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Of a group of 50 households, how many have at least one cat or at

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Of a group of 50 households, how many have at least one cat or at  [#permalink]

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New post 26 Jun 2017, 02:27
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Re: Of a group of 50 households, how many have at least one cat or at  [#permalink]

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New post 15 Nov 2017, 17:26
Bunuel wrote:
Of a group of 50 households, how many have at least one cat or at least one dog, but not both?

(1) The number of households that have at least one cat and at least one dog is 4.
(2) The number of households that have no cats and no dogs is 14.


We have a group of 50 households and need to determine how many of those households have at least one cat or at least one dog, but not both.

We can use the following formula:

total = # with at least one dog only + # with at least one cat only + # with both + # with neither

50 = # with at least one dog only + # with at least one cat only + # with both + # with neither

So, we need to determine # with at least one dog only + # with at least one cat only

Statement One Alone:

The number of households that have at least one cat and at least one dog is 4.

So, we have:

50 = # with at least one dog only + # with at least one cat only + 4 + # with neither

46 = # with at least one dog only + # with at least one cat only + # with neither

Since we don’t know the # with neither, we can not determine # with at least one dog only + # with at least one cat only. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

The number of households that have no cats and no dogs is 14.

So, we have:

50 = # with at least one dog only + # with at least one cat only + # with both + 14

36 = # with at least one dog only + # with at least one cat only + # with both

Since we don’t know the # with both, we cannot determine # with at least one dog only + # with at least one cat only. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two, we have:

50 = # with at least one dog only + # with at least one cat only + 4 + 14

50 = # with at least one dog only + # with at least one cat only + 18

32 = # with at least one dog only + # with at least one cat only

Answer: C
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Of a group of 50 households, how many have at least one cat or at  [#permalink]

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New post 26 Jun 2017, 03:00
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P(Total) = 50
P(at least one Dog) = x
P(at least one Cat) = y
P(Both at least one dog and at least one cat) = z
P(Neither) = Households which have neither a dog nor a cat.

P(Total) = P(at least one Dog) + P(at least one Cat) + P(Both at least one dog and at least one cat) + P(Neither)

1) The number of households that have at least one cat and at least one dog is 4 - z = 4
Since we do not have any information about houses with neither, we cannot clearly
tell how many households have at least one cat or at least one dog(but not both). (Insufficient)

2) The number of households that have no cats and no dogs is 14 - P(Neither) = 14
Since we do not have any information about houses with both, we cannot clearly
tell how many households have at least one cat or at least one dog(but not both). (Insufficient)

Combining information from both the statements, 50 = x + y + 4 + 14 | x+y = 32 (Sufficient - Option C)
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Re: Of a group of 50 households, how many have at least one cat or at  [#permalink]

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New post 03 Jul 2017, 01:04
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As in the attached picture.

Answer should be C.
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Re: Of a group of 50 households, how many have at least one cat or at  [#permalink]

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New post 08 Aug 2017, 09:43
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Bunuel wrote:
Of a group of 50 households, how many have at least one cat or at least one dog, but not both?

(1) The number of households that have at least one cat and at least one dog is 4.
(2) The number of households that have no cats and no dogs is 14.


Total = 50
Households with at least 1 cat OR 1 dog = ?

1) Households with at least 1 cat AND 1 dog = 4
Remaining Households = 46
We cannot determine the number of households with at least 1 cat OR 1 dog.
Insufficient.

2) No Cats and No Dogs = 14
Remaining Households = 36
We cannot determine the number of households with at least 1 cat OR 1 dog.
Insufficient.

1+2)
Total = 50
Households with 1 cat AND 1 dog = 4
Households with NO cats and dogs = 14
=> Households with at least 1 cat OR 1 god = 32

Sufficient. C is the answer.
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Re: Of a group of 50 households, how many have at least one cat or at  [#permalink]

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New post 27 Aug 2017, 19:47
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pushpitkc wrote:
P(Total) = 50
P(at least one Dog) = x
P(at least one Cat) = y
P(Both at least one dog and at least one cat) = z
P(Neither) = Households which have neither a dog nor a cat.

