Hi here it goes:

Let gold spending limit = x
Hence Platinum limit = 2x
Gold Balance = 1/3 x
Platinum Balance = 1/5*2x = 2/5x
X'fer gold balance to platinum = (1/3 + 2/5)x = 11/15x
Thus total amount spent = 11/15x

Now the questions asks
"what portion of her limit on the platinum card will remain unspent?"..
Platinum Limit - Amount spent
=> 2x-11/15x
=> 19/15 x............(1)
We require the portion of the amount unspent on the platinum card whose limit is 2x & NOT x..

Hence multiply & divide eqn (1) by 2
=> 19 / (15*2) 2x
=> 19/30

There u go...lemme kno if still in doubt...

Let me offer two explanations to tackle this problem....

The first method is based on assumption and I consider this method quite easy and the quickest one to solve this problem..

Let 30 be the spending limit of the gold card & 60 be the spending limit of the platinum card...( I chose 30 & 60 because its divisible by both 3 & 5)
It is given that the balance on gold card is one third of the spending limit of gold card (i.e 10) & the balance on platinum card is two third of the spending limit of platinum(i.e 12).
When the balance on the gold card is transferred to the platinum card's balance the new balance becomes 22(10+12)
therefore the amount spent on platinum card is 22/60=11/30

But the question that is being asked is the amount that is unspent...so the ans will be 1-11/30=19/30 which is choice D

If you are running out of time in the GMAT this method is the best approach to adopt... 8)

Now for the second method (...a bit time consuming)

Let SL(G) & SL(P) be the spending limit of gold card & platinum card respectively and B(G) & B(P) be the balance on gold card & platinum card respectively..

Given: SL(P)=2SL(G).....1
B(G)=1/3SL(G)
B(P)=1/5SL(P)

Now the gold card's balance is transferred to the platinum card's balance
So the new balance will be 1/3SL(G) + 1/5SL(P)....2
Substituting 1 in 2
we get 11/30SL(P)

the amt spent is given by 11/30SL(P)/SL(P) = 11/30
Amt unspent = 1-11/30 = 19/30

Hope this explanation helps....

Your 1st method is really helpful...provided we assume the correct number..
Thanks

Guys thanx for the quick reply............but i still dont get one thing.....when it is said the "balance" on her gold card is sumthing do they mean the spent amount or the unspent amount on her card?.............coz as far as my knowledge goes balance on the spending amount shud be the unspent amount and not the spent amount.............please explain that part to me.............