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

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18 Jul 2019, 12:05
1
40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?

40% of dogs are microchipped. Therefore 60% of the dogs will be non microchipped.
If total no. of dogs = 100 then non microchipped dogs = 60.
Similarly if total no. of dogs = 200 then non microchipped dogs = 120
Therefore from the statements we need to find the total no. of dogs in the animal shelter.

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
This statement talks about 37.5% of dogs that have been microchipped are either spayed or neutered.
This does not give us the total no. of dogs.

Insufficient.

(2) There are less than 50 dogs at the animal shelter
Since no. of dogs at the shelter is less than 50, the total no. of dogs could be 40 or 30 or anything < 50.
This also does not give us total no. of dogs.

Insufficient.

By taking both statements together again it is not possible to find the total no. of dogs in the shelter.
Hence we cannot answer by considering both statements together.

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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, 12:39
40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?

Microchipped = 40% T
Not Microchipped = 60% T

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

37.5/100 = 15/40 = 3/8 = have been micro-chipped
Not microchipped = 5/8

All we have is a ratio... we do not have actual numbers

2 There are less than 50 dogs at the animal shelter

40% =4/10=2/5*(<50) = multiple possibility
3/5(<50) = multiple possibility
Again gives only ratio and it Could be a multiple of 5
..... we are not sure of the total number... Not sufficient

Taking A and B into consideration.

Remember : number of dogs can only be an integer!!!!!!!! not a decimal

total number of dogs has to be a multiple of 5 and 8.. because ratio in A is 3/8 and B is 2/5.
total number of dogs has to be 40

Consider:
5 - 10 - 15 - 20 - 25 - 30 - 35 - 40 - 45 - 50
8- 16 -24 - 32 - 40- 48

The only number common to both is 40

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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, 13:50
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

First of all, let's imagine the give situation: we have X dogs, 0.4X are microchipped. 0.6X are not.
From the first statement we can conclude that microchipped dogs are divided in at least 2 categories, and one of them (spayed or neutered) constitutes 37.5%.
It means that the ratio of dogs in this category to all microchipped dogs is 3:8.
This statement is not sufficient.

The second statement is also not sufficient, because there may be 40 dogs in total or 20 dogs in total (all numbers are less than 50).

Both statements together are also not sufficient, because 3:8 is possible in at least 2 situations:
a) there are 16 microchipped dogs and 6 of them are spayed or neutered (37.5%)
b) there are 8 microchipped dogs and 3 of them are spayed or neutered (37.5%)

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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, 13:54
1
Statement 1: As we don't know how many total no. of dogs or any information about no. of or % or ratio of dogs not microchipped, its not sufficient : Insufficient

Statement2 : Less than 50, , no;s can be any 49,48,47, giving different solutions : Insufficient

Combining both : Still insufficient as exact no of dogs are not known : 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, 14:19
1
from the given, microchipped : Un-microchipped = 2:3 , with total 5 parts

from sentence (1), Spayed/Neutered vs Non-Spayed/Neutered = 3:5, with total 8 parts
so microchipped must be a multiple of 8.
By merging this info with what is given in the stimulus, the ratio is pair will be (8:12)=20 or (16:24)=40 or (24:36) = 60 ....
so the number of Un-mircochipped dogs are multiple of 12: 12,24,36, ..... --> insufficient

from statement (2)
, the total number of dogs can be 5,10,15,20,25,30,35,40,45
and the number of Un-mircochipped dogs can be 3,6,9,12,15,18,21,24,27 --> insufficient

Combining (1),(2) the total number can be either 20 or 40,
and the number of Un-mircochipped dogs can be 12 or 24 --> insufficient

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, 14:51
1
40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?

Let number of dogs =d
Let number of microchipped dogs =m
Let number of non microchipped dogs= n
Given (40/100)•d=m

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
.: (37.5/100)m = spayed /neutered
No information on the number of dogs
(Not sufficient)

(2) There are less than 50 dogs at the animal shelter
.: d <50
Now number of dogs can be 40,20,10 etc . (Not sufficient)

(1+2) Still we can’t find the total number of dogs (Not sufficient)

Posted from my mobile device
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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, 14:51
1

A/Q,
40% dogs are microchipped and the question is asking how many dogs are not micrchipped?
Therefore if we know the total no. of dogs then we can find the no.of dogs that are not microchipped.

St.1 - 37.5% of the dogs that have been microchipped are also either spayed or neutered. We do not know anything about how many dogs are there. Insufficient

St.2 - There are less than 50 dogs at the animal shelter. Again we do not know about the actual no.of dogs, it can 20, 30, 40...So Insufficient

St.1 & 2- Even if we take both statements together we cannot tell how many dogs are there. 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, 15:42
1
40% = 2/5
37.5% = 375/100 = 3/8.

