prachich1987 wrote:If one of jean's credit cards charges more than 2 % interest each month on any balance,and this month Jean paid more than $17.85 in interest,what is the least possible amount of Jean's balance for this month?

1) $ 357.00
2) $ 357.50
3) $ 892.00
4) $ 892.50
5) $ 893.00

Say the balance in Jean's card for that month is $x, interest rate is r% and interest for this month is $I.

Therefore, x*(r/100) = I => x = 100*(I/r)
Thus to minimize x, we have to minimize I and maximize r.

Now r > 2 and I > 17.85
Therefore minimum possible value of I is something just greater than 17.85 but maximum possible value of r can be anything greater than 2. Let us assume the minimum possible value of I be 17.85.

Thus, minimum possible x = 100*17.85/(Maximum possible r)
As we don't know the maximum possible value of r, we can not uniquely determine minimum possible value of x. Therefore the minimum possible value of x is the minimum value out of the options, i.e. 357.00.

Let's see if that holds.
x = 357.00 and I = 17.85 => r = 100*(I/x) = 100*(17.85/357.00) = 5 > 2
Now remember that we assumed I to be 17.85, but actually it is something just greater than 17.85. In that case also we can maintain x = 357.00 by taking a value of r which is also just greater than 5 and thus more than 2.

Thus our logic holds and least possible amount of Jean's balance for this month is whatever minimum amount is available to us.

he correct answer is A.

prachich1987 wrote:@Anurag:

Thanks for your explanation.
But when I calculate 2% interest on 357,I get a value much lesser than 17.85.
if you could, plz advise what's wrong with HPEngineer's method.

Why should you do that?
Interest is not 2%. It is something more than 2%, which I calculated as something just greater than 5% for $357 balance.

Problem with HPEngineer's method:

• As I have shown in my solution, Balance = Interest/Interest Rate
  Now to minimize balance we have to minimize interest and maximize the interest rate. Now minimum interest and minimum interest rate are available but maximum interest rate is not. What HPEngineer has done is considered 2% as the interest rate (which is minimum interest rate) while calculating minimum balance. Now as interest rate is in the denominator, minimizing it maximizes the expression and thus maximizes balance.

Hope it is clear now.

Note: I think the question should read like the following for the OA to be true and also HPEngineers method

• If one of jean's credit cards charges less than 2% interest each month on any balance,and this month Jean paid more than $17.85 in interest,what is the least possible amount of Jean's balance for this month?

HPengineer wrote:@ anurag

I see your point now... Technically we can take the smallest amount listed from answer choice and since intrest is greater then 2 it could for instance be 20% which would give us a value larger then 17.35 with the lowest balance listed.

Am i with you?

Correct!