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PS - MGMAT Credit CARD LIMIT

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siddhans: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Sun Aug 22, 2010 2:55 pm

by siddhans » Wed Jun 22, 2011 1:33 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?

11/30
29/60
17/30

19/30
11/15

Can someone please tell me why is this wrong?
Let 'x' be the limit on her gold card
'2x' be the limit on her platinum card

Bal(gold)= x/3

Bal(platinum)=2x/5

After balance was transferred

Bal on plat => x/3 + 2x/5 = 11x/15

Amt unspent = 2x - 11x/15 = 19x/15.... but OA has base 30 ??? hOw do you get that ???

i got E but OA D

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Source: Beat The GMAT — Problem Solving | Wed Jun 22, 2011 1:33 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Jun 22, 2011 1:55 am

siddhans 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

Can someone ans these questions?

1) Is balance = unspent ??? So i have a limit of 1000 and if i spent 200$ then my balance is 800$ which is the unspent portion?

2)
Can someone please tell me why is this wrong?
Let 'x' be the limit on her gold card
'2x' be the limit on her platinum card

Bal(gold)= x/3

Bal(platinum)=2x/5

After balance was transferred

Bal on plat => x/3 + 2x/5 = 11x/15

i got E but OA D

Balance means the amount remaining.
In reference to a credit card, balance means the amount remaining to be paid; in other words, the amount owed.

In your approach, x=gold spending limit.
Thus, you determined the following:
11/15 = (amount owed)/(gold limit)

Since the platinum spending limit is twice the size:
11/30 = (amount owed)/(platinum limit)

Thus, fraction unspent = 19/30.

Easiest approach is to plug in:

Let G = gold spending limit, P = platinum spending limit.
Let G = 15 and P = 30.
G balance = 1/3 * 15 = 5.
P balance = 1/5 * 30 = 6.
Combined balances = 5+6 = 11.
Amount of P unspent = 30-11 = 19.
Fraction unspent = 19/30.

The correct answer is D.

Last edited by GMATGuruNY on Wed Jun 22, 2011 2:00 am, edited 1 time in total.

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siddhans: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Sun Aug 22, 2010 2:55 pm

by siddhans » Wed Jun 22, 2011 1:57 am

Thanks Gmatguru ,

but can you also explain why is this wrong?

Let 'x' be the limit on her gold card
'2x' be the limit on her platinum card

Bal(gold)= x/3

Bal(platinum)=2x/5

After balance was transferred

Bal on plat => x/3 + 2x/5 = 11x/15

Amount unspent = 2x - 11x/15 = 19x/15 ...How do you get base 30???? I just dont get it

Last edited by siddhans on Wed Jun 22, 2011 2:00 am, edited 1 time in total.

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Wed Jun 22, 2011 2:00 am

siddhans wrote:Thanks Gmatguru ,

but can you also explain why is this wrong?

Can someone please tell me why is this wrong?
Let 'x' be the limit on her gold card
'2x' be the limit on her platinum card

Bal(gold)= x/3

Bal(platinum)=2x/5

After balance was transferred

Bal on plat => x/3 + 2x/5 = 11x/15

Amount unspent = 2x - 11x/15 = 19x/15 ...How do you get base 30???? I just dont get it

Hi,
fraction is (19x/15)/2x = 19/30

Cheers!

Things are not what they appear to be... nor are they otherwise

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siddhans: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Sun Aug 22, 2010 2:55 pm

by siddhans » Wed Jun 22, 2011 2:17 am

what fraction and how did we get fraction here now??

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Wed Jun 22, 2011 2:21 am

siddhans wrote:what fraction and how did we get fraction here now??

what portion of her limit on the platinum card will remain unspent?
You have got the value as 19x/15 right?
You have considered '2x' the limit on platinum card.
So portion = (19x/15)/2x = 19/30

Cheers!

Things are not what they appear to be... nor are they otherwise

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vishu1414: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Jan 04, 2011 10:43 pm

by vishu1414 » Wed Jun 22, 2011 2:22 am

Balance mean - Amount outstanding ,which you have to PAY still!
So Amount unspent = (2x)-[Balance remaining] = 2x -11x/15=19x/15

Ratio = 19x/15 * 2x =19/30

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Jun 22, 2011 5:06 am

siddhans wrote:Thanks Gmatguru ,

but can you also explain why is this wrong?

Let 'x' be the limit on her gold card
'2x' be the limit on her platinum card

Bal(gold)= x/3

Bal(platinum)=2x/5

After balance was transferred

Bal on plat => x/3 + 2x/5 = 11x/15

Amount unspent = 2x - 11x/15 = 19x/15 ...How do you get base 30???? I just dont get it

Your equation mixes the two limits: 2x - 11x/15 = PLATINUM limit - fraction spent of the GOLD limit.

To avoid this confusion, put everything in terms of the platinum limit:

Let P = platinum limit.
Then gold limit = P/2.
Balance on gold = (1/3)(P/2)= P/6.
Balance on platinum = P/5.
Balances combined = P/6 + P/5 = (11/30)P.
Thus, fraction unspent = P - (11/30)P = (19/30)P.

But I see no advantage to algebra here. Plugging in is both safer and faster. It would be virtually impossible to answer this question incorrectly if you plugged in numbers (as long as you understood the meaning of the word balance).

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tapanu: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Thu Apr 28, 2011 12:45 am; Thanked: 1 times

by tapanu » Wed Jun 22, 2011 7:35 am

Let Gold limit be 90 than
Platinum card limit - 180

Balance in GOld card - 30
Balance in platinum - 36

After transfer -
Balance in platinum - 66

Amount remained unspent - 180 -66 = 114

Fraction unspent - 114/180 = 19/30

The will to win is worthless if you do not have the will to prepare.

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edvhou812: Master | Next Rank: 500 Posts; Posts: 143; Joined: Sat Nov 06, 2010 9:06 pmFollowed by: 1 member; Thanked: 10 times

by edvhou812 » Wed Jun 22, 2011 7:41 pm

Pick number that is multiple of 5 and 3. I picked 1,500 and made that the Gold balance.

Gold Limit: 1,500
Platinum Limit: Gold*2 = 3,000

Gold Balance: 1,500*1/3 = 500
Platinum Balance: 3000*1/5 = 600

Platinum Balance After Transfer 500+600 = 1,100

1,100/3,000 = 11/30 Fraction of Platinum's available balance: 1-11/30 = 19/30

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