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.
