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

Question

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

Can the pundits here please suggest the best possible way to solve this problem?

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

Bunuel · Accepted Answer

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.

Answer: B.

Similar questions to practice:
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Hope it's clear.

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thearch · Answer

B 16
I backsolved this way.
If 18 are rented out, then on Saturday morning you have 2(not rented)+50% of 18=11
If 16 are out, then on Saturday morning you have 4(not rented)+8=12

KarishmaB · Answer

There are numerous ways in which you can solve this question. Brute force method if the relation between rented and non-rented trucks in not very clear:

Monday morning - 20 trucks
Saturday morning - at least 12 trucks
50% trucks rented in the week were returned.
maximum no of trucks rented out = ?

I want to maximize the no. of trucks rented so I say - If 20 trucks were rented (i.e. all of them), then we should have 50% i.e. 10 of them back. But we have more; we have at least 12.
So the no. of trucks rented out must be less than 20 (because they cannot be more than 20).
What about 18? If 18 trucks are rented out, 2 remain in the lot through the week. Out of 18, 9 are returned so total 11 are in the lot. But we need at least 12 in the lot.
Let's go further down and try 16. 4 trucks do not leave the lot. Out of 16, 8 come back so we have 12 trucks in the lot.
(As we keep reducing the number of trucks rented out, the total number of trucks in the lot of Saturday morning keeps increasing. We need to maximize the number of trucks rented out which will be at the minimum possible value of total number of trucks in the lot.)
Therefore, 16 trucks must have been rented out.

Algebraic approach:
As we increase the number of trucks rented, the total number of trucks in the lot on Saturday morning decreases since out of the rented trucks only 50% come back (while all non-rented trucks stay in the lot).
(e.g If none of the 20 trucks are rented, the lot will have 20 trucks on Saturday. If 18 trucks are not rented, the lot will have 19 (18 + 1 rented comes back) trucks on Saturday morning.) 
So maximize the number of trucks rented, we should try to minimize the number of trucks in the lot on Saturday morning i.e. make it 12.
N - Not rented trucks; R - Rented trucks
N + R = 20 
N + R/2 = 12
R = 16

pushkarajg · Answer

I guess the best way to solve this problem in short time is rephrase and/or back solve
1. At least 12 were back on Saturday i.e at max 8 were out on Saturday
2. Now assume 0% instead 50% were returned i.e  at max 8  were rented out  
3. 50% of those 8 were returned = 4  
4. 12+4=16

Hope this helps

KarishmaB · Answer

There are numerous ways in which you can solve this question. Brute force method - if you are not very clear about the relation between rented and non-rented trucks:

Monday morning - 20 trucks
Saturday morning - at least 12 trucks
50% trucks rented in the week were returned.
maximum no of trucks rented out = ?

I want to maximize the no. of trucks rented so I say - If 20 trucks were rented (i.e. all of them), then we should have 50% i.e. 10 of them back. But we have more; we have at least 12.
So the no. of trucks rented out must be less than 20 (because they cannot be more than 20).
What about 18? If 18 trucks are rented out, 2 remain in the lot through the week. Out of 18, 9 are returned so total 11 are in the lot. But we need at least 12 in the lot.
Let's go further down and try 16. 4 trucks do not leave the lot. Out of 16, 8 come back so we have 12 trucks in the lot.
(As we keep reducing the number of trucks rented out, the total number of trucks in the lot of Saturday morning keeps increasing. We need to maximize the number of trucks rented out which will be at the minimum possible value of total number of trucks in the lot.)
Therefore, 16 trucks must have been rented out.

Algebraic approach:
As we increase the number of trucks rented, the total number of trucks in the lot on Saturday morning decreases since out of the rented trucks only 50% come back (while all non-rented trucks stay in the lot i.e. 100% non rented trucks are in the lot on Saturday morning).
(If none of the 20 trucks are rented, the lot will have 20 trucks on Saturday. If 18 trucks are not rented, the lot will have 19 (18 + 1 rented comes back) trucks on Saturday morning.)
So let's make the number of trucks in the lot on Saturday morning equal to 12.
N - Not rented trucks; R - Rented trucks
N + R = 20
N + R/2 = 12
R = 16

PareshGmat · Answer

Answer = (B) 16

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

x = 16 = Answer

b2bt · Answer

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

Answer B
Difficulty level - 650
Time Taken - 3:29

russ9 · Answer

Hi karishma,

This statement is what gets me  "So maximize the number of trucks rented, we should try to minimize the number of trucks in the lot on Saturday morning i.e. make it 12."

Logically speaking, since 50% of the trucks do return back, therefore to maximize the number of trucks rented, we should also maximize the number of returned trucks, at least that's what I put together. Which means that if I want to maximize the number of trucks that were rented, then i need to minimize the number of trucks that were NOT rented, but you are using a different approach?

Can you please explain why my logic is flawed?

KarishmaB · Answer

Why do the number of trucks go down? The ones which are not rented stay there. Out of the ones which are rented, only half come back. So if more trucks are rented, the dent in the number of trucks on Sat morning will be more. 
If no trucks are rented, there will be 20 trucks on Sat morning.
If all trucks are rented, there will be only 10 trucks on Sat morning.

So as you rent more and more trucks out, you will be left with fewer trucks on Sat morning...(ranging from 20 to 10)
So if we minimize the number of trucks on Sat morning, we will maximize the no of trucks rented.

