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465 pet owners were surveyed to determine whether they owned
[#permalink]
09 Sep 2020, 10:56

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Question Stats:

465 pet owners were surveyed to determine whether they owned cats or dogs. 355 said they had at least one cat and 260 said they had at least one dog. Assuming that every couple surveyed had at least one cat or dog, which of the following statements must be true?

Indicate all such statements.

A. More than half of the cat owners are also dog owners

B. More than half of the dog owners are also cat owners

C. None of the pet owners have both cats and dogs

Indicate all such statements.

A. More than half of the cat owners are also dog owners

B. More than half of the dog owners are also cat owners

C. None of the pet owners have both cats and dogs

Re: 465 pet owners were surveyed to determine whether they owned
[#permalink]
09 Sep 2020, 10:56

Expert Reply

Post A Detailed Correct Solution For The Above Questions And Get A Kudos.

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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!

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Re: 465 pet owners were surveyed to determine whether they owned
[#permalink]
08 Mar 2021, 16:12

2

1

Total = 465

Cats = 355

Dogs = 260

Total = C + D - (C&D)

More than half of the cat owners are also dog owners

(C&D) = 178+

Total = 355+260-178 = 437

Since 437 is less than actual total - this cannot be valid

More than half of the dog owners are also cat owners

(C&D) = 130+

Total = 355 + 260 - 130 > 465 .

Here 130 is considered as the least value, so more than half of dog owners being cat owners is possible.

None of the pet owners have both cats and dogs

Since C+D != Total, this is false

Cats = 355

Dogs = 260

Total = C + D - (C&D)

More than half of the cat owners are also dog owners

(C&D) = 178+

Total = 355+260-178 = 437

Since 437 is less than actual total - this cannot be valid

More than half of the dog owners are also cat owners

(C&D) = 130+

Total = 355 + 260 - 130 > 465 .

Here 130 is considered as the least value, so more than half of dog owners being cat owners is possible.

None of the pet owners have both cats and dogs

Since C+D != Total, this is false

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Re: 465 pet owners were surveyed to determine whether they owned
[#permalink]
08 Mar 2021, 23:07

Carcass wrote:

465 pet owners were surveyed to determine whether they owned cats or dogs. 355 said they had at least one cat and 260 said they had at least one dog. Assuming that every couple surveyed had at least one cat or dog, which of the following statements must be true?

Indicate all such statements.

A. More than half of the cat owners are also dog owners

B. More than half of the dog owners are also cat owners

C. None of the pet owners have both cats and dogs

Indicate all such statements.

A. More than half of the cat owners are also dog owners

B. More than half of the dog owners are also cat owners

C. None of the pet owners have both cats and dogs

Total = 465

At-least 1 Cat = 355

At-least 1 Dog = 260

Both = 355 + 260 - 465 = 150

So, Only Cats = 355 - 150 = 205

Only Dogs = 110

A. More than half of the cat owners are also dog owners - NO

Dog owners are 150 which are 42.2% of the ones who own Cats

B. More than half of the dog owners are also cat owners - YES

Cat owners are 150 which are 57.6% of the ones who own Dogs

C. None of the pet owners have both cats and dogs - NO

355 + 260 ≠ 465

Hence, option B

Re: 465 pet owners were surveyed to determine whether they owned
[#permalink]
06 Mar 2024, 22:46

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