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One week a certain truck rental lot had a total of 20 trucks
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05 Feb 2020, 07:43
05 Feb 2020, 07:43
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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?
(A) 18
(B) 16
(C) 12
(D) 8
(E) 4
(A) 18
(B) 16
(C) 12
(D) 8
(E) 4
Re: One week a certain truck rental lot had a total of 20 trucks
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05 Feb 2020, 23:09
05 Feb 2020, 23:09
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Asif123 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 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
(A) 18 (B) 16 (C) 12 (D) 8 (E) 4
On my first try answered it wrong.
A great example of how relatively simple problem can be complicated by tricky wording. So, it needs to be approached in small logical steps.
IF R – rented trucks and N - not rented trucks then:
R + N = 20
If 50% of trucks that were rented are back by the end of the week there are over 12 trucks there then:
0.5R + N = 12 (or more)
On the one hand N = 20 – R
On the other hand N = 12 (or more) – 0.5R
20 – R = 12 (or more) - 0.5R
0.5R = 8 (or less)
R = 16 (or less)
So, the maximum number of trucks is 16.
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Re: One week a certain truck rental lot had a total of 20 trucks
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05 Nov 2020, 08:11
05 Nov 2020, 08:11
2
Asif123 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 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
(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
