Problem Solving

one day a car rental agency rented 2/3 of its cars, including 3/5 of its cars with CD players. if 3/4 of its cars have CD players, what percentage of the cars that were not rented had CD players ?

a. 10%
b. 35%
c. 45 %
d. 66.7%
e. 90%

i gt 45% but the answer given is E
i dun understand

thanks for helping

Let's assume they have 60 cars.

This means that 20 of the cars were NOT rented.

Meanwhile, we also know that 4/5 of their cars have CD players... So 45 (4/5*60) cars have CD players.

Given that 3/5 of it's CD player equipped cars were rented, we know that they currently have 2/5 left. 2/5*45 = 18.

The question asks us to find the percentage of all remaining (not rented) cars that have CD players... so 18/20 = 90/100 = 90%

hi egybs,

your explanation is correct but there are some typos..

Here is rewritten explanation;

Assume total cars = 60

Rented = (2/3) * 60 = 40; Not Rented = 20

Cars with CDs = (3/4) * 60 = 45,
Cars Rented with CDs = (3/5) * 45 = 27

Cars Not Rented with CDs = 45 - 27 = 18

% of Cars with CDs Not Rented to Cars Not Rented = (18/20) * 100 = 90%

Cheers

oops... i gotta reread what i write... thx

I don't get it...
I go over and over again that problem and I keep having the same result..35% (B)
Is there any other solution other than assuming that we have 60 cars?
Can someone pls enlighten me?

Malolo355 wrote:I don't get it...
I go over and over again that problem and I keep having the same result..35% (B)
Is there any other solution other than assuming that we have 60 cars?
Can someone pls enlighten me?

Here's my calculation.. sorry i assumed 120.. so all the figures for 60 would be half of 120.

Don't get hung up on the 60. After a brief look at the answer choices, you don't need to be precise here. My first move was to pick 100. The other approaches actually end up easier, but here's another look since you're still puzzled.



After picking 100 for the total, you can calculate all the numbers in white based on information in the stimulus. Again, since we don't need to be precise, 66 is close enough to 2/3rds of 100

From there, you are able to populate all the fields in yellow (again, 34 is close enough to 1/3 of 100). Now that we have our double matrix fully populated, let's double check that we're answering the right question. I think this is where you've been getting caught up.

We want "not rented cars with CD players" as a percentage of "total not rented cars". Referring to the table, that's 30 / 34. Hopefully it's clear that 30 / 34 (or 15/17) is closest to 90%.

Again, seeing the other approaches, picking 60 comes out much cleaner and I would advise that approach for this problem. Just make sure you're answering the right question and you should be fine!

Cheers

Malolo355 wrote:I don't get it...
I go over and over again that problem and I keep having the same result..35% (B)
Is there any other solution other than assuming that we have 60 cars?
Can someone pls enlighten me?

charmaine wrote:one day a car rental agency rented 2/3 of its cars, including 3/5 of its cars with CD players. if 3/4 of its cars have CD players, what percentage of the cars that were not rented had CD players ?

a. 10%
b. 35%
c. 45 %
d. 66.7%
e. 90%

This is an EITHER/OR group problem.
Every car EITHER was rented OR was not.
Every car EITHER has a CD player OR does not.
For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data.

Let R = rented, NR = not rented, CD = CD player, NCD = no CD player.
In the grids below, the entries in any given row or column must add up to the TOTAL of that row or column.

Let the total = the LCM of the denominators in the problem (3, 4, 5) = 60:


Now complete the grid step by step.
Calculate the EASIEST values first.

Rented 2/3 of its cars.
3/4 of its cars have CD players.


Rented 3/5 of its cars with CD players.
Thus, of the 45 cars with CD players, the number rented = (3/5) * 45 = 27, yielding the following grid:


Thus:
(not rented with CD players)/(total not rented) = 18/20 * 100 = 90%.

The correct answer is E.

Thanks everyone! I found the cross tabulation table really helpful..
It seems that i couldn't have the result simply beacuse i didn't do (notRented with Cd / 1:3 total cars)
Thanks again!