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

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

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18 Jul 2019, 08:00
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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

 This question was provided by Veritas Prep for the Game of Timers Competition

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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, 08:11

Answer required in number only, not in %age.

st 2 - confirm no. is less than 50
st 1 - confirm the dogs % age

hence combine the choice can give answer of "How many of the dogs have not been microchipped?
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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, 08:24
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, 08:26
1
Let the total number of dogs be $$x$$

$$40%$$ or $$\frac{2}{5}x$$ dogs are microchipped. We need to find $$1-\frac{2}{5}x$$

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

This says $$\frac{3}{8}$$ of $$\frac{2}{5}x$$ are either spayed or neutered. That is $$\frac{3}{20}x$$ dogs are neutered. Gives us no information about the non microchipped dogs or total number of dogs but we can only infer that the total number of dogs is a multiple of 20

1 is insufficient

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

If there are 40 dogs, 16 are microchipped and 34 are not microchipped
If there are 20 dogs, 8 are microchipped and 12 are not microchipped

2 is insufficient

(1) + (2)

The total number of dogs is a multiple of 20 and the total number of dogs is less than 50

The total number can still be 40 or 20

As seen in (2) this is still insufficient

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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, 08:27
1
40% chipped -> 60% not chipped

1) Tells us nothing about number of dogs. Not sufficient.
2) This tells us less than 30 dogs not chipped. Not sufficient.

1 and 2 together are not sufficient either.

Hence option E
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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, 08:28
1
CBD; option E

Taking A+B together there are two possible scenarios:-
Case # 1 Total:20
8 mc, 12 not mc
8 further segregated into 3 and 5.

Case # 2 Total: 40
16 mc, 24 not mc
16 further segregated into 6 and 10.
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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, 23:14
1
Let, X = total dogs in the animal shelter.
Then, 0.4X = Microchipped
Thus, we have 0.6X = Not Microchipped
We need to find the exact value of 0.6X

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
We have 0.4X microchipped, so
X(0.4)(0.375) = X(0.15) is S or N ->(a)
Therefore X(0.25) = not S or N -> (b)

From this, we will not be able to determine the exact value of 0.6X.

Not Sufficient.

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

Given, X < 50
X can have various values, thus 0.6X can have various values.

Not Sufficient.

(1) + (2)

Now, from (a), (b) and other known details we know that X(0.4), X(0.6), X(0.15), X(0.25) all need to be integer. As the number of dogs will always be an integer.

It is possible with both X = 20 and X = 40
Not Sufficient

Originally posted by Sayon on 18 Jul 2019, 08:28.
Last edited by Sayon on 18 Jul 2019, 23:14, edited 1 time in total.
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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, 08:29
1
it's given that 40% of the dogs at animal shelter are microchipped
in order to find how many dogs are not microchipped we need to know the total number of dogs

option A gives us the percentage of the microchipped dogs that are either sprayed or neutered
but nothing about total number of dogs
Hence option A is insufficient

option B tells us that there are less than 50 dogs. less than 50 can be any number from 40-41-42 etc
We have no information about the exact number of dog animals in the shelter
so option B is also insufficient

on combining we have no information about the total number of dogs, hence is not possible to find the number of dogs that are not microchipped.

Hence E
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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, 08:29
1
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, 08:32
1

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.
This is not relevant, we need the total number of dogs.

(2) There are less than 50 dogs at the animal shelter
if there are 50 dogs then: 50*40%=20. and 50-20=30 dogs with no microchip.
However it says less than 50 so it could be 49 total dogs, 40 total dogs, 20 total dogs..? not sufficient.

1&2= not sufficient. we can't get the total # of dogs. statement one only refers to dogs with microchip and statement two gives you an estimate of total dogs. answer is E.
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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, 08:35
1

clearly statement A by itself cannot be sufficient as we cannot determine the number of non microchipped dogs.
same with statement B
we just need to check a+b is suff or not:

(40D/100)*37.5/00 is an integer --> 3D/20 is an integer. therefore D can be 20 or 40, Two diff answers so not suff.
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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, 08:37
A - converting into ratio

37.5% of 40% = (3/8)X(2/5) = 3/20
Total dogs would be multiple of 20.
A is insufficient.

