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

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Manager
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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, 09:00
40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?

Let's suppose total dogs are X.
0.40X = microchipped
0.60X = not microchipped

We need to find X.

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

First of all, 37.5% can be written as 3/8 as a fraction. That will make our life easier.
So, 0.60X*(3/8) = either spayed or neutered
The simplified form would be 9/40X= either spayed or neutered
Can't help to find X.
X can be any number multiple of 40. Because dogs are of course integers.
Insufficient.

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

X<50
Multiple possibilities exist.
Insufficient.

If we combine (1) & (2)

9/40X is an integer and x<50.
So, x has to be 40.
Sufficient.
Hence answer should be (C)
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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, 09:04
1
IMO E

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

Given that 40% of dogs have been microchipped, then 60% have not been microchipped.
So, we just need to calculate the total number of dogs in the shelter.

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
St.1 has no information about the total no. of dogs or the no. of dogs not have been microchipped.
Insufficient

(2) There are less than 50 dogs at the animal shelter
St.2 says Total < 50, no other information given about the dogs have been or not have been microchipped
That means the total no. of dogs that have not been microchipped is < 50*0.6 ,i.e., 30
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, 09:06
1
Required = No. of dogs (not percent) not been microchipped. i.e 60% of total dogs at the animal center

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered. - Insufficient (No. number information given. only percents)
(2) There are less than 50 dogs at the animal shelter - Insufficient - Dogs can be 40 or 30 which will give a different number of non microchipped dogs
(3) Combined - Still Insufficient, Dogs can be 40 or 30 which will give a different number of non microchipped dogs

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, 09:09
1
IMO-E

Total Dogs = x
Dogs Microchipped= 40% of x= 2/5 * x
finding x will suffice the requirement.

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

Dogs Either spayed or neutered= 37.5% of (2/5 * x) = 3/8 * 2/5 * x = 3/20 * x

Now, x can take any value that is a multiple of 20. [ for no. to be integer]

x= 20, 40, 60 ......, 20K [k=integer]

Not Sufficient

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

x < 50

From Ques, for integral values, x= 5,10,15.........5K [k=integer]

Not Sufficient

Together:----
x<50 & x= 20K
Therefore, x = 20, 40
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, 09:09
1
I will go with E

We are given 40% are microchipped

Bit then we are given 37.5 % microchipped as well as either spayed or...

We can't solve by this

BCE

Now.no..of.itmes.are less than 50

Still we can't find no
of. Not.microchipped ( variable values)

So we have CE

Combining we can't solve
Answer is E !!!!!

E it is !!!

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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, 09:11
1
Given that 40% was microchipped

To find the number that is not microchipped

Statement 1: says that 37.5% of the dogs that have been microchipped are also either spayed or neutered

This is not suffcient (BCE)

Statement 2: There are less than 50 dogs at the animal shelter

Since we cannot determine the exact number of dogs in the animal shelter

Statement 2 is not sufficient (CE)

Combining statement 1 and 2 is also not helping our course

Hence not sufficient

Answer choice E.

Thank you for kudos.
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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, 09:12
combining both 1 and 2 will not give a number as there are no number in both the options . less than 50 is too vague.
Answer 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, 09:14
1
Given: 40% of the dogs at the shelter are micro-chipped.
Implied: 60% of the dogs at the shelter are not micro-chipped.

Question: Number of dogs that are NOT micro-chipped?

So if we find out a way to calculate the total number of dogs at the shelter then we can compute the ones that are not micro-chipped. Lets see if the statements have the info:

St-1: 37.5% of the dogs that have been micro-chipped are also either spayed or neutered. - Introduces 2 more categories, i.e. neutered and sprayed, but gives us no info on the number of dogs in any of the categories. Not Sufficient.

St-2: There are less than 50 dogs at the animal shelter - Leads to multiple values for e.g. if number of dogs is 45 then dogs Not MC= $$\frac{60}{100}*45=27$$; if number of dogs is 40 then dogs Not MC= $$\frac{60}{100}*40=24$$ and so on. Not Sufficient.

Sidenote: total dogs has to be a multiple of 5 as both the number of chipped and not chipped dogs has to be an integer and 60% (=$$\frac{4}{5}$$) or 40% (=$$\frac{2}{5}$$) of a value not divisible by 5 will yield a non-integer value.

Even after considering both statements together, we are unable to determine the number of dogs at the shelter, answer is therefore 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, 09:24
40% of dogs are MC.
Let total dogs be D.
We have to find 0.6D. For this we need value of D.

