + 39)/ (x + 1) = 49 ( x + 1 refers to the one additional lap of 39 secs)

solving this, u get x = 5


Hope this helps...

fc135 wrote:Hello, need help in solving the below problem...

For the past x laps around the track, stevens avg time per lap was 51 sec. If a lap of 39 sec would reduce his avg time per lap to 49 sec, what is the value of x?

Regards
Manju

This is a weighted average problem. We could use the alligation method.

To combine an average of 51 with an average of 39 to get a goal average of 49:

The proportion needed of 51-second laps is the positive difference between the other average (39) and the goal average (49): 49-39=10.
The proportion needed of 39-second laps is the positive difference between the other average (51) and the goal average (49): 51-49=2.

51-second laps:39-second laps = 10:2 = 5:1.

So if we have 1 39-second lap, we need 5 51-second laps.
x = 5.

Since the GMAT is a multiple choice test, another approach would be to plug in the answer choices, one of which would say that x=5. When we plug in x=5, we'd see that:

5*51 = 255 seconds.
1*39 = 39 seconds.
Total time = 255+39 = 294.
Total laps = 5+1 = 6.
Average = 294/6 = 49 seconds. Success!