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# In a city, 80% households have two-wheeler automobiles and 70% househo

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Re: In a city, 80% households have two-wheeler automobiles and 70% househo [#permalink]
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80% have 2 wheelers and 70% have 4 wheelers.

Assuming that the 70% is all part of the 80%, we are left with 20% that could not have either. Answer is B.
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In a city, 80% households have two-wheeler automobiles and 70% househo [#permalink]
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CONCEPT: Set Theory (Intersection, Maximum/Minimum)

SOLUTION: Best case scenario for “neither” of the vehicles would be when the set of 4-wheelers is entirely a subset of 2-wheelers and hence there is nobody who owns “only "a 4-Wheeler.

Hence (100-80) %=20% is the set of people who own neither a 2-wheeler nor a 4-wheeler.

Thus,observing the options, appropriate choice thus is 0-20% (B)

Hope this helps. Keep studying!
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Re: In a city, 80% households have two-wheeler automobiles and 70% househo [#permalink]
ScottTargetTestPrep wrote:
In a city, 80% households have two-wheeler automobiles and 70% households have four-wheeler automobiles. The percentage of households having neither can vary between which of the following ﬁgures?

A. 0% to 10%

B. 0% to 20%

C. 0% to 30%

D. 0% to 50%

E. 20% to 30%

Source: Experts Global GMAT
Difficulty Level: 600

100 = 80 + 70 - both + neither

100 = 150 - both + neither

At the minimum, both must be 50. In that case neither = 0.

At the maximum, both can be 70. In that case neither = 20.

At the minimum, both must be 50. In that case neither = 0.

Hi, does the minimum case imply that there is total overlap ?
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Re: In a city, 80% households have two-wheeler automobiles and 70% househo [#permalink]
ScottTargetTestPrep wrote:
In a city, 80% households have two-wheeler automobiles and 70% households have four-wheeler automobiles. The percentage of households having neither can vary between which of the following ﬁgures?

A. 0% to 10%

B. 0% to 20%

C. 0% to 30%

D. 0% to 50%

E. 20% to 30%

Source: Experts Global GMAT
Difficulty Level: 600

100 = 80 + 70 - both + neither

100 = 150 - both + neither

At the minimum, both must be 50. In that case neither = 0.

At the maximum, both can be 70. In that case neither = 20.

Hello,
shouldn't the Min and Max figures reversed? My assumption is if 80% have 2 wheelers and 70% have 4 wheelers then the min is the 70% of the people amongst the 80% of the group and the maximum would be two separate batches of 70+80=150.
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Re: In a city, 80% households have two-wheeler automobiles and 70% househo [#permalink]
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Jaya6 wrote:
ScottTargetTestPrep wrote:
In a city, 80% households have two-wheeler automobiles and 70% households have four-wheeler automobiles. The percentage of households having neither can vary between which of the following ﬁgures?

A. 0% to 10%

B. 0% to 20%

C. 0% to 30%

D. 0% to 50%

E. 20% to 30%

Source: Experts Global GMAT
Difficulty Level: 600

100 = 80 + 70 - both + neither

100 = 150 - both + neither

At the minimum, both must be 50. In that case neither = 0.

At the maximum, both can be 70. In that case neither = 20.

Hello,
shouldn't the Min and Max figures reversed? My assumption is if 80% have 2 wheelers and 70% have 4 wheelers then the min is the 70% of the people amongst the 80% of the group and the maximum would be two separate batches of 70+80=150.

Response:

It might be helpful to use actual numbers so that it’s clear how we can determine the minimum and the maximum values of “neither.” Let’s assume that there are 1000 households. According to the given information, 1000 x 0.8 = 800 households have two-wheelers and 1000 x 0.7 = 700 households have four-wheelers.

To determine the maximum number of households that have neither, let’s assume that all 700 households with four-wheelers also have two-wheelers. Notice that this is equivalent to saying that both = 700. In this scenario, the number of households that have either a two-wheeler or a four-wheeler (or both) is 800. Thus, 1000 - 800 = 200 households have neither, which is 20% of all households.

