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A certain library assesses fines for overdue books as follow

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GMATINSECT
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Re: A certain library assesses fines for overdue books as follow [#permalink] New post   11 Feb 2019, 10:14
Bunuel wrote:
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 either increased by $0.30 or doubled, whichever results in the 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

Notice that, fines are already cumulative: "For each additional day that the book is overdue, the total fine is ..."

1st day fine - 0.1
2nd day fine - 0.1*2 = 0.2 (as doubling gives lower value)
3rd day fine - 0.2*2 = 0.4 (as doubling gives lower value)
4th day fine - 0.4 + 0.3 = 0.7 (as doubling gives higher value we add 0.3 this time)

Answer: B.


Hi Bunuel,
The question states doubling. So aren't we supposed to double the first day's fine ??
Somewhere I'm lost.
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Re: A certain library assesses fines for overdue books as follow [#permalink] New post   11 Feb 2019, 13:23
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Hi GMATINSECT,

The prompt tells us that for each additional day that a book is overdue, the total fine increases in one of two ways:

1) The total fine increases by $0.30

or

2) The total fine is doubled

We're told that whichever of the two options leads to a LOWER total fine is the fine that is administered. From the various explanations, you can see that on the 2nd day and 3rd days, the total fine is doubled (since that would be less of an increase than adding $0.30 on each day). However, on the 4th day, the fine is increased by $0.30 (since that would be less than doubling the total fine).

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Re: A certain library assesses fines for overdue books as follow [#permalink] New post   07 Aug 2019, 10:11
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sandranjeim wrote:
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 either increased by $0.30 or doubled, whichever results in the 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


1st day - $0.10

2nd day - $0.20 or $0.40 (double or add $0.30)
$0.20 is the lesser amount

3rd day - $0.40 or $0.50 (double or add $0.30)
$0.40 is the lesser amount

4th day - $0.80 or $0.70 (double or add $0.30)
$0.70 is the lesser amount

The correct answer is B

Cheers,
Brent
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Re: A certain library assesses fines for overdue books as follow [#permalink] New post   02 Jun 2021, 05:19
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Solution:

The fines charged are already cumulative

=>Fine for the 1st day = $ 0.1

=>Fine for the 2ndday = 0.1*2 = $ 0.2 (as doubling gives lower value than adding $ 0.3 to $ 0.1)

=>Fine for the 3rd day = 0.2*2 = $ 0.4 (as doubling gives lower value than adding $ 0.3 to $ 0.4)

=>Fine for the 4th day = 0.4 + 0.3 = 0.7 (as doubling $0.4 gives higher value as compared to adding $ 0.3 )

(option b)

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Re: A certain library assesses fines for overdue books as follow [#permalink] New post   28 Sep 2021, 21:27
Hello experts Bunuel, chetan2u, jeffrey Miller

I have a query.

Normally we add the value when we are said " increased by something" so in this example why we did not increase the fine as 0.1+0.30=0.4 for successive days.

thanks in adavnce.
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Re: A certain library assesses fines for overdue books as follow [#permalink] New post   28 Sep 2021, 23:02
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kadamhari825 wrote:
Hello experts Bunuel, chetan2u, jeffrey Miller

I have a query.

Normally we add the value when we are said " increased by something" so in this example why we did not increase the fine as 0.1+0.30=0.4 for successive days.

thanks in adavnce.



You are correct and here too increase by means 0.1 +0.3 or 0.4, but doubled gives 0.1*2 or 0.2.
As we are looking for least amount, we take 0.2 and continue the same for next days too.
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Re: A certain library assesses fines for overdue books as follow [#permalink] New post   02 Jun 2023, 02:21
Total day one: 0.1

Total day two: [0.1] + 0.1

Total day three: [0.1 + 0.1] + 0.2

Total day four: [0.1 + 0.1 + 0.2] + 0.3 = 0.7
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Re: A certain library assesses fines for overdue books as follow [#permalink]
02 Jun 2023, 02:21
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