B - Less than 50 can be anything so insufficient

combining A and B
Number of dogs can be 20,40

No unique solution.

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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, 08:39
1
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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Re: 40% of the dogs at a certain animal shelter have been microchipped. Ho  [#permalink]

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18 Jul 2019, 08:42
Let's say X = total no of dogs
40% of the dogs have been microchipped = $$\frac{2}{5}$$ X

Possible values of X could be 5, 10, 15, 20, 25, 30, 35, 40, 45, ......80..... i.e multiple of 5

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
37.5% = $$\frac{3}{8}$$ X ..... i.e X is multiple of 8 , in above set there are at-least two multiples of 8 = 40, 80, ...it could result in many , hence, not sufficient

(2) There are less than 50 dogs at the animal shelter
X<50 , there are many values for X if X<50, listed above less than 50. not sufficient.

Combined we get the limited set to work with
stmt 2 - X< 50 = 5, 10, 15, 20, 25, 30, 35, 40, 45
stmt 1 - X is multiple of 8 -> Only one - 40
clearly sufficient.

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

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Updated on: 19 Jul 2019, 08:38
Quote:
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% or 2/5 of total are micro'd so 60% or 3/5 of total are not;

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered: no info about total, insufficient.
(2) There are less than 50 dogs at the animal shelter: there are many multiples of 5 < 50 that could be the total, insufficient.

(C) spayed/neutered basically means the same thing;
so the dogs micro'd and neutered are 3/8*2/5*total=3/20*total and micro'd not spayed/neutered is 5/8*2/5*total=1/4*total;
the LCM(20,4)=20, so the total could be 20 or 40, both <50, insufficient.

Originally posted by exc4libur on 18 Jul 2019, 08:45.
Last edited by exc4libur on 19 Jul 2019, 08:38, edited 1 time in total.
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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, 08:50
1
IMO correct answer is E - Both statement together not sufficient;

explanation is provided as attachment.
Attachments

IMG_20190718_211450.JPG [ 801.77 KiB | Viewed 1252 times ]

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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, 08:52
Clearly E

S1: No info about dogs that are not microchipped- Not Sufficient
S2: No of dogs given but no other info. 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, 08:52
1
40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?

60% of the dogs have not been microchipped

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
Not sufficient. But we can calculate how many dogs were spayed. and it is 40%*0,375=15% of the total number of dogs were spayed. But, as I said, it gives us nothing.

(2) There are less than 50 dogs at the animal shelter
Not sufficient. Many possible solutions.

Taking both together.
I thought it would be C, but I found at least 2 possible solutions.
case 1. 40 dogs total. 15%= 6; 60%=24
case 2. 20 dogs total. 15%=3; 60%=12

Thus E
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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, 08:53
1
E

Assuming total no of dogs is x. 40% of them are 0.4x that are microchipped, remaining are 0.6x that are not microchipped. We basically need to find x.

St 1: 37.5% of those microchipped are also spayed or neutred. So, 0.375*0.4*x = 0.15 x . We cant find x here, not sufficient
St 2: x < 50 Clearly not sufficient

Combined st 1 and 2:

So, basically we can see 0.15x < 0.15*50 = 7.5

Now, the no of dogs spayed or neutred have to be an integer value. So, 0.15x can be 7,6,5,4,3,2,1

Also, x has to be an integer so two values are possible, x = 40 or 20

Since, we cant find unique solution. answer is 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, 20:05
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, 08:54.
Last edited by Mizar18 on 18 Jul 2019, 20:05, edited 1 time in total.
40% of the dogs at a certain animal shelter have been microchipped. Ho   [#permalink] 18 Jul 2019, 08:54

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