Quant Review question

[rakaisraka]

This is a quant review question im not able to understand. Cany anyone help.

0ne week a certain truck rental lot had a total of
20 trucks, all of which were on the lot Monday morning.
lf 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

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Hi rakaisraka,

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

[Brent@GMATPrepNow]

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

[Max@Math Revolution]

Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


==> First you need to check one thing.

1) Remember that number of Truck rental lot has 20 trucks altogether.

2) at least=min. Since the question asks for the greatest number, the minimum number of remaining trucks gives us the maximum number of trucks rented. In other words, we need 12 remaining trucks. 13..14 will not work, since 12 is the minimum.

Back to the question,

if we put (trucks rented, trucks returned, trucks remaining)=(a,b,c), then since 50% of the trucks returned, a= 2b and since there are altogether 20 trucks, a+c = 20. Since the remaining trucks is 12, b+c = 12.

(a,b,c)=(24,12,0) <==impossible (since 24+0>20)
(a,b,c)=(22,11,1) <==impossible (since 22+1>20)
(a,b,c)=(20,10,2) <==impossible (since 20+2>20)
(a,b,c)=(18,9,3) <==impossible (since 18+3>20)
(a,b,c)=(16,8,4) <== possible (since 16+4=20 and 8+4=12)
Therefore the answer is B.


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