Since the sum of the households with two-wheelers and with four-wheelers is greater than the total number of households, it is possible that neither = 0. We should observe that it is possible to make neither = 0 simply by assuming that 300 households have only two-wheelers, 200 households have only four-wheelers and 500 households have both kinds of vehicles. If the sum of the two groups was less than 1000 --for instance, if there were only 500 households with two-wheelers and 400 households with four-wheelers-- then there would be at least 100 households that have neither because even if we assume that there are no households with both kinds of vehicles, the number of households with either two-wheelers or four-wheelers would have been 500 + 400 = 900. The remaining 1000 - 900 = 100 households must belong to the “neither” group.
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Re: In a city, 80% households have two-wheeler automobiles and 70% househo [#permalink]
Quote:
Response:

It might be helpful to use actual numbers so that it’s clear how we can determine the minimum and the maximum values of “neither.” Let’s assume that there are 1000 households. According to the given information, 1000 x 0.8 = 800 households have two-wheelers and 1000 x 0.7 = 700 households have four-wheelers.

To determine the maximum number of households that have neither, let’s assume that all 700 households with four-wheelers also have two-wheelers. Notice that this is equivalent to saying that both = 700. In this scenario, the number of households that have either a two-wheeler or a four-wheeler (or both) is 800. Thus, 1000 - 800 = 200 households have neither, which is 20% of all households.

Since the sum of the households with two-wheelers and with four-wheelers is greater than the total number of households, it is possible that neither = 0. We should observe that it is possible to make neither = 0 simply by assuming that 300 households have only two-wheelers, 200 households have only four-wheelers and 500 households have both kinds of vehicles. If the sum of the two groups was less than 1000 --for instance, if there were only 500 households with two-wheelers and 400 households with four-wheelers-- then there would be at least 100 households that have neither because even if we assume that there are no households with both kinds of vehicles, the number of households with either two-wheelers or four-wheelers would have been 500 + 400 = 900. The remaining 1000 - 900 = 100 households must belong to the “neither” group.

­
I got the same answer: 10% to 20%.
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Re: In a city, 80% households have two-wheeler automobiles and 70% househo [#permalink]
RenB wrote:
Quote:
Response:

It might be helpful to use actual numbers so that it’s clear how we can determine the minimum and the maximum values of “neither.” Let’s assume that there are 1000 households. According to the given information, 1000 x 0.8 = 800 households have two-wheelers and 1000 x 0.7 = 700 households have four-wheelers.

To determine the maximum number of households that have neither, let’s assume that all 700 households with four-wheelers also have two-wheelers. Notice that this is equivalent to saying that both = 700. In this scenario, the number of households that have either a two-wheeler or a four-wheeler (or both) is 800. Thus, 1000 - 800 = 200 households have neither, which is 20% of all households.

Since the sum of the households with two-wheelers and with four-wheelers is greater than the total number of households, it is possible that neither = 0. We should observe that it is possible to make neither = 0 simply by assuming that 300 households have only two-wheelers, 200 households have only four-wheelers and 500 households have both kinds of vehicles. If the sum of the two groups was less than 1000 --for instance, if there were only 500 households with two-wheelers and 400 households with four-wheelers-- then there would be at least 100 households that have neither because even if we assume that there are no households with both kinds of vehicles, the number of households with either two-wheelers or four-wheelers would have been 500 + 400 = 900. The remaining 1000 - 900 = 100 households must belong to the “neither” group.

­
I got the same answer: 10% to 20%.

­Why 10%?
Consider this: Of 100, 80 people have two wheelers. The other 20 have four wheelers but no 2 wheeler. 50 people have both.
All our constraints are met. People who have None = 0

Alternatively,
100 - None = 80 + 70 - Both
Both = 50 + None

When None = 0, Both = 50 (All good) (Minimum value of None and Both)
When None = 20, Both = 70 (Maximum value of None and Both)

Here is a video on maximising minimising on overlapping sets:
https://youtu.be/oLKbIyb1ZrI

Re: In a city, 80% households have two-wheeler automobiles and 70% househo [#permalink]
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