Percentage problem-tricky question, PLS HELP

Question

If one of Jean's credit cards charges more than 2 percent 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?
A) $357.00 B)357.50 C)892.00 D)892.50 E)893.50

OA is E. And this is how they would have solved:

Let the balance be B and interest paid is I (I>2% from the highlighted clause). So we form an equation B*I>17.85 and keeping I as 2% we could get the base line or minimum value for B, so B>892.50 and hence we select E as the answer.

But this is my doubt: value of I can be anything greater than 2%, let it be 3%. then B*3/100>17.85 or B>595$. As i increase I, the least possible value on B keeps further decreasing, making either this highlighted section wrongly worded or I am going in the wrong direction.

Pls help me figure this out...

mathewmithun · Answer

Just an after thought, if the question was to find maximum possible amount of Jean's balance, I guess the solution provided and the OA sufficed. Oh God, I am seriously confused!!! Pls help me folks...

Brent@GMATPrepNow · Answer

I think there are a few issues with the question.
If the balance is $892.50, then 2% interest is exactly $17.85 . . . fine.
We're told that the interest is more than 2%, and Jean paid more than $17.85 in interest.
So, perhaps the interest is 2.0001% and Jean paid $17.86, then the balance was $892.96 (approx).
Perhaps the question's author is discounting any balances (or any interests) that don't result in whole cents. However, I don't think this is an issue in real life (some rounding occurs).

So, given all of this, I don't think we can conclude that $893.50 (E) is the least possible amount of Jean's balance.

What's the source?

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Brent@GMATPrepNow · Answer

mathewmithun wrote:If one of Jean's credit cards charges more than 2 percent 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?
A) $357.00 B)357.50 C)892.00 D)892.50 E)893.50

Hold the phone.
I just found the original question, and it doesn't say "What is the least possible amount of Jean's balance for this month?" The question says, "Which of the following could be Jean's balance for this month?"

So, if the balance is $892.50, then 2% interest is exactly $17.85.
Since we're told that the interest is more than 2%, and Jean paid more than $17.85 in interest, then the balance must be greater than $892.50, in which case E is the correct answer.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

mathewmithun · Answer

Brent@GMATPrepNow wrote: Hold the phone.
I just found the original question, and it doesn't say "What is the least possible amount of Jean's balance for this month?" The question says, "Which of the following could be Jean's balance for this month?"

So, if the balance is $892.50, then 2% interest is exactly $17.85.
Since we're told that the interest is more than 2%, and Jean paid more than $17.85 in interest, then the balance must be greater than $892.50, in which case E is the correct answer.

Cheers,
Brent

Hi Brent, The source was GMAT princeton review 1012 practice question.
Brent correct me if I am wrong: interest paid by Jean=balance*interest percent which is greater than $17.85. Interest is more than 2%,say 2.5%. so balance*2.5/100>17.85 therefore balance>1785/2.5, which means balance>$714. In fact, when we keep increasing the interest percentage, the balance keeps decreasing and so all the choices can fall in the possible balance range. Example, in the above question since we get balance>714, choice C D and E are possibilities. And i am sure if we increase interest % to a higher value, choice A to E will fall in the range.

Brent@GMATPrepNow · Answer

mathewmithun wrote: Hi Brent, The source was GMAT princeton review 1012 practice question.
Brent correct me if I am wrong: interest paid by Jean=balance*interest percent which is greater than $17.85. Interest is more than 2%,say 2.5%. so balance*2.5/100>17.85 therefore balance>1785/2.5, which means balance>$714. In fact, when we keep increasing the interest percentage, the balance keeps decreasing and so all the choices can fall in the possible balance range. Example, in the above question since we get balance>714, choice C D and E are possibilities. And i am sure if we increase interest % to a higher value, choice A to E will fall in the range.

Hmmm, I think you're absolutely right.

In fact, it could be the case that the balance is $1, and the interest is 1800%, in which case the interest is $18.00 (which is greater than $17.85).
So, it seems that, as you state, the correct answer could be any of A to E.

Great catch!

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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