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Car X can come with any of these 5 additional features: sunr
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02 Feb 2020, 04:35
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Car X can come with any of these 5 additional features: sunroof, stereo, tinted windows, leather seats and cruise control. Any car might have none of those, or any one of those, or any combination of more than one, or even all five together.
Quantity A
Quantity B
Number of different combinations possible
25
A. The quantity in Column A is greater B. The quantity in Column B is greater C. The two quantities are equal D. The relationship cannot be determined from the information given
Car X can come with any of these 5 additional features: sunr
[#permalink]
03 Feb 2020, 10:25
3
huda wrote:
Car X can come with any of these 5 additional features: sunroof, stereo, tinted windows, leather seats and cruise control. Any car might have none of those, or any one of those, or any combination of more than one, or even all five together.
Quantity A
Quantity B
Number of different combinations possible
25
A. The quantity in Column A is greater B. The quantity in Column B is greater C. The two quantities are equal D. The relationship cannot be determined from the information given
Take the task of choosing additional features and break it into stages
Stage 1: Determine whether the car will have a sunroof There are only two options here: get the sunroof OR don't get the sunroof So, we can complete stage 1 in 2 ways
Stage 2: Determine whether the car will have a stereo There are only two options here: get the stereo OR don't get the stereo So, we can complete stage 2 in 2 ways
The same set up applies to the remaining three stages...
Stage 3: Determine whether the car will have tinted windows We can complete the stage in 2 ways
Stage 4: Determine whether the car will have leather seats We can complete the stage in 2 ways
Stage 5: Determine whether the car will have cruise control We can complete the stage in 2 ways
By the Fundamental Counting Principle (FCP), we can complete all 5 stages in (2)(2)(2)(2)(2) ways (= 32 ways)
We get: QUANTITY A: 32 QUANTITY B: 25
Answer: A
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
Re: Car X can come with any of these 5 additional features: sunr
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20 Jan 2022, 06:54
Hamzaa wrote:
Hi, Can anyone draw the tree for stages? How it goes upto 5 stages? 0 features: 0C5 = 1 1 feature: 1C5 = 5 2 features: 2C5 = 10 3 features: 3C5 = 10 4 features: 4C5 = 5 5 features: 5C5 = 1
There are five stages because there are five features that can be added to the car. For each feature, we can either have the feature or not have the feature (so there are two ways to complete each stage)
Your solution is also valid (except the combinations are written backwards. It should be 5C2, not 2C5.
In fact, your solution brings up a useful property. Notice that 5C0 + 5C1 + 5C2 + 5C3 + 5C4 + 5C5 = 2^5 = 32
In general, nC0 + nC1 + nC2 + nC3 + . . . . + nCn = 2^n
_________________
Re: Car X can come with any of these 5 additional features: sunr
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23 Feb 2023, 00:11
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