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

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Re: One week a certain truck rental lot had a total of 20 trucks, all of [#permalink] New post   16 Feb 2018, 10:24
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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


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
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Re: One week a certain truck rental lot had a total of 20 trucks, all of [#permalink] New post   05 Nov 2020, 09:11
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cloaked_vessel wrote:
One week, a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 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 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


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
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Re: One week a certain truck rental lot had a total of 20 trucks, all of [#permalink] New post   17 Nov 2020, 00:08
Let R = the No. of trucks rented out during the Week

Let N = the No. of trucks that remained on the Lot

We are told in the beginning, there are 20 trucks, some of which are Rented out, some of which stay on the Lot

R + N = 20


Furthermore, 50% (1/2) of the Rented Out Trucks are returned by Saturday morning and there is AT LEAST 12 Trucks on the Lot Saturday Morning

Trucks on Lot Saturday Morning = (1/2)R + N >/= 12

The Amount of Trucks NOT Rented out = N = (20 - R)

(1/2)R + (20 - R) >/= 12

----multiply both sides of the inequality by *2-----

R + 40 - 2R >/= 24

-R >/= -16

----Multiply both sides of the inequality by * (-)1-----

R </= 16

16 is the MAX No. of different trucks that could be Rented out during the week

-B-


or you could plug in numbers starting with -A- and see which could work
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One week a certain truck rental lot had a total of 20 trucks, all of [#permalink] New post   24 Dec 2020, 04:47
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)
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Re: One week a certain truck rental lot had a total of 20 trucks, all of [#permalink] New post   01 Apr 2021, 23:38
thearch wrote:
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


This is how I approached it as well.

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Re: One week a certain truck rental lot had a total of 20 trucks, all of [#permalink] New post   04 Apr 2021, 01:37
Sabby wrote:
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)


Hey, Sabby :)
I share your point, alike solution
x/2 is the number of trucks not returned back
Then,
20 - x/2=12
8 = x/2
x =16
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Re: One week a certain truck rental lot had a total of 20 trucks, all of [#permalink] New post   18 May 2022, 02:56
Hello experts,

Is this method correct;

Let x be the number of trucks that were rented out
50/100x=12
x=24
We only have 20 tho. So there is an overlap of 4. Hence answer should be 20-4=16

Posted from my mobile device
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Re: One week a certain truck rental lot had a total of 20 trucks, all of [#permalink] New post   10 Feb 2024, 00:21
­n = not rented
r = rented

n+r = 20 ->1st equation

n + r/2 >= 12 ->2nd equation

1st equation in second

(20 - r) + r/2 >= 12
20 -r/2 >= 12
-r/2 >= -8
r/2 <= 8
r <= 16

we need maximum r(rented)
therefore r = 16.
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Re: One week a certain truck rental lot had a total of 20 trucks, all of [#permalink]
10 Feb 2024, 00:21
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