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

Question

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

Salsanousi · Accepted Answer

Please refer to the attachment

The maximum it can be is 20. Because the not 2 wheeler can be a maximum of 20.

So it is between 0 and 20%

Posted from my mobile device

ScottTargetTestPrep · Answer

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.

Answer: B

MsInvBanker · Answer

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.

CrackverbalGMAT · Answer

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!

Devmitra Sen

Keep studying!

Devmitra Sen

Pranjal3107 · Answer

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

Hi, does the minimum case imply that there is total overlap ?

Jaya6 · Answer

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.

ScottTargetTestPrep · Answer

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.

RenB · Answer

I got the same answer: 10% to 20%.
 Bunuel   KarishmaB  can you please help?

KarishmaB · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards