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GMAT Prep Exam 1- Library Fine

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by nsuen » Sun Jun 12, 2016 5:55 am
Hi-

A certain library assesses fines for overdue books as follows: On the first day that a book is overdue, the total fine is 0.1. For each additional day that the book is overdue, the total fine is either increased by 0.3 or doubled, whichever results in the lesser amount. What is the total fine for a book on the fourth day it is overdue?

My thinking process
Day 1 0.1+ Day 2 0.2 ( because double is lesser than +0.3) , + Day 3 will be 0.4 + Day 4 will be 0.7 ( as this time increased by 0.3 is lesser than doubled) total will be 1.1 but 1.1 is not the answer so I assume it is 0.7 ( Day 1- Day 3) but the question said on the fourth day it is overdue, so I thought it should count the 4th day or there is something wrong with my calculation? I guess it correctly as the answer is 0.7. Thanks!
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by Brent@GMATPrepNow » Sun Jun 12, 2016 6:33 am
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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by [email protected] » Sun Jun 12, 2016 10:15 am
Hi nsuen,

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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by OptimusPrep » Wed Jun 15, 2016 8:13 pm
nsuen wrote:Hi-

A certain library assesses fines for overdue books as follows: On the first day that a book is overdue, the total fine is 0.1. For each additional day that the book is overdue, the total fine is either increased by 0.3 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

My thinking process
Day 1 0.1+ Day 2 0.2 ( because double is lesser than +0.3) , + Day 3 will be 0.4 + Day 4 will be 0.7 ( as this time increased by 0.3 is lesser than doubled) total will be 1.1 but 1.1 is not the answer so I assume it is 0.7 ( Day 1- Day 3) but the question said on the fourth day it is overdue, so I thought it should count the 4th day or there is something wrong with my calculation? I guess it correctly as the answer is 0.7. Thanks!
You are taking the cumulative sum for the fines each days. The rule is given for fines on each day.

Day 1 fine: 0.1
Day 2 fine: 0.1*2 = 0.2
Day 3 fine: 0.2*2 = 0.4 or 0.2+0.3 = 0.5
Since 0.4 < 0.5, fine = 0.4

Day 4 fine: 0.4*2 = 0.8 or 0.4 + 0.3 = 0.7
Since 0.7 < 0.8, fine = 0.7

Correct Option: B
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by Matt@VeritasPrep » Thu Jun 23, 2016 4:45 pm
This one is surprisingly tricky, by the way - I see students miss one similar to it in class a lot - so don't feel bad for struggling at first!
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