A certain library assesses fines for overdue books

[Harish Dorai]

A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.10. For each additional day that the book is overdue, the total fine is increased by $0.30 or doubled, whichever results in a lesser amount. What is the total for a book on the fourth day it is overdue?

A) $0.60
B) $0.70
C) $0.80
D) $0.90
E) $1.00

[GMAT 2007]

First day fine = $0.10

2nd day fine = 0.10*2 = 0.20 (doubled or +0.30, whichever results in lesser amount)

So total for the book on 3rd day = 1st day fine + fine calculated on 2nd day = 0.10 + 0.20 = 0.30

Similarly,

3rd day fine = 0.30*2 or 0.30 + 0.30 both results to 0.60.

So total for the book on 4th day = 0.30 + 0.60 = 0.90

The answer is (D)

Hope it helps

GMAT 2007

[Harish Dorai]

I did the same way and got the same answer. But the answer is different.

[GMAT 2007]

What is OA?

[givemeanid]

1st day = 0.1
2nd day = 0.1*2 = 0.2
3rd day = 0.2*2 = 0.4
4th day = 0.4 + 0.3 = 0.7

I don't think the fines are cumulative. On any given day, the fine is calculated for that day without adding all the previous fines.

[Harish Dorai]

$0.7 is the correct answer.

[Satish]

Is that not incorrect? The question specifically says that Total fine is either increased by $0.3 or doubled.

That would mean that the fine is cumulative. Right?

Strange to see that GMAT prep s/w has such discrepancies.

Please correct me if I am wrong.

[RonPurewal]

Is that not incorrect? The question specifically says that Total fine is either increased by $0.3 or doubled.

That would mean that the fine is cumulative. Right?

Strange to see that GMAT prep s/w has such discrepancies.

Please correct me if I am wrong.

you are correct: the fine is cumulative. but you are incorrect in asserting that $0.70 is the wrong answer: that's exactly the answer you get from taking the fine to be cumulative.

if you like sequence notation, then, if a(sub n - 1) is the cumulative fine for all days up to day (n - 1), then a(sub n) is either 2*a(sub n - 1) or a(sub n - 1) + 0.30, whichever is smaller. notice that these fines are 'cumulative' (recursive is a more proper word) because, at all times, you are indeed dealing with the total fine.

were you to look at non-cumulative fines - meaning just the daily fines - you'd see an awfully non-interesting pattern: after day three, it'd just be 0,30 every day.

--

go back and look at the previous post under username 'givemeanid', which is entirely correct. notice that, at each step, you are indeed dealing with the 'total' or 'cumulative' fine to figure out the next value.

--

it also appears that 'givemeanid' him/herself didn't really understand that the fines are already 'cumulative' either. one would never add all the fines in this context; to do so would be utterly ridiculous (it would make about as much sense as adding together 1 + 2 + 3 + ... + 28 to figure out how old you are on your 28th birthday: whatever number you'd get from that would be totally meaningless, as 28 is already your 'cumulative' age on that birthday).

[Guest]

Hi,

In the above post

"were you to look at non-cumulative fines - meaning just the daily fines - you'd see an awfully non-interesting pattern: after day three, it'd just be 0,30 every day. "

I did not quite understand the above statement, even if I do it cumulative way it gives me an uninteresting pattern of 0.30 every day after 3rd day

Day 1 - 0.1
Day 2 - 0.2 (Doubling 0.1)
Day 3 - 0.4 (Doubling 0.2)
Day 4 - 0.7 (Doubling would give 0.8)
Day 5 - 1.0 (Doubling would give 1.6 or 1.4 depending on earlier figure)

So practically this also leads to 0.30 everyday after the third day ..

What is wrong in my thought process ?

Thanks for all your help.

[RonPurewal]

I did not quite understand the above statement, even if I do it cumulative way it gives me an uninteresting pattern of 0.30 every day after 3rd day

if you do it the cumulative way (the correct way), you get 0.1, 0.2, 0.4, 0.7, 1.0, ..., as you wrote in the post above. these are the correct numbers, and, while the pattern is still somewhat uninteresting, it's at least not trivial.
the differences between these values are all 0.3 after a few terms, but you aren't tracking the differences; you're tracking the numbers themselves (as you're supposed to).

if you track non-cumulative daily fines, then you will think that the actual numbers you're tracking are 0.1, 0.1, 0.2, 0.3, 0.3, 0.3, 0.3, ... (the amount of the fine each individual day). that is the wrong approach.

[robertbruder]

Apparently you do not compound the fines.

[RonPurewal]

basically, guys, you just have to follow the directions that are in the problem.

the problem talks about exactly one quantity, which is called "total fine"; there is no mention whatsoever of a daily fine, so there are no daily amounts for you to add together.

so, call this "total fine" = x. once you've done that, you either double x or add 0,30 to x, and then keep whichever yields a smaller result.
then report the 4th value of x.

remember to follow the directions exactly as given; the gmat is, in the main, quite good about giving extremely specific directions.
if you find that the directions are ambiguous, then the most likely interpretation of that finding is that you aren't reading the directions carefully or specifically enough.

[email2sharad]

fine on 1st day overdue = 0.10
fine on 2nd day overdue = 0.10 * 2 (this is lesser than 0.10 +0.30)
fine on 3rd day overdue = 0.20 * 2 (same reason as above)
fine on 4th day overdue = 0.40 + 0.30

hence 0.70

-Sharad

[jnelson0612]

fine on 1st day overdue = 0.10
fine on 2nd day overdue = 0.10 * 2 (this is lesser than 0.10 +0.30)
fine on 3rd day overdue = 0.20 * 2 (same reason as above)
fine on 4th day overdue = 0.40 + 0.30

hence 0.70

-Sharad

Very nice! Exactly the way to think about something like this. :-)