P(Total) = P(at least one Dog) + P(at least one Cat) + P(Both at least one dog and at least one cat) + P(Neither)

1) The number of households that have at least one cat and at least one dog is 4.
z = 4
Since, we do not have any information about houses with neither,
we cannot clearly tell how many households have at at least one cat or at least one dog(but not both). Insufficient.

2) The number of households that have no cats and no dogs is 14.
P(Neither) = 14.
Since, we do not have any information about houses with both,
we cannot clearly tell how many households have at at least one cat or at least one dog(but not both). Insufficient.

Combining information from both the statements,
50 = x +y +4 +14
x+y = 32(Sufficient) (Option C)


I'm not understanding the fact that, isn't the formula for this set problem is total=(a+b-both+neither)? Why are you adding "both" here? Could you please clarify me.
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Re: Of a group of 50 households, how many have at least one cat or at  [#permalink]

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New post 13 Oct 2018, 23:23
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How to solve this question with a double set matrix ?
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Re: Of a group of 50 households, how many have at least one cat or at  [#permalink]

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New post 26 Oct 2018, 14:37
pks02 wrote:
How to solve this question with a double set matrix ?


waiting for the same.
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Of a group of 50 households, how many have at least one cat or at  [#permalink]

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New post 26 Oct 2018, 15:42
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Hi sakuac and pks02

Please refer to the attached image I hope it helps.

Posted from my mobile device
Attachments

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Re: Of a group of 50 households, how many have at least one cat or at  [#permalink]

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New post 21 Feb 2019, 10:13
Salsanousi: How are you getting 32? Because according to your picture -z + z = 0.
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Re: Of a group of 50 households, how many have at least one cat or at  [#permalink]

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New post 25 Feb 2019, 08:09
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It should be P(Total) = P(at least one Dog) + P(at least one Cat)-P(Both at least one dog and at least one cat) + P(Neither)
Not P(Total) = P(at least one Dog) + P(at least one Cat) + P(Both at least one dog and at least one cat) + P(Neither)

But anyway, you don't need to get an accurate number, Im just saying.
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Re: Of a group of 50 households, how many have at least one cat or at  [#permalink]

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New post 29 Mar 2019, 23:42
chetan2u VeritasKarishma
Salsanousi wrote:
Hi sakuac and pks02

Please refer to the attached image I hope it helps.

Posted from my mobile device


This is wrong because X + Z + Y + 14 should always be equal to total sum i.e 50

moreover, Z will cancel out and which variable is 32 then ??

I guess the first statement is incorrect, it should rather say

"The number of households that have at least one cat and at least one dog but not both is 4"

because in that scenario

X+Y+Z+14 = 50

we know, X+Y = 4

which gives Z= 32.


please correct me, experts
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Re: Of a group of 50 households, how many have at least one cat or at  [#permalink]

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New post 30 Mar 2019, 23:23
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Bunuel wrote:
Of a group of 50 households, how many have at least one cat or at least one dog, but not both?

(1) The number of households that have at least one cat and at least one dog is 4.
(2) The number of households that have no cats and no dogs is 14.


It is fairly simple.

You have 50 households. No of households with no cats and no dogs = 14.
So 50 - 14 = 36 households have at least one cat or at least one dog or both.

So 36 households lie in the two overlapping circles, some in yellow region (only at least 1 cat), some in blue (only at least 1 dog) and 4 in green (both).

Attachment:
Screenshot 2019-03-31 at 11.50.25.png
Screenshot 2019-03-31 at 11.50.25.png [ 44.06 KiB | Viewed 2707 times ]


Question: "how many have at least one cat or at least one dog, but not both?"
There are 4 households in both region. So number of households in yellow + blue only = 36 - 4 = 32
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Re: Of a group of 50 households, how many have at least one cat or at  [#permalink]

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New post 11 May 2019, 04:21
Are we not double counting the middle of the diagram? Is it not included when you calculate x or z since those houses are counted? For example, if z = 20 then wouldnt counting the 4 houses that have cats as well as the 4 that have dogs be double counting since we have already included them in the calculation for z? I am reading the equation as this.

P(total) = z+x-y+neither
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Re: Of a group of 50 households, how many have at least one cat or at   [#permalink] 11 May 2019, 04:21
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