swerve wrote: ↑Thu Dec 17, 2020 5:34 am
Jevan must paint 3 rooms in a house. Room A can be painted orange, red or green. Room B can be painted orange, white or red. Room C can be painted white, red or green. The 3 rooms cannot all be painted the same color. In how many different ways could Jevan paint the 3 rooms?
A. 24
B. 26
C. 27
D. 63
E. 64
The OA is
B
Source: Magoosh
Take the task of painting the 3 rooms and break it into
stages.
Stage 1: Select a color for Room A
Room A can be painted orange, red or green
So, we can complete stage 1 in
3 ways
Stage 2: Select a color for Room B
Room B can be painted orange, white or red.
So we can complete this stage in
3 ways.
Stage 3: Select a color for Room C
Room C can be painted white, red or green.
So we can complete this stage in
3 ways.
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus paint all 3 rooms) in
(3)(3)(3) ways (= 27 ways)
However, some of these 27 possible outcomes BREAK the condition that
the 3 rooms cannot all be painted the same color.
Given the different color options for each room, we can see that the ONLY way that the 3 rooms can be the same color is when all 3 rooms are painted RED.
Since there is only 1 way to BREAK the given condition, the number of GOOD outcomes = 27 - 1 = 26
Answer: B
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch this video:
https://www.gmatprepnow.com/module/gmat- ... /video/775
You can also watch a demonstration of the FCP in action:
https://www.gmatprepnow.com/module/gmat ... /video/776
Then you can try solving the following questions:
EASY
-
https://www.beatthegmat.com/what-should- ... 67256.html
-
https://www.beatthegmat.com/counting-pro ... 44302.html
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https://www.beatthegmat.com/picking-a-5- ... 73110.html
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https://www.beatthegmat.com/permutation- ... 57412.html
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https://www.beatthegmat.com/simple-one-t270061.html
MEDIUM
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https://www.beatthegmat.com/combinatoric ... 73194.html
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https://www.beatthegmat.com/arabian-hors ... 50703.html
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https://www.beatthegmat.com/sub-sets-pro ... 73337.html
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https://www.beatthegmat.com/combinatoric ... 73180.html
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https://www.beatthegmat.com/digits-numbers-t270127.html
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https://www.beatthegmat.com/doubt-on-sep ... 71047.html
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https://www.beatthegmat.com/combinatoric ... 67079.html
DIFFICULT
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https://www.beatthegmat.com/wonderful-p- ... 71001.html
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https://www.beatthegmat.com/permutation- ... 73915.html
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https://www.beatthegmat.com/permutation-t122873.html
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https://www.beatthegmat.com/no-two-ladie ... 75661.html
-
https://www.beatthegmat.com/combinations-t123249.html
Cheers,
Brent