A) no total number of dogs at animal shelter is given. Not sufficient
B) <50, could be 5 dogs, 10 dogs, etc. Not sufficient.

A+B) We know that for sure 2/5 * 3/8 needs to be whole number. Since 3/20 needs to be whole number.
# of dogs at animal shelter (N) = 20*q (multiple of 20).

Since we have two possibilities N = 20 or 40, A+B) is not sufficient.

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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, 17:50
Let total number of dogs= N
Number of dogs that are micro chipped=$$\frac{2}{5}*N$$
As $$\frac{2}{5}*N$$ is an integer, N must be a factor of 5.

N= 5k....where k is a positive integer.

Statement 1- 37.5% of the dogs that have been microchipped are also either spayed or neutered
($$\frac{3}{8}$$)* $$\frac{2}{5}*N$$ must be an integer.
N is also a multiple of 8.

We can write N as 5*8*x=40x, x is an integer.
If x=1, Dogs that don't have microchip= (3/5)*40=24
If x=2, Dogs that don't have microchip= (3/5)*80=48
Insufficient

Statement 2
N<50
We know that N is multiple of 5. N can be 5, 10, 15......40 or 45
If N=5, Dogs that don't have microchip= (3/5)*5=3
If N=10, Dogs that don't have microchip= (3/5)*10=6

Insufficient

Combining both statements
N is multiple of 40, and 0<N<50.
Only value N can take is 40
Dogs that don't have microchip= (3/5)*40=24
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, 18:33
1
#1
37.5% of the dogs that have been microchipped are also either spayed or neutered.
total dog population is not know insufficient
#2
<50 dogs in shelter ; so answer would keep varying for not microchipped dogs insufficient
from 1 &2
we would still get many values for microchipped dogs so insufficient
IMO E

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

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18 Jul 2019, 19:09
1
Just as the number of dogs with microchip (40%) is a positive integer, so too is the number of dogs without microchip (60%) . As a result, the total number of the dogs has to be both a positive integer and in multiple of 5, e.g. 20, 25, 40, 50, 60 etc

Question: how many of the dogs have not been micro-chipped?

Statement (1): 37.5% of the dogs that have been microchipped are also either spayed or neutered.
This statement tells us that the number of the dogs that have been both micro-chipped and spayed/ neutered is $$37.5 * 40 =15$$% and this has to be a positive integer. As a result, the total number of dogs has to be both a positive integer and in multiple of 20, e.g. 20, 40, 60, etc.
No other information is available to determine the exact number of the dogs that have not been micro-chipped. NOT SUFFICIENT

Statement (2): There are less than 50 dogs at the animal shelter
This statement only tells us that the total number of dogs is anything less than 50, e.g. 20, 25, 40, etc. No other information is available to determine the exact number of the dogs that have not been micro-chipped. Clearly NOT SUFFICIENT

Combining Statements (1) and (2),
We now understand that the total number of dogs has to be a positive integer, that is less than 50 and in multiple of 20. This leaves us with only two possible total number of dogs: 20 and 40. Consequently, the number of dogs that have not been micro-chipped could be 12 or 24.
However, no other information is given to determine the exact number of the dogs that have not been micro-chipped.
NOT SUFFICIENT

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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, 21:03
1
We know that 40% are microchipped, other 60% must have not been microchipped. We need to find exact number of either microchipped, not chipped, or total number of dogs, then we will be able to answer to the questions.

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered. - Not sufficient. We just know that 40% of 100 must be integer and that 37.5% of 40% of 100% also must be integer. But there are many such numbers. A is eliminated

(2) There are less than 50 dogs at the animal shelter - at least 45 dogs must be present at shelter or else 40% will not be integer. But 40, 35, etc all multiples of 5 work as well. We have many options, thus not sufficient again. B is gone too.

Combined, we still do not know the total number of dogs because two numbers satisfy condition above 37.5%*40%*100%. Those numbers are 40 dogs total, out of which 16 ($$\frac{2}{5}$$*40) are microchipped, 24($$\frac{3}{5}$$*40) not chipped. And of those chipped(16*$$\frac{3}{8}$$), 6 are also sprayed. Another number that matches is 20 dogs total, out of which 8 ($$\frac{2}{5}$$*20) are chipped and 12 ($$\frac{3}{5}$$*20) not chipped. Out of those chipped ($$\frac{3}{8}$$*8), 3 are also sprayed. We arrived at two different values, thus not sufficient again.
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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, 21:21
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% dogs are microchipped
This makes 40% of x = some definite number
now
using statement 1
37.5% of the dogs that have been microchipped are also either spayed or neutered.
thus it means
$$\frac{37.5}{100}* \frac{40}{100} * d$$
should be a number
simplify
37.5/100 * 40/100 * d
$$\frac{3}{40}*d$$should be a number but now
d can be 40 , 80 , 120
hence not sufficient

Take Stmt 2
dogs are less than 50 , does not help
combine 1 and 2

d can be 40 , 80 , 120 and d is less than 50
only one solution
d = 40
Hence combining 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, 21:25
1
40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?

