Problem Solving

TariqOmar wrote:- A certain library assesses fines for overdue books as follows. On the first date 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 $0.3 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

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)
$0.70 is the lesser amount

The correct answer is B

Cheers,
Brent

Hi TariqOmar,

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, whichever 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

TariqOmar wrote:- A certain library assesses fines for overdue books as follows. On the first date 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 $0.3 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

On day 1, the fine is $0.10.

On day 2, we have two options:

1) 0.10 + 0.30 = $0.40

2) 0.10 x 2 = $0.20

Since option 2 is the lesser of the 2 fines, the total fine, as of day 2, is $0.20.

On day 3 we have two options:

1) 0.20 + 0.30 = $0.50

2) 0.20 x 2 = $0.40

Since option 2 is the lesser of the 2 fines, the total fine, as of day 3, is $0.40.

On day 4 we have two options:

1) 0.40 + 0.30 = $0.70

2) 0.40 x 2 = $0.80

Since option 1 is the lesser of the 2 fines, the total fine, as of day 4, is $0.70.

Answer: B