Why am I off by 1?

by **Guest** Fri Feb 22, 2008 1:10 pm

I'm trying to answer question 9 in the manhattan equations/vic book and for some reason my answer is off by 1 from the books solution. I don't understand what is going on here. Take a look at my reasoning:

This year, the GMAT All-stars tripled the number of wins and halved the number of losses that they had last year. By what factor did their "competitive edge" increase? Competitive edge of a baseball team is defined by the formula w^3/l^2, where W represents the number of wins and L represents the number of losses.

I solved this by plugging in #s.

Original:
W = 2 and L = 2 so...
2^3/2^2 = 2

Then I tripped the wins and halves the losses..so...
w = 6 and l = 1 soo..
6^3/1^2 = 216

Now we do percentage change: 216 - 2 = 214/original

214/2 = 107...but the books answer is 108. Can anyone explain where I messed up? I just don't see it

by **tmmyc** Fri Feb 22, 2008 1:56 pm

The question asks for the factor increase of their competitive edge, not the percentage increase.

The confusing part is the term "factor increase". Here is the dictionary definition.
factor - A quantity by which a stated quantity is multiplied or divided, so as to indicate an increase or decrease in a measurement

Using your example, then, the team went from 2 to 216. The team increased their competitive edge by a factor of 108 since 2*108 = 216.

by **StaceyKoprince** Mon Feb 25, 2008 6:24 pm

yes - factor increase is different than percentage increase. Nice explanation tmmyc.