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40% of the dogs at a certain animal shelter have been microchipped. Ho

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Joined: 02 Sep 2009
Posts: 64314
40% of the dogs at a certain animal shelter have been microchipped. Ho  [#permalink]

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18 Jul 2019, 07:00
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Question Stats:

82% (01:20) correct 18% (01:42) wrong based on 227 sessions

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40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
(2) There are less than 50 dogs at the animal shelter

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Re: 40% of the dogs at a certain animal shelter have been microchipped. Ho  [#permalink]

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18 Jul 2019, 07:24
1
IMO : E

40% of the dogs at a certain animal shelter have been micro chipped. How many of the dogs have not been micro chipped?

(1) 37.5% of the dogs that have been micro chipped are also either spayed or neutered.
(2) There are less than 50 dogs at the animal shelter

Sol:

1 ) 37.5 % are micro chipped that means we still dont know how many dogs are there because ther may be 40 or 400... and so on,
So insufficient.

2 ) there are less than 50 dogs, and 40% dogs are micro chipped and we know that dogs cannot be decimals so the number has to be a integer to be correct.

then the possible out come:

5 2
10 4
15 6
20 8
25 10
30 12
35 14
40 16
45 18

only the above combination give whole number of dogs, but we dont know the exact number even ow.

So it is insufficient.

C ) 37.5 percent has to be also a integer to be a right solution.

so we take 37.5 and estimate, only 40 and 20 (total dogs) gives as integer 3 and 6 respectively.

we still dont know what will bet he exact number so not sufficient.

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Re: 40% of the dogs at a certain animal shelter have been microchipped. Ho  [#permalink]

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18 Jul 2019, 07:29
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40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?

The question is regarding the overlapping sets. We are asked to find the number of dogs that have not been microchipped.
To find that we need the Total number of dogs at the animal shelter.
Let's see the statements.

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
This gives subsection, hence not telling us the total number of dogs.
This statement is insufficient.

(2) There are less than 50 dogs at the animal shelter
We still don't know the total number of dogs. If the number is 10 that means 6 are not chipped and if the number is 20 that means 12 are not chipped.
This statement is insufficient.

Combining the statement we know that 37.5% of 40% of the total dogs have to be an integer.
But again if you have 40 dogs, that means 16 are microchipped and 6 are either spayed or neutered.
If you have 20 dogs 8 are microchipped and 3 are either spayed or neutered.

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Re: 40% of the dogs at a certain animal shelter have been microchipped. Ho  [#permalink]

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18 Jul 2019, 07:39
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40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
(2) There are less than 50 dogs at the animal shelter

Given: 40% of the dogs at a certain animal shelter have been microchipped.
Asked: How many of the dogs have not been microchipped?

40% of the dogs at a certain animal shelter have been microchipped
=> 60% of the dogs at the animal shelter have not been microchipped

Let the number of dogs at the shelter be x dogs
40% of x have been microchipped
=> 40% x = 2x/5 is an integer
=> 60% x = 3x/5 is also an integer
=> x = 5k format => x is a multiple of 5 (i)

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
37.5% = 3/8 of the dogs that have been microchipped are also either spayed or neutered.
=> 3/8 of 2x/5 is also an integer
=> 3x/20 is also an integer
=> x = 20k x is a multiple of 20
If x= 20y = total no of dogs
=> 8y = Number of the dogs that have been microchipped &
=> 3y = Number of the dogs that have been microchipped are also either spayed or neutered.
But y can take multiple values
NOT SUFFICIENT

(2) There are less than 50 dogs at the animal shelter
If there are less than 50 dogs at the animal shelter
=> no of dogs may be 5, 10, 15, 20,25,30, 35, 40,45
NOT SUFFICIENT

Combining (1) & (2)
(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
=> x = 20y format => number of dogs are multiple of 20
(2) There are less than 50 dogs at the animal shelter
Number of dogs = 20 or 40
Number of dogs which have not been microchipped = 12 or 24
NOT SUFFICIENT

IMO E
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40% of the dogs at a certain animal shelter have been microchipped. Ho  [#permalink]

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Updated on: 18 Jul 2019, 19:05
1
40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?

From (1) 37.5% of the dogs that have been microchipped are also either spayed or neutered:

We do not have enough information to get the number of dogs we just have percentages, so clearly insufficient.

From (2) There are less than 50 dogs at the animal shelter:

We can have several combinations to get the split of 40% / 60%:

4 - 6
8 -12
12 -18
24 - 16

So, clearly insufficient.

From (1) and (2) we have 2 possibilities: 8 - 12 and 24 - 16, so it is not sufficient

Originally posted by Mizar18 on 18 Jul 2019, 07:54.
Last edited by Mizar18 on 18 Jul 2019, 19:05, edited 1 time in total.
40% of the dogs at a certain animal shelter have been microchipped. Ho   [#permalink] 18 Jul 2019, 07:54