Spending limit

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paridhi: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Mon Jun 30, 2008 3:07 am; Thanked: 5 times

Spending limit

by paridhi » Fri Jul 30, 2010 7:00 am

Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/5 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent?
(A) 11/30
(B) 29/60
(C) 17/30
(D) 19/30
(E) 11/15

[spoiler]OA is D. Should it not be A, as the question is asking the amount unspent which is nothing but the remaining balance on the card? Please explain. [/spoiler]

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Source: Beat The GMAT — Problem Solving | Fri Jul 30, 2010 7:00 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Fri Jul 30, 2010 7:29 am

paridhi wrote:Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/5 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent?
(A) 11/30
(B) 29/60
(C) 17/30
(D) 19/30
(E) 11/15

[spoiler]OA is D. Should it not be A, as the question is asking the amount unspent which is nothing but the remaining balance on the card? Please explain. [/spoiler]

Let x=spending limit of gold card
Let 2x=spending limit of platinum card

Gold card balance = (1/3)x
Platinum card balance = (1/5)2x

Transfer --> new platinum card balance = (1/3)x + (1/5)2x = x/3 + 2x/5 = 5x/15 + 6x+15 = 11x/15

First we'll find the ratio: (platinum card balance)/( platinum card spending limit) = (11x/15)/(2x) = 11/30
So, Sally has used up 11/30 of her platinum card spending limit, which means she has 19/30 remaining to spend.

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