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# A certain library assesses fines for overdue books as follows. On the

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Intern
Joined: 08 Feb 2008
Posts: 21
A certain library assesses fines for overdue books as follows. On the  [#permalink]

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28 Feb 2010, 11:21
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Difficulty:

25% (medium)

Question Stats:

68% (01:06) correct 32% (01:53) wrong based on 90 sessions

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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

here is my reasoning:

Day 1 \$0.10
Day 2 \$0.20 ( doubled since its lesser that \$0.30)
Day 3 \$0.30 (since the double would be \$0.40>\$0.30)
Day 4 \$0.30 (since the double would be \$0.60>\$0.30)
Total \$0.90

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/a-certain-li ... 92821.html
Senior Manager
Joined: 25 Jun 2009
Posts: 273
Re: A certain library assesses fines for overdue books as follows. On the  [#permalink]

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28 Feb 2010, 11:32
1
divanshuj wrote:
This is frustrating me

A certain library assess fines for overdue books as follow. On the fist day that a book is overdue, the total fine is \$0.10. For each additional day that book is overdue, the total fine is either increased by \$0.30 or doubled, whichever results in the lesser amount. What is the total fine for a book on the fourth day its overdue?

a) \$0.60
b) \$0.70
c) \$0.80
d) \$0.90
e) \$1.00

here is my reasoning:

Day 1 \$0.10
Day 2 \$0.20 ( doubled since its lesser that \$0.30)
Day 3 \$0.30 (since the double would be \$0.40>\$0.30)
Day 4 \$0.30 (since the double would be \$0.60>\$0.30)
Total \$0.90

Day 1 fine = 0.10
Day 2 Fine = 0.20 ( in total) As we doubled it
Day 3 Fine = 0.40 ( Doubled it because after doubling the fine is 0.40 < 0.50 ( .2 + .3)
Day 4 fine = 0.40 + 0.30 = 0.70 ( increased by 0.30)

PS: its asking for the total fine on the 4th day ..!

Hope that helps ..!
Intern
Joined: 22 Nov 2009
Posts: 23
Re: A certain library assesses fines for overdue books as follows. On the  [#permalink]

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01 Mar 2010, 08:34
1
divanshuj wrote:
This is frustrating me

A certain library assess fines for overdue books as follow. On the fist day that a book is overdue, the total fine is \$0.10. For each additional day that book is overdue, the total fine is either increased by \$0.30 or doubled, whichever results in the lesser amount. What is the total fine for a book on the fourth day its overdue?

a) \$0.60
b) \$0.70
c) \$0.80
d) \$0.90
e) \$1.00

C

1st day: 0.1
2nd day: lesser(0.4,0.2) = 0.2
3rd day: lesser(0.5,0.4) = 0.4
4th day: lesser(0.7,0.8) = 0.7
_________________
kudos +1 ?
Intern
Joined: 22 Nov 2009
Posts: 23
Re: A certain library assesses fines for overdue books as follows. On the  [#permalink]

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01 Mar 2010, 08:36
divanshuj wrote:
here is my reasoning:

Day 1 \$0.10
Day 2 \$0.20 ( doubled since its lesser that \$0.30)
Day 3 \$0.30 (since the double would be \$0.40>\$0.30)
Day 4 \$0.30 (since the double would be \$0.60>\$0.30)Total \$0.90

You have to compare b/n adding 0.3 cents to previous day and doubling:
Here is where you are wrong
Day 3 \$0.40 (since the double would be \$0.40<\$0.50)
_________________
kudos +1 ?
Math Expert
Joined: 02 Sep 2009
Posts: 54371
Re: A certain library assesses fines for overdue books as follows. On the  [#permalink]

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26 Aug 2017, 05:49
1
1
divanshuj 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

here is my reasoning:

Day 1 \$0.10
Day 2 \$0.20 ( doubled since its lesser that \$0.30)
Day 3 \$0.30 (since the double would be \$0.40>\$0.30)
Day 4 \$0.30 (since the double would be \$0.60>\$0.30)
Total \$0.90

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)

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/a-certain-li ... 92821.html
_________________
Re: A certain library assesses fines for overdue books as follows. On the   [#permalink] 26 Aug 2017, 05:49
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