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 ?
Counting amount of fine everyday
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- utkalnayak
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1st day - $0.10utkalnayak 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
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
Cheers,
Brent
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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- Brent@GMATPrepNow
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The question states that each additional day, the TOTAL fine is EITHER increased by 30 cents OR doubled, whichever is less.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 ?
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
- utkalnayak
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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 !
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
Utkal