Interest | Problem Solving

Question

If one of Jennifer's credit cards charges more than 2 percent interest each month on any balance, and this month she paid more than $17.85 in interest, which of the following can be the balance for this month?

A. $357.00
B. $357.50
C. $892.00
D. $892.50
E. $893.00

My doubt: I could calculate that 2% of 892.50 is 17.85. However, the interest charged is more than 2% and interest paid is more than 17.85, then how come only E is possible (What if more than 2% = 100% on option A)? Unable to understand what am I missing here.

ArvindCrackVerbal

experian007 · Answer

embyforyou  : The question says card charges  more than 2%  on monthly balance and Jennifer paid  more than $17.85  in interest

So what amount will it be for which 2% is $ 17.85, if we calculate it comes out $892.50 as you also say.

But remember that card charges more than 2% and Jennifer paid more than 17.85 $. So the amount must be greater that 892.50$ for which E is only option left

Hope it helps

iammanas · Answer

That's correct. But see more than 2% interest can be anything right? Let's say that more than 2%, in this case, is 100%. And the amount is 357. Now, interest would be 372 which is more than 17.85. This is the confusion I have. Is there a limit to how much more than 2% can the interest be?

iammanas · Answer

ArvindCrackVerbal

iammanas · Answer

ArvindCrackVerbal

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CrackverbalGMAT · Answer

Embyforyou,
If you take assume that line of thinking, then all the 5 options are possible answers, right? Because some or the other percentage will end up giving you the numbers shown in the 5 options. Then, you have no solution to this question.

That’s never going to be the case on a GMAT type question. You will always have ONE answer.

You have to understand that this problem is testing your ability to deal with boundary values. The most important boundary value here is 2%. You also need to understand that the answer that you pick should remain true for all values more than 2%. Do you think that happens with 357 or 357.50?? Think about it.

We know that the interest charged is more than 2% of the balance and we also know that the interest paid by Jenni is more than 17.85. 
Let’s consider boundary values by taking 2% of balance on one side and 17.85 on the other. So,

\frac{2}{100}  (Balance) > 17.85

which gives us Balance > 892.50 and there is only one answer option like that.

Still not convinced? Pick up a calculator. Type in the following cases and check what happens (make sure that you type the exact number I have typed here)
Find 2.0000000001 % of 892.5 and 2.0000000001% of 893. What do you observe?

That the answer is exactly 17.85 in the first case and 17.86 in the second? Well, there you go. I hope that has convinced you enough to deal with boundary values from now on in similar problems.

Hope that helps!
Arvind.

Interest | Problem Solving

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