Credit - DS MCAT

[manish9]

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

Unable to get the logic, of how we are getting the answer 19/30, as answer?

thanks,

[gokul_nair1984]

Let the Spending limit on the Gold Card be X
Therefore, Spending limit on the Platinum Card = 2X

Balance on the Gold Card = x/3--Given
Balance on the Platinum Card = 2x/5--Given

After Sally Transfer's the balance from the gold card to her platinum card:
New Balance on the platinum card = x/3 + 2x/5 = 11x/15

Therefore, Unspend amount left on platinum card =2x - 11x/15 =19x/15

Total of 2x.

Therefore 19x/15/2x = 19/30

Makes sense Manish?

[mschwrtz]

Nice work.

You can also do this without the algebra. Whenever there are no actual values in a question, just percents of or fractions of various unknown wholes, you can assign to those unknown wholes whatever numbers you'd like.

Pick smart numbers to make your work easy. In this case, since the denominators are 3 and 5, let's assign to the gold card a limit of 15, which will determine for the platinum card a limit of 30.

So Sally has a balance of 5 on the gold card and 6 on her platinum card. If she transfers the entire balance to her platinum card, she will have a balance of 11 and an 19/30 of her limit still available.

[graphica]

You can plug in values too to make it simpler.

GC limit = 900 (taking 900 since it is easily divisible by 3)
PC Limit = 1800 (double of GC)

Balance on GC= 1/3(900) = 300
Balance on PC = 1/5(1800)=360

If she transfers balance on GC to PC total balance on PC = 660

That means she has 1800-660=1140 spending limit which is unspent.

Therefore:
The portion of her limit on the platinum card will remain unspent = 1140/1800 = 19/30

[mschwrtz]

Right. That's the same approach, just with bigger numbers. Use the easiest numbers that are divisible by all divisors.