Balance is the amount that has been spent, but not yet paid off, on the card.

Gold Limit - G Gold Balance - 1/3G
Platinum - 2G Platin Balance- 1/5(2G)

(1/3)G is transferred to platinum, platinum has total balance of = (1/5)(2G) + (1/3)G = (11/15)G
Amount unspent is = Spending Limit - Balance = 2G - (11/15)G = (19/15)G
Question - what portion of spending limit on platinum is unspent.
(19/15)G = x times 2G
Therefore x = (19/30)

Balance - how much money she has in her account.

Alternative solution method: don't mess around with fractions, use real numbers:
We want numbers easily divisible by 3 and 5, so start with $15 limit on gold car, making the platinum limit twice that, or $30.
Balances: On gold, she currently has a third of the limit = $5
On Platinum, she has 1/5 of the limit, or 1/5*30 = $6.

If she transfers the $5 in her gold to her platinum, she has $11 - meaning that she has the remaining $19 unspent until she reaches her $30 limit.

The benefit of this approach is that $5 sitting in an account are much easier to conceptualize than 1/5*2G dollars - thus the approach is ess taxing in energy, provides more confidence in correct result, and makes sure that your mind isn't too occupied with fraction manipulation to notice that the question asks for unspent amount, rather than spent amount - Exactly what the question writers wanted you to do.

guys i'm confused. first, if balance is the amount spent, yes your solution is correct and that's also the OA. but usually i consider balance to be whatever you have left after spending. - how will i distinguish between the 2 meanings in GMAT? although I've never seen gmat to state the word balance and mean it to be the 'spent amount'.

but if balance IS whatever you have in your account, then balance = unspent amount? So after you transfer the balance from gold to platinum and add both balances, why subtract from total limit?

clawhammer wrote:guys i'm confused. first, if balance is the amount spent, yes your solution is correct and that's also the OA. but usually i consider balance to be whatever you have left after spending. - how will i distinguish between the 2 meanings in GMAT? although I've never seen gmat to state the word balance and mean it to be the 'spent amount'.

but if balance IS whatever you have in your account, then balance = unspent amount? So after you transfer the balance from gold to platinum and add both balances, why subtract from total limit?

*scratch head* you know, you might have a point. I'm (we're?) just so used to this trick of setting up a calculation and then hitting you with a zinger looking for the complementary fraction, I never stopped to think about the real meaning of the words - I went with the writer's "spirit" and obvious intention, not with actual meaning. Huh.

The way I see it, the problem is not with "balance" (which is money you have left in your account, used in particular in the case of loans/interest question as the initial/final baseline), but rather with the word "unspent": if all Sally does is shift the balance from one pocket to another, nothing is actually "spent", so i don't see how you can talk about "unspent". I think Manhattan can do a slightly better job of sharpening the phrasing, thought the writer's intention is clear to me.