Strategy guide, Algebra Page 123 Chapter 5: Problem 7

[coolprasanth]

"The Competitive edge of a baseball team is defined by sqrt(w/l) where W=Wins, L=Losses. This year GRE All-stars had 3 times as many wins and one-half as many losses as they had last year. By what factor did the competitive edge increase?"

The answer key provided assumes 2 Wins and 2 Losses for the previous season and the answer is listed as sqrt(6). But when we assume any other number the answer differs, for example when I assume the wins as 2 and Losses as 8 the answer is sqrt(3/2). Is this a error in the book or is there something I'm not seeing....thanks in advance.....

[xerocoool]

Last year -

Wins : 2
Loss : 8

Present year -

3 times as many wins as they had last year : 3 x 2 = 6
one half many losses as they had last year : 8/2 = 4

last year : C = sqrt (2/8) => sqrt (1/4) => sqrt (0.25) => 0.5
present year : C = sqrt (6/4) => sqrt (3/2) => sqrt (1.5) => 1.2247

competitive edge increase => 1.2247/0.5 => 2.4494 => sqrt(6)

Hope that helps :)

[tommywallach]

Hey Cool,

Actually, the numbers you pick don't matter. The mistake you seem to be making is you aren't answering the question they asked. They aren't asking for the competitive edge itself, they're asking "by what factor" it increased. Thus you have to look at both the ORIGINAL competitive edge (with whatever numbers you want to plug in) and then the NEW competitive edge (when the W has been multiplied by 3 and the L has been halved), then divide the latter by the former to find the percent increase (i.e. "the factor by which" it's increased).

-t

P.S. Xero shows you the math perfectly!

[hhussain85]

Hey t,

Please correct me if I'm wrong but I believe you're confusing the percentage increase with the factor increase.

The percentage increase is 145% and the factor increase is 2.45.

Please advise.

[tommywallach]

Hey HH,

There's no such thing as a factor increase. That's not a term recognized by the GRE. I've never even heard it before, and I've been teaching GMAT/GRE for 6 years. So...no! : )

-t