It is currently 24 Nov 2017, 06:23

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# One week a certain truck rental lot had a total of 20 trucks

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 42356

Kudos [?]: 133204 [0], given: 12439

One week a certain truck rental lot had a total of 20 trucks [#permalink]

### Show Tags

27 Feb 2014, 07:09
Expert's post
35
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

68% (01:50) correct 32% (02:15) wrong based on 678 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

One week a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?

(A) 18
(B) 16
(C) 12
(D) 8
(E) 4

Problem Solving
Question: 120
Category: Arithmetic; Algebra Percents; Applied problems
Page: 77
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!
[Reveal] Spoiler: OA

_________________

Kudos [?]: 133204 [0], given: 12439

Math Expert
Joined: 02 Sep 2009
Posts: 42356

Kudos [?]: 133204 [0], given: 12439

Re: One week a certain truck rental lot had a total of 20 trucks [#permalink]

### Show Tags

27 Feb 2014, 07:09
Expert's post
17
This post was
BOOKMARKED
SOLUTION

One week a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?

(A) 18
(B) 16
(C) 12
(D) 8
(E) 4

First how to deal with "at least" and "greatest number" part of the question.

General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.

So to maximize the # of trucks rented we should minimize # of trucks at the lot on Saturday. We are told that # of trucks at the lot on Saturday was at least 12, so to minimize it, we should consider this number to be 12 (minimum possible).

Next, the # of trucks at the lot on Saturday, 12, equals to {the # of trucks not rented} plus {half of the # of trucks rented} --> $$(20-R)+\frac{1}{2}R=12$$ --> $$R=16$$.

Or: as "50% of the trucks that were rented out during the week were returned" then another 50% of the trucks that were rented were not returned --> not returned = 20-12=8 trucks, which is 50% of the trucks that were rented --> # of truck were rented = 2*8 = 16.

_________________

Kudos [?]: 133204 [0], given: 12439

Retired Moderator
Joined: 20 Dec 2013
Posts: 185

Kudos [?]: 75 [2], given: 71

Location: United States (NY)
GMAT 1: 640 Q44 V34
GMAT 2: 710 Q48 V40
GMAT 3: 720 Q49 V40
GPA: 3.16
WE: Consulting (Venture Capital)
Re: One week a certain truck rental lot had a total of 20 trucks [#permalink]

### Show Tags

27 Feb 2014, 20:28
2
KUDOS
1
This post was
BOOKMARKED
Rented Trucks (R)

20-R+.5R>=12
R<=16

B
_________________

Kudos [?]: 75 [2], given: 71

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1851

Kudos [?]: 2724 [4], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
One week a certain truck rental lot had a total of 20 trucks [#permalink]

### Show Tags

28 Feb 2014, 01:13
4
KUDOS
1
This post was
BOOKMARKED

Total trucks = 20
Say rented trucks = x
Balance trucks = (20-x)

Half of the rented trucks returned early $$= \frac{x}{2}$$ returned

So now the balance trucks are $$(20-x) + \frac{x}{2}$$

Availability = 12 trucks, so equating

$$20-x + \frac{x}{2} = 12$$

$$\frac{x}{2} = 8$$

_________________

Kindly press "+1 Kudos" to appreciate

Last edited by PareshGmat on 22 Oct 2014, 04:33, edited 1 time in total.

Kudos [?]: 2724 [4], given: 193

Current Student
Joined: 25 Sep 2012
Posts: 283

Kudos [?]: 177 [4], given: 242

Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Re: One week a certain truck rental lot had a total of 20 trucks [#permalink]

### Show Tags

28 Feb 2014, 06:29
4
KUDOS
The difficulty of this problem is the way it has been written. So lets diagonise each sentence and try to make an equation

One week a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning
Total trucks = 20 Day:Monday

If 50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and

Lets say 'x' trucks were rented. We can conclude two things :
No. of trucks remaining in lot = 20 - x Day:unknown
No. of trucks returned to lot = 0.5x Day: Various days (at this point we get a hint that days might not be important)

if there were at least 12 trucks on the lot that Saturday morning
No. of truck in lot >= 12 Day:Saturday

what is the greatest number of different trucks that could have been rented out during the week?

No. of trucks rented out i.e. x

It should be fairly easy to analyze

20-x + 0.5x >= 12
20 -0.5x >= 12
0.5x =< 8
x =< 16

Difficulty level - 650
Time Taken - 3:29

Kudos [?]: 177 [4], given: 242

Retired Moderator
Joined: 29 Oct 2013
Posts: 286

Kudos [?]: 491 [0], given: 197

Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Re: One week a certain truck rental lot had a total of 20 trucks [#permalink]

### Show Tags

20 May 2014, 13:06
I mean this is quite obvious, but has anyone else also noticed that we could solve this problem far more quickly if we just plug in answer choices
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Kudos [?]: 491 [0], given: 197

Current Student
Joined: 25 Sep 2012
Posts: 283

Kudos [?]: 177 [0], given: 242

Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Re: One week a certain truck rental lot had a total of 20 trucks [#permalink]

### Show Tags

20 May 2014, 22:32
MensaNumber wrote:
I mean this is quite obvious, but has anyone else also noticed that we could solve this problem far more quickly if we just plug in answer choices

I think "plugging choices" is based upon how comfortable you are in any topic and it's the best method if you, indeed, are comfortable.

