A certain library assesses fines for overdue books as follow

Question

A certain library assesses fines for overdue book 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.

$0.60
$0.70
$0.80
$0.90
$1.00

OA:B

i know, this seems simple, but couldnt crack it,,,,,,,,,,,,,i dont know what my brain is thinking,,,,may be a movie or a budlight,,,,,,,

A. $0.60
B. $0.70
C. $0.80
D. $0.90
E. $1.00

Bunuel · Accepted Answer

A certain library assesses fines for overdue book 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.

$0.60
$0.70
$0.80
$0.90
$1.00

OA:B

i know, this seems simple, but couldnt crack it,,,,,,,,,,,,,i dont know what my brain is thinking,,,,may be a movie or a budlight,,,,,,,

A. $0.60
B. $0.70
C. $0.80
D. $0.90
E. $1.00

Notice that, fines are already  cumulative : "For each additional day that the book is overdue, the  total  fine is ..."

1st day fine - 0.1
2nd day fine - 0.1*2 = 0.2 (as doubling gives lower value)
3rd day fine - 0.2*2 = 0.4 (as doubling gives lower value)
4th day fine - 0.4 + 0.3 = 0.7 (as doubling gives higher value we add 0.3 this time)

Answer: B.

Bunuel · Answer

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shrouded1 · Answer

Day 1 : 0.1
Day 2 : Min{0.1x2,0.1+0.3}=0.2
Day 3 : Min{0.2x2,0.2+0.3}=0.4
Day 4 : Min{0.4x2,0.4+0.3}=0.7

And thus B

sandranjeim · Answer

I am a little bit lost. Don't we have to add:

0.1+0.2+0.4+0.7

Thanks

Bunuel · Answer

Fines are already cumulative.

"For each additional day that the book is overdue,  the total fine  is ..."

Hope it's clear.

DaVagabond · Answer

the total fine is  increased by $0.30 or doubled , whichever results in a  lesser amount  - Keep the bolded phrases in mind .. it is quite confusing though ..
Day 1 - $.10 
Day 2- $.10 *2 or $.10+$.30 (Whichever results in a lesser amount), hence its $.20
Day 3 - $.20*2 or $.20+$.30, $.40 as its lesser
Day 4 - $.40*2 or $.40+$.30,  $.70  as this is lesser

So, Ans B.

daviesj · Answer

This one's tricky for sure.
Easy to fall for D.
Here's the solution
 Day 1  =  0.1$ 
 Day 2  ( Double or increase by 0.3$, chose the minimum one)
Option1: Double -> 0.1*2= 0.2$
Option2: Increase by 0.3$ -> 0.1+0.3 = 0.4$
Minimum one:  0.2$ 
 Day 3 
Option1: Double -> 0.2*2=0.4$ 
Option2: Increase by 0.3$ -> 0.2+0.3=0.5$
Minimum one:  0.4$ 
 Day 4  
Option1: Double -> 0.4*2=0.8$
Option2: Increase by 0.3$ -> 0.4+0.3=0.7$
Minimum one:   0.7$   
hence the OA.

PareshGmat · Answer

For the ease of calculation, I removed the decimal point from the question as well as from the OA's

1st day = 10

2nd day = 10*2 = 20 {10+30>10*2}

3rd day = 20*2 = 40 {20+30>20*2}

4th day = 40+30 = 70 {40+30 < 40*2}

Answer = B

shreygupta3192 · Answer

hey bunuel
I followed the wrong strategy earlier.
Do u have more questions like this to practice..
Thanx.

EMPOWERgmatRichC · Answer

Hi ALL,

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

EMPOWERgmatRichC · Answer

HI dina98,

Many Test Takers become overly-obsessed with the implied 'level' of a question, when their focus should really be on whether the question was 'gettable' or not.

Ultimately, you should be measuring a question on a few key points:
1) Could you have gotten the question correct?
2) Was the work involved just too difficult (or was it actually really easy work)?
3) What could you do differently to make the overall process of dealing with the prompt easier (note-taking, organization, Tactics, etc.)?

The math involved in this prompt is remarkably low-level arithmetic, but the real 'test' here is how well you can organize the information involved and follow the instructions that the prompt gives you.

GMAT assassins aren't born, they're made,
Rich

OptimusPrepJanielle · Answer

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

pra1785 · Answer

I still don't get this

day adding 0.30 doubling 1 0.10 0.10 2 0.40 0.20 3 0.70 0.40 4 1 0.80 Where am i going wrong?

EMPOWERgmatRichC · Answer

Hi pra1785,

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

zonebp · Answer

This line in the question has killed me:
"the  total fine  is either increased by $0.30 or doubled."

What I have done:
Day 1: 0.1
Day 2: Double: 0.2
Day 3: Add 0.3
Day 4: Add 0.3
Then add all of them: 0.1+.2+.3+.3 = 0.9
The test writer has successfully tricked me to pick this incorrect option D by just one term in question prompt "Total Fine" 
Please advise how to avoid such traps.

EMPOWERgmatRichC · Answer

Hi zonebp,

The prompt states that the we are supposed to use the fine each day that ends in the "LESSER AMOUNT." Based on the work that you did, on Day 3 you did NOT choose the fine that ended in the lesser amount (doubling .2 to .4 would be less than adding .3 to .2).

Most little mistakes can be avoided by taking the proper notes on your pad.

GMAT assassins aren't born, they're made,
Rich

JeffTargetTestPrep · Answer

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

GMATINSECT · Answer

Hi Bunuel,
The question states doubling. So aren't we supposed to double the first day's fine ?? 
Somewhere I'm lost.

EMPOWERgmatRichC · Answer

Hi GMATINSECT,

The prompt tells us that for each additional day that a book is overdue, the total fine increases in one of two ways:

1) The total fine increases by $0.30

or

2) The total fine is doubled

We're told that whichever of the two options leads to a LOWER total fine is the fine that is administered. From the various explanations, you can see that on the 2nd day and 3rd days, the total fine is doubled (since that would be less of an increase than adding $0.30 on each day). However, on the 4th day, the fine is increased by $0.30 (since that would be less than doubling the total fine).

GMAT assassins aren't born, they're made,
Rich

A certain library assesses fines for overdue books as follow

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A certain library assesses fines for overdue books as follow

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