Statement 1:
37.5% of (0.4D) should be an INTEGER. => 75/200 * (4/10) * D => 3/20 * D is an INTEGER. For this D can be 20,40,60,80,... INSUFFICIENT

Statement 2:
D < 50. For this to be true and 4/10 * D to be an integer, D could be 45,40,35,30,... . NOT SUFFICIENT

Combining Both:
3/20*D and 4/10*D should both be INTEGER and D < 50. This all is possible at a unique value of D = 20. So 0.6D = 12
There are 12 NON MC Dogs ( SUFFICIENT)

Answer -> C.

Regards,
Rishav
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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, 09:27
1
Quote:
40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?

This is Data Sufficiency (DS) question and we need to identify if the statements below are sufficient or not.
Microchipped dogs - 40%
Not microchipped dogs number = ?

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

37.5% of 40% dogs are spayed of neutered, what means that 37.5% * 40% = 15% of total number of dogs are either spayed or neutered.
However, it does not give us any indication of how many dogs are not microchipped. Clearly insufficient.
Insufficient.

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

Total number of dogs < 50

While the number of dogs is less than 50, it can be 20 or 40 for example. We do not know exact numbers, and for this reason, cannot identify number of dogs which were not microchipped.
Insufficient.

Statements 1 + 2 together:
In addition to the initial information, we know that 15% dogs are either spayed or neutered, and that the total number of dogs is less than 50.
If the number of spayed dogs is 15%, then total number of dogs should be multiple of 20 as 15%=3/20.
However, there are two numbers below 50 that can be dividable by 20: 20 itself and 40.
As we do not have any additional information, we cannot tell the exact number of dogs which are not microchipped.
Both statements together are still insufficient to answer the question.

Answer: 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, 09:29
1
40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?

Given:
T =total number of dogs integer
40% * T = microchipped = integer
60% * T = not microchipped = integer

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered. --> insufficient, we can't say number from %: (either spayed or neutered) & microchipped = 37.5% * microchipped = 37.5% * 40% * T = integer
(2) There are less than 50 dogs at the animal shelter --> insufficient, T < 50, microchipped = 40% * T = 40T/100 = 2T/5, so T has to be multiple of 5, T = 5n < 50, where n = 1(1)9, T = {5, 10, 15, 20,...., 40, 45}.so microchipped = 2T/5 = 2n = {2, 4, 6, 8, ...., 18}
Combining (1) & (2)
From (1), 37.5% * 40% * T should be integer
So, 37.5% * 40% * T = 37.5*40*T /10^4=375*40T/10^5 = 15000T/10^5=15T/100= 3T/20 = 3*5n/20=3n/4, so n=4 or 8
T = 20 or 40 --> insufficient
So not microchipped dogs= 12 or 24-->
insufficient
So the 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, 09:34
1
IMO E.

Let's assume the total number of dogs to be 'N'.
0.4N are microchipped and 0.6N are not.

Statement 1: 37.5% of the dogs that have been microchipped are also either spayed or neutered.
This does not give us any information about the number of dogs not microchipped.
Hence , this statement alone is not sufficient.

Statement 2: There are less than 50 dogs at the animal shelter.
This does not give us any information about the total number of dogs. It could be any number less than 50. Hence, we cannot find the number of dogs not microchipped.
Hence , this statement alone is not sufficient.

Clubbing them together, we have 37.5% of 40% spayed or neutered and there are less than 50 dogs.
Hence, both statements together also are not sufficient. Hence, 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, 09:35
1
First of all, let's assume that the total number of dogs is x
0.4x= microchipped
0.6x= not chipped; We are asked to find 0.6x, so if we find x our job is done

1 stm --> x*0.4*0.375=0.15*x chipped dogs that are also either spayed or neutered. The only thing we can infer from here is that x is such integer that gives integer value after multiplying by 0.15 and we can find lots of x values that satisfy that constraint

Not Sufficient

2 stm --> clearly insufficient, x can have several values

Bot statements together: 0.15x must be an integer and x<50
If x=20; 0.15x=3; 0.6x=12
If x=40; 0.15x=6; 0.6x=24

Still, several cases of x and therefore 0.6x are possible

IMO
Ans: 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, 10:58
1
Let no of dogs be x
Given: No of dogs microphoned: 0.4x = 2x/5
To find: no of dogs not microphoned = 0.6x??

