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BALANCE SPENDING

by g.shankaran » Thu May 26, 2011 6:06 pm
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?

11/30

29/60

17/30


19/30


11/15
Ans: 11/30 or 19/30?
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by vineeshp » Thu May 26, 2011 6:25 pm
Wording is confusing on this one.

the problem is with the tearm balance, right?

I think the answer is 19/30 cos it means spent amount.
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by SoCan » Thu May 26, 2011 6:26 pm
Let x = spending limit on platinum card in dollars. Therefore x/2 = spending limit on gold card.

Balance of 1/3 on gold card means balance of x/6. Balance of 1/5 on platinum means balance of x/5.

Moving the balance from the gold to the platinum, (x/6)+(x/5) = 11x/30.

That means out of your x dollar limit, you have a balance of 11/30. Your remaining credit line is 1-(11/30) = 19/30.
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by SoCan » Thu May 26, 2011 6:30 pm
vineeshp wrote:Wording is confusing on this one.

the problem is with the tearm balance, right?

I think the answer is 19/30 cos it means spent amount.
Yes, credit card balance is how much you owe.
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by cans » Fri May 27, 2011 5:33 am
I think it should be 11/30 (A)
because the balance is 11/30 and hence amount unspent..
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by g.shankaran » Fri May 27, 2011 5:36 am
cans wrote:I think it should be 11/30 (A)
because the balance is 11/30 and hence amount unspent..
SoCan explanation is correct. This is an MGMAT question
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by GMATGuruNY » Fri May 27, 2011 7:01 am
g.shankaran 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?

11/30

29/60

17/30


19/30


11/15
Ans: 11/30 or 19/30?
Balance means the amount that remains.
Used in reference to a bank account, balance means the amount that remains in the account (how much money you have left to spend).
Used in reference to a credit card, balance means the amount that remains to be paid (how much money you still owe).

We can plug in values here.

Let gold limit = 15, let platinum limit = 2*15 = 30.
Gold balance = (1/3)*15 = 5.
Platinum balance = (1/5)*30 = 6.
With gold balance added, increased platinum balance = 6+5 = 11.
Amount of platinum unspent = 30-11 = 19.
Unspent/Limit = 19/30.

The correct answer is D.
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by Ozlemg » Fri May 27, 2011 9:40 am
Actually I spent 15 mins and still could not get how this Q would be solved without plug in any numbers?should not it be like this?

GOlD: x limit, Balance : x/3
Plat: 2x limit, Balance: 2x/5

After transfering the balance of Gold to Plat., x/3 (which is x/6 for a Plat.limit) plus 2x/5 --> 17/30

Where am I wrong?
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by GMATGuruNY » Fri May 27, 2011 9:53 am
Ozlemg wrote:Actually I spent 15 mins and still could not get how this Q would be solved without plug in any numbers?should not it be like this?

GOlD: x limit, Balance : x/3
Plat: 2x limit, Balance: 2x/5

After transfering the balance of Gold to Plat., x/3 (which is x/6 for a Plat.limit) plus 2x/5 --> 17/30

Where am I wrong?
When you said x = the Gold limit, you assigned the variable to the wrong limit. The answer must be in terms of the Platinum limit.

Let P = Platinum limit, (1/2)P = Gold limit.
Then P balance = (1/5)P, Gold balance = (1/3)(1/2)P = (1/6)P.
Combined balances = (1/5)P + (1/6)P = (6/30)P + (5/30)P = (11/30)P.
Thus, fraction of P unspent = P - (11/30)P = (19/30)P.

Plugging in numbers is much safer and likely quicker.
Last edited by GMATGuruNY on Fri May 27, 2011 9:54 am, edited 1 time in total.
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by SoCan » Fri May 27, 2011 9:53 am
Ozlemg wrote:Actually I spent 15 mins and still could not get how this Q would be solved without plug in any numbers?should not it be like this?

GOlD: x limit, Balance : x/3
Plat: 2x limit, Balance: 2x/5

After transfering the balance of Gold to Plat., x/3 (which is x/6 for a Plat.limit) plus 2x/5 --> 17/30

Where am I wrong?
You're defining x as the gold limit (always try to define your variable in relation to what's being asked - in this case it's asking for the remaining credit on the platinum card). You can still solve it this way, but it involves the extra step of redefining your answers in terms of the platinum card.

x/3 + 2x/5 = 11x/15. This means that 11/15 of the spending limit of the gold card is used up. But remember that we care about the platinum card. Since it has double the limit, 11/30 of the platinum card is used up.

You redefined the gold balance in terms of platinum limit by making it x/6, but then you left the platinum balance defined in terms of the gold limit at 2x/5.
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