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09 Jun 2016, 03:46
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B
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Difficulty:
15%
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Question Stats:
80% (01:08) correct
20%
(01:27)
wrong
based on 501
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For dinner at a restaurant, there are x choices of appetizers, y + 1 main courses, and z choices of dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1 dessert for your meal?
A. x + y + z + 1
B. xyz + xz
C. xy + z + 1
D. xyz + 1
E. xyz + 1/2
A. x + y + z + 1
B. xyz + xz
C. xy + z + 1
D. xyz + 1
E. xyz + 1/2
Updated on: 17 May 2021, 07:17
Originally posted by BrentGMATPrepNow on 30 Aug 2020, 06:09.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:17, edited 1 time in total.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:17, edited 1 time in total.
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Bunuel
Take the task of " building of a meal" and break it into stages.
Stage 1: Select an appetizer
Since there are x choices, we can complete stage 1 in x ways
Stage 2: Select a main course
Since there are y+1 choices, we can complete stage 2 in y+1 ways
Stage 3: Select a dessert
Since there are z choices, we can complete stage 3 in z ways
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and build the meal) in (x)(y+1)(z) ways (= xyz + xz ways)
Answer: B
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
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General Discussion
09 Jun 2016, 04:03
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Bunuel
x appetizers,
y + 1 main courses,
z dessert
Required: 1 appetizer, 1 main course, and 1 dessert
Number of ways possible = xC1*(y+1)C1*zC1 {NC1 = N! / (N-1)!*1! = N}
Hence, number of ways = x(y+1)z = xyz + xz
Correct Option: B
