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Counting amount of fine everyday

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by utkalnayak » Sat Jan 24, 2015 5:08 pm
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 30 cents or doubled, whichever results in the lesser amount. What is the total fine 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

OA: B
=============================
My approach (which is incorrect) was :
D1: 10 cents
D2: Is 10*2 < 30 => 20 cents
D3: Is (20+10)*2 < 30 => 30 cents
D4: Is (60+10)*2 < 30 => 30 cents

Total : 90 cents. but clearly this is wrong, what is my mistake ?
Thanks,
Utkal
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by Brent@GMATPrepNow » Sat Jan 24, 2015 5:15 pm
utkalnayak 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 30 cents or doubled, whichever results in the lesser amount. What is the total fine 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)
[spoiler]$0.70[/spoiler] is the lesser amount

The correct answer is B

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Brent
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by [email protected] » Sat Jan 24, 2015 5:19 pm
Hi utkalnayak,

This question includes a 'conditional statement' that effects how you're supposed to handle each "step" in the math:

"for each additional day....., the total fine is EITHER increased by 30 cents OR doubled, which results in the LESSER AMOUNT."

Since we're asked to calculate a book that is 4 days overdue, we just have to consider each possible outcome on each day, then choose the one that leads to the "lesser amount"

Day 1: 10 cents

Day 2: 10 + 30 = 40 cents; 10(2) = 20 cents
20 cents is LOWER, so the fine is NOW 20 cents

Day 3: 20 + 30 = 50 cents; 20(2) = 40 cents
40 cents is LOWER, so the fine is NOW 40 cents

Day 4: 40 + 30 = 70 cents; 40(2) = 80 cents
70 cents is LOWER, so the final fine is 70 cents.

Final Answer: B

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Rich
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by Brent@GMATPrepNow » Sat Jan 24, 2015 5:19 pm
utkalnayak 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 30 cents or doubled, whichever results in the lesser amount. What is the total fine 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

OA: B
=============================
My approach (which is incorrect) was :
D1: 10 cents
D2: Is 10*2 < 30 => 20 cents
D3: Is (20+10)*2 < 30 => 30 cents
D4: Is (60+10)*2 < 30 => 30 cents

Total : 90 cents. but clearly this is wrong, what is my mistake ?
The question states that each additional day, the TOTAL fine is EITHER increased by 30 cents OR doubled, whichever is less.

So, for example, on Day 2, the TOTAL fine is EITHER increased by 30 cents (to give us a total of 40 cents) OR doubled (to give us a total of 20 cents). Of the two values (40 cents or 20 cents), 20 cents is the lesser. So, the TOTAL fine as of Day 2 is 20 cents. And so on...

I think you have misread the question.

Cheers,
Brent
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by utkalnayak » Sat Jan 24, 2015 6:54 pm
Thank you Brent, Rich.
I completely misunderstood the phrase "increased by 30 cents". I thought the fine for that day becomes 30 cent, which was the mistake. I guess I should be spending more time on English than on Quants :)

You guys saved my day !
Thanks,
Utkal
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