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 for a book on the fourth day it is overdue?

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 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

This is a question from the GMAT prep software tests 1 and 2 so if you haven’t done those yet go ahead and skip this one so you keep the tests as fresh as possible. First thing to do on this word problem: read carefully. Don’t rush the read. Don’t worry about solving as you’re reading. Yes, think about the context of the questions. Yes, try to digest what the question is driving at. But, again, you don’t have to make all of the inferences all at once at the beginning of the question. They will come with organized setup and follow through.

Next let’s go ahead and define the question. It’s generally the last sentence: What is the total for a book on the fourth day it is overdue?

Then come up with a plan. It looks like a fixed rate + variable rate question and with the variable rate we need to MINIMIZE the total fine: On the first day that a book is overdue, the total fine is $0.10 (fixed rate) + For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled (variable rate). So we just need to follow the rules. We start with a $0.10 fine then we need to add the lesser of $0.30 or doubling the fine.

$0.10

$0.20 is double vs 0.40 which would be the total adding $0.30

$0.40 is double vs $0.50 which would be adding $.30

$0.70 is adding $0.30 vs $0.80 which would be doubling $0.40

The answer is B.

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