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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?

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: 1. Please provide your solutions to the questions; 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.

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.

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

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28 Feb 2014, 06:29

4

This post received 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?

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

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

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

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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. What are your views?

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

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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. What are your views?

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
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Please contact me for super inexpensive quality private tutoring

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

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

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?

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: 1. Please provide your solutions to the questions; 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.
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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?

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: 1. Please provide your solutions to the questions; 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