EgmatQuantExpert · Answer

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:

https://s17.postimg.org/ygww2tzvj/TSR.png

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

aguirrestom · Answer

Quick question-- I have noted some of the Quant questions on the Quant OG tend to be worded more poorly or ambiguously than the full comprehensive OG (such as question 110 about a clock), is this because they are older questions. Are current questions that appear on the exam a bit more clear than this, or should we be fully prepared to see this type of phrasing?

EMPOWERgmatRichC · Answer

Hi aguirrestom,

The GMAT has gone through several 'iterations' over the last 15+ years, so what you're noticing is the logical 'progression' of the material - the question writers have become more consistent in the ways that they word questions, the 'testing phase' for each question is more sophisticated (and rigorous) and certain 'patterns' have been phased out over time.

As such, for the most realistic practice, you should be sticking to more recent materials (and avoiding questionable sources for practice content).

To answer your question though, you're not likely to run across many (if any) questions on Test Day that are poorly worded.

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

EMPOWERgmatRichC · Answer

Hi All,

This question can be solved in a couple of different ways. Here's how you can solve it by TESTing THE ANSWERS.

We're told given a number of facts to work with: 
1) A rental lot had a total of 20 trucks on the lot (on Monday). 
2) Of the trucks that were rented out during the week, 50% of the team were returned on (or before) Saturday. 
3) At least 12 trucks were on the last on Saturday.

We're asked for the GREATEST number of trucks that could have been rented out during that week.

Since the prompt asks for the GREATEST number, let's TEST Answer A first...

IF....18 trucks were rented out.... 
20-18 = 2 were NOT rented out 
50%(18) = 9 were returned by Saturday 
2+9 = 11 trucks --> This does NOT match what we were told (there are supposed to be 12 trucks on the lot). 
Eliminate Answer A

Next, let's TEST Answer B....

IF....16 trucks were rented out.... 
20-16 = 4 were NOT rented out 
50%(16) = 8 were returned by Saturday 
4+8 = 12 trucks --> This DOES match what we were told, so this MUST be the answer.

Final Answer:  B

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

ScottTargetTestPrep · Answer

We are given that a truck rental lot had a total of 20 trucks, that 50% of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and that at least 12 trucks were on the lot that Saturday morning.

We can let t = the total number of trucks rented. Then, (20 - t) trucks were not rented at all. Since 0.5t of the trucks were returned, there were (20 - t) + 0.5t = 20 - 0.5t trucks on the lot Saturday morning. Thus, we can create the following inequality:

20 - 0.5t ≥ 12

8 ≥ 0.5t

16 ≥ t

We see that the greatest possible value of t is 16.

Answer: B

BrentGMATPrepNow · Answer

Here's an algebraic approach:

Monday : trucks in lot = 20

Let R = # of trucks rented out from Tuesday to Friday. 
So, # of trucks remaining in lot =  20 - R

50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning  
In other words,  R/2  trucks (half) were returned

Saturday : trucks in lot =  (20 - R)  +  R/2 
=   20 - R/2

There were at least 12 trucks on the lot that Saturday   
So,   20 - R/2  >  12    ....solve for R 
Rearrange to get: 20 - 12  >  R/2
Simplify to get: 8  >  R/2
Multiply both sides by 2 to get: 16  >  R
Since R is less than or equal to 16, the maximum value of R is 16

Answer: B

Cheers,
Brent

Sabby · Answer

Hi,

I used the following logic to solve this question:

We have 20 trucks on Monday and on Saturday morning, we have 12 trucks ( we minimize the number of trucks on saturday to maximize the number of rented trucks)
50% were returned and 50 % were NOT RETURNED
NOT RETURNED = 20-12 = 8
If 8 represents 50% of the rented trucks, then the total number of rented trucks is 16

Answer B)

HarshavardhanR · Answer

Hi folks,

I wanted to highlight something that has been troubling me about this question.

Crux of my problem with the question

Even if some trucks were rented out on Sunday or even Saturday evening, those trucks would be considered as "rented that week".

So, imagine a scenario where, say, 20 trucks were rented that week in total.

Say, 10 trucks were rented and also returned before Saturday morning.
The other 10 trucks were rented out on Saturday evening (or on Sunday).

In such a scenario,

Number of trucks rented that week = 20.
50% of the number of trucks rented that week = 10 trucks were returned to the lot before Saturday morning.
The number of trucks on the lot on Saturday morning = 20 (at the start of the week) - 10 (rented out before Saturday morn) + 10 (returned before Saturday morn) = 20. The condition that this number has to be >=12 (at least 12 trucks) is also being met.

So, given the possibility of such a scenario, is the real correct answer here 20?

Anyway, I just thought of sharing this because I didn't find anyone else talking about this. If I misinterpreted something/made an error somewhere, I am happy to be corrected

.

Cheers!

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ggvaram · Answer

That actually doesn't make sense. If we want the maximum rented trucks then the returned trucks must be more too. 50% of something bigger is more than something of lesser value. Hence if you rent more trucks, 50% of those more trucks returned will also be more. So intuitively you should maximize the returned cars to maximize the number of rented cars.

Bunuel · Answer

It will make perfect sense if you read the question carefully. We are told that '50 percent of the trucks that were rented out during the week were returned to the lot,' so the number of returned trucks is already directly tied to the number of trucks rented. The key is minimizing the trucks left on the lot, which allows us to maximize the rented trucks. The solution is correct, and the doubt you've raised misses the point.

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

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