Could be that 60% of the dogs are not microchipped, but to find a value for this, we need the total number of dogs.

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
--> Does not give us any info about the total number of dogs or any way to find the # of dogs not microchipped. Hence not sufficient.

(2) There are less than 50 dogs at the animal shelter
Clearly insufficient, because there could be 20 dogs 40 dogs, any number of possibilities for the total number of dogs.

Stmts 1 + 2 together also doesn't provide any additional information.

Hence E.
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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, 21:47
1
let the total number of dogs be x

40% of x microchipped = $$\frac{2x}{5}$$ (from here we know that total number of dogs are multiple of 5)

we have to find 60% of x = $$\frac{3x}{5}$$

STATEMENT (1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
Dogs that have been microchipped =$$\frac{2x}{5}$$
$$\frac{37.5}{100}$$*$$\frac{2x}{5}$$ are either spayed or neutered = $$\frac{3x}{20}$$
from here we know that total number of dogs are multiple of 20
x can be = 20,40,60......
INSUFFICIENT

STATEMENT (2) There are less than 50 dogs at the animal shelter
We know that the total number of dogs are multiple of 5
so from here, the total number of dogs can be = 5,10,15........,45
INSUFFICIENT

STATEMENT (1)&STATEMENT (2) combined
we know from statement (1) that the total number of dogs is a multiple of 20
and from statement (2) that the number of dogs is less that 50

we get total number of dogs = 20 and 40
we cant find the total number of dogs not been microchipped
so 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, 22:10
1
What we know from the stem itself is that the number of dogs must be an integer. Additionally, $$40$$% of this number must also be an integer.

$$x$$ - is the number of dogs. $$\frac{2}{5}*x$$ - must be an integer.

ST1 says that $$37.5$$% of the $$40$$% of $$x$$ also must be an integer. That means that $$\frac{3}{8} * \frac{2}{5} * x$$ must be an integer. More importantly, $$x$$ must be a fixed number so that we are able to find the number of not-microchipped dogs. However, if simplified, $$\frac{3}{20}*x$$ can be different integers depending on $$x$$. For example:

If $$x=20$$, then $$\frac{3}{20}*20= 3$$
If $$x=40$$, then $$\frac{3}{20}*40= 6$$
Insufficient

ST2 says that $$x<50$$. From the stem we know that $$\frac{2}{5}*x$$ - must be an integer. There are many numbers less than $$50$$ that can meet this requirement. For example:

If $$x=20$$, then $$\frac{2}{5}*20=8$$
If $$x=40$$, then $$\frac{2}{5}*40=16$$
Insufficient

ST1+ST2. Now $$\frac{3}{20}*x$$ must be an integer provided that $$x<50$$. Once again, there are two numbers that can meet both of these requirements:

If $$x=20$$, then $$\frac{3}{20}*20= 3$$
If $$x=40$$, then $$\frac{3}{20}*40= 6$$
Insufficient

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, 22:26
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

For knowing the number of dogs has not been microchipped, statement should provide some numeric value.
Stmt 1: it doesn't provide any numeric value. so knowing percentage information is not enough. so insufficient.
Stmt 2: it shows condition like dogs<50. but, many answer can be possible . so insufficient.
Combining 1 and 2, still many answer can be possible.
So, the correct anwer choice 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, 23:00
1
(1) 37.5% of the dogs that have been micro chipped are also either spayed or neutered.

Does not talk about total number

Insufficient

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

Does not talk about further division of micro chipped

Insufficient

Combining (1) & (2)

X can take values that are multiples of 20
--> Possible values of x = 20 or 40

Insufficient

IMO 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, 23:03
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.
37.5% of 40% of microchipped = 15%. Not enough to determine the number not microchipped.

(2) There are less than 50 dogs at the animal shelter
Total < 50 dogs
Not enough

Combine both together, 15% of (<50) should be a whole number.

The total number of dogs could be 20 or 40.
Total number of dogs not microchipped could be 12 or 24.
Both together are not enough.

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, 23:21
1
Let the total dogs be D.

40% of D = micro-chipped = X

Hence, 60% D = Not micro-chipped = Y.

We need to find numerical value Y. For that we need to find D.

D can be found if X is given.

St: 1

37.5% of 40% of D = 37.5% of X = spayed or neutered.

We are not given a definite numerical value, and hence, we cannot get D and hence Y.

St 1 not sufficient.

St: 2
D<50.
Multiple values possible. St 2 not sufficient.

St1 + St2: Even both statements together don't give definite value of D and hence, that of Y.

Re: 40% of the dogs at a certain animal shelter have been microchipped. Ho   [#permalink] 18 Jul 2019, 23:21

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