Problem Solving

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

Cheers,
Brent

baalok88 wrote:Hi,
Can somebody tell me what went wrong with my approach in solving the attached question?

Thanks!

On the 4th day, you have $0.80 or $1.00
It should be $0.80 or $0.70 (add $0.30)

Hi baalok88,

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

baalok88 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 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

We need to determine the total amount of a fine for a book that is 4 days overdue. Let's determine each fine levied for when the book is overdue 1, 2, 3, or 4 days.

1 day overdue: $0.10

2 days overdue: The lesser of ($0.10 + $0.30 = $0.40) or (2 x $0.10 = $0.20)

Thus, the total fine for a book that is 2 days overdue is $0.20.

3 days overdue: The lesser of ($0.20 + $0.30 = $0.50) or (2 x $0.20 = $0.40)

Thus, the total fine for a book that is 3 days overdue is $0.40.

4 days overdue: The lesser of ($0.40 + $0.30 = $0.70) and (2 x $0.40 = $0.80)

Thus, the total fine for a book that is 4 days overdue is $0.70.

Note that the problem says the "total fine" is either increased by $0.30 or doubled. That's why, for each day's second calculation, we didn't need to add the previous day's fine. If you don't read carefully, you might end up doubling the fine and adding it to the previous day's fine.

Answer: B