OG #213 TRUCK RENTAL

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
(8) 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

Hi oquiella,

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