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The total number of 85 households with at least one pet

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The total number of 85 households with at least one pet [#permalink] New post   05 May 2021, 02:04
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Quantity A
Quantity B
The total number of households with at least one pet
85



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.

Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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The total number of 85 households with at least one pet [#permalink] New post   20 Jun 2021, 01:46
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kumarneupane4344

Refer Below Image

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image.jpg
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Now the catch in the problem is that a household can have only a dog, only a cat, only one other pet, or a combination of these. Like a dog and a cat, a dog and other pet, a cat and other pet or all of them also.
Now if they would have given that a household can have only one pet then total number of households will be number of dogs + number of cats + number of other pets = 25 + 41 + 19 = 85
But, that is not the case. So a household can have a combination of them also.
SO, the total number of households which have at least one pet will be <= 85

=> Quantity A <= Quantity B, which means that we do NOT have sufficient information to answer the question.

So, answer will be D
Hope it helps!
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Re: The total number of 85 households with at least one pet [#permalink] New post   05 May 2021, 22:02
Consider this question in form of sets;
Set Dog, Set Cat, Set Other.

Now if you draw the three sets, you might understand there are many possibilities how they might intersect.

Case #1 :
All three sets are different from one another and do not intersect at all in which case the union and total number of distinctive households will be:
Dog U Cat U Other = 25 + 41 + 19 = 85;
Distinct households = 85;

Case #2 :
It might be possible that Cat is the biggest set which totally includes Dog and Other sets inside of it. In this case the distinct households would be equal to the set Cat:
Distinct households = 41;

More explanation on Case #2 : This happens because it is nowhere mentioned that one household cannot have more than one pet. It might be possible that out of the 41 households who own a cat, 25 also own a dog while 19 own other pets. Hence, the distinct households would only be 41.

This two cases are enough to get to the answer choice D.
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Re: The total number of 85 households with at least one pet [#permalink] New post   05 May 2021, 23:11
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if all are mutually exclusive, then no of household= 25+41+19=85

but in case some are common (one household having both cat and dog for example)-

Under this situation, the no of household must be less than 85.
therefore, D is the answer
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Re: The total number of 85 households with at least one pet [#permalink] New post   20 Jun 2021, 00:40
rx10 KarunMendiratta BrushMyQuant sir , please elaborate this solution.
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Re: The total number of 85 households with at least one pet [#permalink] New post   20 Jun 2021, 01:04
Hey,

This can be solved by venn Diagram. But not much detail is given.

Let's say there is no overlapping in the set. Like - no one has cat and dog both.
So households with at least one pet will be = Those having dogs + Those having cats + Those having other pets = \(25 + 41 + 19 = 85\)

Now what if all the dog owners are also cat owners as well. So households with atleast one pet will be
Those have all dogs & cats + Those have only cats + Those having others = 25 + 16 + 19 = \(60\)

So we can't decide the exact value. Hence \(D\)

kumarneupane4344 wrote:
rx10 KarunMendiratta BrushMyQuant sir , please elaborate this solution.
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Re: The total number of 85 households with at least one pet [#permalink] New post   20 Jun 2021, 17:00
BrushMyQuant wrote:
kumarneupane4344

Refer Below Image

Attachment:
image.jpg


Now the catch in the problem is that a household can have only a dog, only a cat, only one other pet, or a combination of these. Like a dog and a cat, a dog and other pet, a cat and other pet or all of them also.
Now if they would have given that a household can have only one pet then total number of households will be number of dogs + number of cats + number of other pets = 25 + 41 + 19 = 85
But, that is not the case. So a household can have a combination of them also.
SO, the total number of households which have at least one pet will be <= 85

=> Quantity A <= Quantity B, which means that we do NOT have sufficient information to answer the question.

So, answer will be D
Hope it helps!



Perfect explanation Ankit sir!
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Re: The total number of 85 households with at least one pet [#permalink]
20 Jun 2021, 17:00
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