(1) no of dogs microchipped are also either spayed or neutered = (3/8)(2x/5) = 3x/20. Insufficient.
(2) No information regarding exact number of dogs. Insufficient.

(1)+(2) No of dogs are less than 50, it can be 20 or 40 to satisfy 3x/20.
If x =20, no of dogs not microphoned = 12
If x=40, no of dogs not microphoned = 24. Insufficient.

E is correct.
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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, 11:00
1
40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?

Let X be total dogs.... X has to be positive integer

0.4x = microchipped
0.6x = not microchipped.... we need to find 0.6x

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

0.375 * 0.4 * x = spayed or neutered
0.15x = spayed or neutered

No indicatoin of number of animals

(1) IS NOT SIFFICIENT

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

x<50

x could be 40 and not microchipped could be 24
x could be 20 and not microchipped could be 12

(2) IS NOT SUFFICIENT

(1) and (2)

x<50
0.15x has to be a positive integer because number of dogs (spayed and neutered) cannot be negative

We need to find an integer less than 50 which when mulitplied by 0.15 is an integer

If x was 40, 0.15x would be 6... and 0.6x would be 24... this is 1 possible value
If x was 20, 0.15x would be 3... and 0.6x would be 12... this is another possible value

We are not able to narrow it down to 1 value.

ANSWER - E. NONE IS 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, 11:16
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. ....nothing about dogs which are not microchipped...Not suff...
(2) There are less than 50 dogs at the animal shelter.....total no of dogs may be 45 or 40 .........Not suff

combined ,again we cannot say anything about total no of dogs...insuff...

Ans 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, 11:40
1
Let total number of dogs at the animal shelter be x.

Given,

1. 40% of the dogs at the animal shelter are microchipped
=> 0.40 * x -- Microchipped

To find,

How many dogs are not microchipped?

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

Since, we do not know any information about number of dogs this information is also irrelevant.

Hence,

Option 1 alone is insufficient.

Option 2: There are less than 50 dogs at the animal shelter

This also is not enough as there can be 10 or 20 or 40 dogs where 40% of each is an integer.

Hence,

Option 2 alone is insufficient.

Now, let us consider the 2 options together.

=> 37.5 % of 40 % of x should be an integer where x < 50
=> (37.5 / 100) * (40 / 100) * x should be an integer where x < 50
=> 0.15 * x should be an integer where x < 50.

Now let us check how many values of x < 50 have 0.15 * x as an integer.

Only 2 values

1. When x = 20
2. When x = 40

All conditions are satified by these 2 values and hence we are not sure how many dogs were not microchipped.

Hence,

Answer: 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, 11:40
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

40% are MCed, so 60% are not MCed
we need total dogs to have the ans

condition 1

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

ie 3/8 of Mc are spayed or neutered and 5/8 of Mc are not spayed or neutered. as there is no concrete number is given. it can form multiple answers in multiples of 8

ie 3 spayed will result is 8 Mced will result in 12 not mced
6 spayed will result in 16 mced which results in 24 not mced
9 spayed will result in 24 mced which results in 36 not mced so not sufficient

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

clearly we can have any possibility in multiple of 5 from 5 to 45 is the possibility so not sufficient

combining 1 and 2 will give
2 possibility still remains so not sufficient .
3 spayed will result is 8 Mced will result in 12 not mced
6 spayed will result in 16 mced which results in 24 not mced

so the 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, 11:43
1
40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?

Remaining 60% of dogs are not microchipped. To answer the question we need to find total dogs at an animal shelter. That will lead us to the answer.
Now,
(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
Assume there are total X dogs.
So, (4/10)*X dogs are microchipped. Out of these microchipped dogs, 37.5% (3/8th)are spayed.

So, total spayed dogs = (3/8)*(4/10)*X = (3/20)*X (This number can not be a fraction. There can't be a half-dog)

for (3/20)*X to be a fraction, X has to be the multiple of 20.
X can take any value from [20, 40, 60, 80,...].

So, First can not answer the question. (Not an uniques solution.)

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

Second is clearly not sufficient to answer the question independently.

Combine (1) & (2):

We still have 2 possible answers. Because X still can take 2 different values (20 or 40).

So, we can not answer the question based on given information even after combining.

ANSWER: 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, 12:01
E has to be the correct answer.

Because we the total number of dogs could be any even after combining both equations.

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Re: 40% of the dogs at a certain animal shelter have been microchipped. Ho   [#permalink] 18 Jul 2019, 12:01

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