Problem Solving

BTGmoderatorLU wrote:During a Thanksgiving weekend, a car rental company rented seven-tenths of the vehicles with including three fifths of the 4WDs that it had. If 60% of the vehicles are 4WDs, then what percent of the vehicles that were not rented were not 4WDs?

A. 20%
B. 30%
C. 40%
D. 60%
E. 25%

The OA is A.

60% of the vehicles are 4WDs:
60 are 4WDs and 40 are not.

Seven tenths (70%) of the vehicles are rented:
70 rented and 30 not.

Three fifths of the 4WDs were rented:
(3/5)*60 = 36 4WDs were rented and 24 not.

So, out of 30 vehicles that were not rented 24 were 4WDs and 6 not: 6/30 = 20%. Option A.

Please, can anyone explain another way to solve this PS question? Thanks![/b]

Another approach is to use the Double Matrix Method.

This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of vehicles, and the two characteristics are:
- rented or not rented
- 4WD or not 4WD

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

I'll leave it to you to try this approach. Then, once you're familiar with the technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent

BTGmoderatorLU wrote:During a Thanksgiving weekend, a car rental company rented seven-tenths of the vehicles with including three fifths of the 4WDs that it had. If 60% of the vehicles are 4WDs, then what percent of the vehicles that were not rented were not 4WDs?

A. 20%
B. 30%
C. 40%
D. 60%
E. 25%

If we let the total number of cars = 100, then 0.6 x 100 = 60 of the cars are 4WDs. We are given that 0.7 x 100 = 70 cars were rented and 3/5 x 60 = 36 4WD's were rented.

Thus, 100 - 70 = 30 cars were not rented and of those 30 cars, 60 - 36 = 24 were 4WDs. So 30 - 24 = 6 cars that were not rented were not 4WDs.

So we have 6/30 = 1/5 = 20% of the cars that were not rented were not 4WDs.

Answer: A