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A certain car dealership offer its newest...

by swerve » Sat Jan 13, 2018 12:05 pm
A certain car dealership offer its newest model in ten exterior and ten interior colors. If the ten interior colors are identical to the ten exterior colors, and the dealership sells avery pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?

A. 45
B. 81
C. 90
D. 10!/2!
E. 10!

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
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by Brent@GMATPrepNow » Sat Jan 13, 2018 12:09 pm
swerve wrote:A certain car dealership offer its newest model in ten exterior and ten interior colors. If the ten interior colors are identical to the ten exterior colors, and the dealership sells avery pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?

A. 45
B. 81
C. 90
D. 10!/2!
E. 10!
Here's one approach:

Take the task of choosing colors break it into stages.

Stage 1: Choose the exterior color
Since there are 10 color choices, we can complete this stage in 10 ways

Stage 2: Choose the interior color
At this point, we can't choose the color that was used for the exterior.
So, we have 9 color options remaining, which means we can complete this stage in 9 ways

By the Fundamental Counting Principle (FCP) we can complete the 2 stages (and thus design the car) in (10)(9) ways (= 90 ways)

Answer: C

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat- ... /video/775

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Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by [email protected] » Sat Jan 13, 2018 12:10 pm
Hi swerve,

We're told that a certain car dealership offer its newest model in ten exterior and ten interior colors, the ten interior colors are identical to the ten exterior colors, and the dealership sells every pair of colors EXCEPT those that would result in a car with an identically colored interior and exterior. We're asked for the number of different color combinations that are possible.

The exterior of the car can be any of 10 colors. Once we choose a color, then the interior can be any of the colors EXCEPT for the exterior color (meaning that there will then be 9 options for the interior.

(10)(9) = 90 color combinations possible.

Final Answer: C

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by Jeff@TargetTestPrep » Mon Jan 29, 2018 11:08 am
swerve wrote:A certain car dealership offer its newest model in ten exterior and ten interior colors. If the ten interior colors are identical to the ten exterior colors, and the dealership sells avery pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?

A. 45
B. 81
C. 90
D. 10!/2!
E. 10!
The colors can be chosen in 10P2 = 10 x 9 = 90 ways.

Alternate Solution:

There are 10 choices for the exterior color. Since the exterior and interior colors cannot be the same, there are 9 choices for the interior color. In total, there are 10 x 9 = 90 ways.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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