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

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One week a certain truck rental lot had a total of 20 trucks, all of [#permalink]  10 Sep 2010, 03:44
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: one-week-a-certain-truck-rental-lot-had-a-total-of-20-trucks-168062.html
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Re: One week a certain truck rental lot had a total of 20 trucks, all of [#permalink]  10 Sep 2010, 06:21
vanidhar wrote:
truck rental lot had 20 trucks, all in on monday. 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 on 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 states that at least 12 trucks should be on the lot on saturday morning. This means remaining 8 trucks have not been returned to the lot, which is 50% of the 16 trucks which have been rented out. This clearly shows that remaining 4 trucks (not rented) on the lot and 50% returned trucks of 16 (which is 8) equal to number 12 (minimum number required on saturday morning). Henc I will go with option B.

If you take 13 trucks applies the same logic above it shows the maximum number as 14 which is not in option hence our number 16 is confirmed maximum number trucks which could have been rented out during week.

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Re: One week a certain truck rental lot had a total of 20 trucks, all of [#permalink]  10 Sep 2010, 07:22
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vanidhar wrote:
truck rental lot had 20 trucks, all in on monday. 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 on 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.

Hope it's clear.
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Re: One week a certain truck rental lot had a total of 20 trucks, all of [#permalink]  10 Sep 2010, 10:14
I just tested each number in my head..

A) 18 trucks rented means 2 were left and 9 were returned - 11 trucks - no good
B) 16 trucks rented means 4 were left and 8 were returned - 12 trucks - good

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Re: One week a certain truck rental lot had a total of 20 trucks, all of [#permalink]  11 Sep 2010, 13:06
I did same - count them. Though I started with 10 10....10 rented out and 5 returned so count is 15. Not good.

12 rented and 6 returned. So 8+6 on saturday morning = 24...not good

14 ans then 16....

16 rented out - so 4 + 8 on saturday morning.. good answer
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Re: One week a certain truck rental lot had a total of 20 trucks, all of [#permalink]  02 Nov 2010, 23:42
One week a certain truck rental lot had a total 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 that lot that Sunday morning, what is the greatest number of different trucks that could have been rented out during that week?

A.18
B.16
C.12
D.8
E.4
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Re: One week a certain truck rental lot had a total of 20 trucks, all of [#permalink]  02 Nov 2010, 23:46
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Re: One week a certain truck rental lot had a total of 20 trucks, all of [#permalink]  21 Mar 2015, 17:28
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Re: One week a certain truck rental lot had a total of 20 trucks, all of [#permalink]  22 Mar 2015, 04:54
Expert's post
vanidhar 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: one-week-a-certain-truck-rental-lot-had-a-total-of-20-trucks-168062.html
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Re: One week a certain truck rental lot had a total of 20 trucks, all of   [#permalink] 22 Mar 2015, 04:54
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