Spending Limit - where is the answer?

[anukriti.sinha]

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

So I dont get the answer that is 'supposedly correct' in this question. What am I doing wrong? Here is how I approached the problem:

Gold card limit: x Platinum Card limit: 2x
Gold card balance: (1/3)*(x) Platinum Card balance: (1/5)*(2x)

After transfer, new balance on Platinum card: (x/3) + (2x/5)
= (11x/15)

Therefore, unspent amount on platinum card is (2x) - (11x/15)
= (19x/15)

This answer is NOT in the choices - but I dont see what I did wrong!!! The correct answer apparently is D: 19/30

[amitganguly2k12]

You are correct till here.

Therefore, unspent amount on platinum card is (2x) - (11x/15)
= (19x/15).

portion of her limit on the platinum card that remain's unspent =

(19x/15)/2x = 19/30. (d). (Notice the use of proportions like 1/3rd and 1/5th that should ring bells.) :)

Method-wise its better if you take some values like 300 and 600 respectively.Calculations become easier.

Thanks.

[esledge]

Good diagnosis, amitgvlsijune06, thanks!

Simple error (simple to make with algebra, that is!) of calculating the fraction of the wrong balance.

I totally agree that number-picking is the way to go anytime no absolute numbers are given. Scan such questions for all the portions: ...twice.... 1/3.....1/5. Thus, the smallest possible "smart number" is 2*3*5 = 30.

[vivekcall81]

one thing i could'nt understand here is "unspent amount".
i think it should be equal to the balance on the card or (limit-amount spent)=balance on the card.

mods please explain where i am wrong.
Regards,
ViVeK

[RonPurewal]

one thing i could'nt understand here is "unspent amount".
i think it should be equal to the balance on the card or (limit-amount spent)=balance on the card.

mods please explain where i am wrong.
Regards,
ViVeK

this is an understandable difficulty, as "balance" is one of those english words whose multiple meanings are sometimes almost contradictory to each other. (another example is "sanction" -- to be subject to sanctions is to be punished, but to be sanctioned is to be approved.)

in terms of credit cards, though, the sole meaning of "balance" is the amount that has been spent, but not yet paid off, on the card.

[gpgis1]

'Balance' could also mean amount which is unspent on the credit card i.e. amount of credit one can take further.

[RonPurewal]

'Balance' could also mean amount which is unspent on the credit card i.e. amount of credit one can take further.

while i see your point, that's just not how the word "balance" is used, in the english language, with respect to credit cards. it just isn't.

this is just one of those quirks of the language. (another, for instance, is the fact that "inflammable" and "flammable" mean exactly the same thing.)

[as2764]

thanks for the explanation, @RonP and @amitgvlsijune06. i, too, got this question wrong by choosing 11/30 as the answer, instead of 19/30 = 1-11/30.

if you have an online account for a credit card, or happen to read through your monthly credit card statements, it would say "statement balance" or "outstanding balance" or "balance due" - all of which mean amount *spent* and thus need to be paid to the credit card company. unspent limit is the "available credit line".

thus -- spending limit = balance + UNspent limit

ALSO, the "balance" in a bank account is the exact opposite, meaning the $ available that could be withdrawn, and should not be confused with credit card balances.

[jnelson0612]

Good discussion everyone, and I agree with you, as2764. Those are helpful definitions.