Kudos [?]: 177 [0], given: 242

Retired Moderator
Joined: 29 Oct 2013
Posts: 286

Kudos [?]: 491 [0], given: 197

Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Re: One week a certain truck rental lot had a total of 20 trucks [#permalink]

### Show Tags

20 May 2014, 23:17
b2bt wrote:
MensaNumber wrote:
I mean this is quite obvious, but has anyone else also noticed that we could solve this problem far more quickly if we just plug in answer choices

I think "plugging choices" is based upon how comfortable you are in any topic and it's the best method if you, indeed, are comfortable.

Youre right. I am not comfortable with 'plugging choices' myself and I learning this important skill. I could save the day if you get stuck or running out of time
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Kudos [?]: 491 [0], given: 197

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 746

Kudos [?]: 2169 [4], given: 123

Re: One week a certain truck rental lot had a total of 20 trucks [#permalink]

### Show Tags

12 May 2015, 05:30
4
KUDOS
Expert's post
This problem seems difficult at the first glance because of the lengthy sentences in which the information has been conveyed. In questions like this, it's a good idea to try and represent the given information visually as you go through each sentence of the question. Here's one mode of visually representing the information given here:

The trucks on the lot on the Saturday morning = (Trucks that were not rented) + (Trucks that were rented and returned by Saturday)
= $$(20-r) + (\frac{r}{2})$$

As given:

$$(20-r) + (\frac{r}{2})$$ > = 12

Upon solving this inequality, we get: r < = 16

Thus, the maximum possible number of rented trucks = 16

Hope this was useful!

Japinder
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Kudos [?]: 2169 [4], given: 123

Director
Joined: 10 Mar 2013
Posts: 591

Kudos [?]: 482 [0], given: 200

Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Re: One week a certain truck rental lot had a total of 20 trucks [#permalink]

### Show Tags

02 Nov 2015, 03:04
Rented=x
Returned=0,5x
Not Returned=0,5x
20-0,5x(not returned)=12
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Kudos [?]: 482 [0], given: 200

Intern
Joined: 06 Oct 2012
Posts: 27

Kudos [?]: 2 [0], given: 80

Location: India
GMAT 1: 590 Q47 V25
GMAT 2: 710 Q49 V38
GPA: 3
One week a certain truck rental lot had a total of 20 trucks [#permalink]

### Show Tags

12 Sep 2016, 09:11
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

One week a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?

(A) 18
(B) 16
(C) 12
(D) 8
(E) 4

Problem Solving
Question: 120
Category: Arithmetic; Algebra Percents; Applied problems
Page: 77
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

I tried the plug and play approach (it just came to my mind first instead of the conventional one)

If we assume all 20 truck were out, then only 10 truck would have returned Saturday morning.

But we know that at least 12 truck were there on a Saturday morning,

We also know that even number of trucks left else 50% of them could not return (you cannot return half truck can you )

so again, moving to next possible number:

assume 2 were not rented and 18 were rented. On Saturday morning = 2+9= 11

ahh still not there but close:

assume 4 were not rented this time and 16 were rented. On Saturday morning trucks = 4(not rented) + 8(16\2) = 12 -> this is our guy. Note that we need to find max number of truck rented, if we go ahead in the flow i.e 6 were not rented and 14 were (well doesn't matter because 14 is anyways less than 16).

So 16 is the answer, beware of the trap answer 8! (8 were returned but rented were 8*2 and not 8).

thanks.
_________________

A river cuts through rock, not because of its power, but because of its persistence - Never Give up.

Kudos [?]: 2 [0], given: 80

Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 203

Kudos [?]: 18 [0], given: 453

Re: One week a certain truck rental lot had a total of 20 trucks [#permalink]

### Show Tags

16 Oct 2017, 15:19
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

One week a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?

(A) 18
(B) 16
(C) 12
(D) 8
(E) 4

Problem Solving
Question: 120
Category: Arithmetic; Algebra Percents; Applied problems
Page: 77
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

this problem can be elegantly paraphrased as:

total number of trucks - number of trucks rented out + number of trucks returned = 12

cheers

thanks

Kudos [?]: 18 [0], given: 453

Re: One week a certain truck rental lot had a total of 20 trucks   [#permalink] 16 Oct 2017, 15:19
Display posts from previous: Sort by