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

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Manager
Joined: 30 May 2019
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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, 21:25
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.

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

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19 Jul 2019, 00:23
1
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.
But it does not tell us how many dogs are not microchipped.
Insufficient.

2. There are less than 50 dogs at the animal shelter
The number of dogs < 50
It again does not tell us about not microchipped dogs.
Insufficient.

Combining 1 and 2:
Let dogs are 40 =>16 dogs are microchipped and then 6 dogs are also either spayed or neutered. We cannot say anything about not microchipped dogs.
Let dogs are 20 => 8 dogs are microchipped and then 3 dogs are also either spayed or neutered. We cannot say anything about not microchipped dogs.
We don`t have the exact number of dogs.

So, IMO the answer is E.

Please hit kudos if you like the solution.
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Re: 40% of the dogs at a certain animal shelter have been microchipped. Ho  [#permalink]

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19 Jul 2019, 00:54
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.
Since the number of dogs must be integral value, least number of dogs is= $$\frac{40}{100} * \frac{375}{1000} = \frac{3}{20}$$
Therefore, minimum number of total dogs N= 20. But no. of dogs not microchipped will vary based on the N. -Not sufficient.

(2) There are less than 50 dogs at the animal shelter, _Clearly this alone not sufficient.
(1)+(2). If N=20, No.of dogs not micro chipped is 12. But if N=4, which also satifies condition in (2), no. of dogs not micro chipped will be 24. Clearly not sufficient

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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19 Jul 2019, 01:02
1
We are informed in the question that 40% of the dogs in an animal shelter have been microchipped. Based on the given information, we expected to determine the number of dogs that are not microchipped.

Clearly, we know that 60% of the dogs are not microchipped. We therefore need information that leads us to find the total number of dogs in the shelter to enable us find the number of dogs that are not microchipped.

Statement 1 is clearly insufficient since it does not give us any useful information or data about the total number of dogs within the shelter.

From statement 2, we know that there are less than 50 dogs in the shelter. We only know that the number of dogs is less 50, meaning if we argue for the number of dogs microchipped to be an integer, we will still have many possibilities total dogs in the shelter such as: 45, 16, 35, 30, 25, 20, 15, 10 and 5. Hence statement 2 is also insufficient on its own.

Combining 1 and 2. The additional information about the proportion of dogs that were spayed or neutered does not help to narrow down thecpossilities in statement 2 to a definite figure considering taking 37.5% of the dogs that have been microchipped results in fractions. Hence both statements are insufficient.

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

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19 Jul 2019, 01:28
1
40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?

Given 40% of dogs at a shelter are microchipped .
==> 60% not microchipped . But we don't know the total no. of dogs in shelter?

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
We need total of dogs , which we cannot infer from the given data --- So Insufficient

(2) There are less than 50 dogs at the animal shelter
Given n<50 , lets say n = 49 then 60%of 49 = 29.4 = app 30
n =40 , then 60%of 40 =24

If total dogs change , dogs not microchipped change ---Insufficient.

Even if take data from A and B combined , we cannot find ---So Answer to this question 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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19 Jul 2019, 02:25
1
Given 40 percent of dogs being microchipped, and 60 percent not, we need to find what is 60 percent in numerical terms. Statement 1 does not provide us with such information neither does statement 2. Combined we are still not able to find number of dogs not microchipped as total number of dogs can be either 40 or 20. 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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19 Jul 2019, 02:27
1
Statement 2: there are less than 50 dogs at the anial shelter.

Again no substantial information i being povided.Just that we can consider the various value for number of dogs being less than 50 i.e 49,48,..........1.

Not sufficient.

Now combining both ,if we take any value less than 50 , we have to calculate 40% of it which should be a whole number and also 37.5% of 40% of dogs also has to be a whole number.

Now if we take vlaue as 49 and calculate number of dogs which are microchipped then we get 19.6 which is not a whole number also 37.5% of it also wont be a whole number (we get 7.35)

Now if we take number of dogs a 40 and calculate 40% of it we get 16 and 37.5% of it would be 6.It seems that we have arrived at the solution .But there is another value of dogs which gives a whole number as the answers and that number is 20.We get microchipped dogs as 8 and 37.5% of it would be 3.Hence we get two values and that cant hold to be true.
Hence E IMO
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Re: 40% of the dogs at a certain animal shelter have been microchipped. Ho  [#permalink]

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19 Jul 2019, 03:12
1
Let the total no. of dogs be x.

No. of dogs microchipped = 0.4x
No. of dogs not microchipped = 0.6x

We need to find the value of 0.6x (or simply the value of x)

Statement 1:
No. of dogs that have been microchipped that are also either spayed or neutered = 37.5% of 0.4x = 0.15x
No. of dogs that have been microchipped that are neither spayed or neutered = 0.4x-0.15x = 0.25x
This info doesn't help in finding the value of x.
Not sufficient.

Statement 2:
x<50
If x=40, no. of dogs not microchipped = 0.6x = 24
If x=30, no. of dogs not microchipped = 0.6x = 18
Not sufficient.

Statement 1 & 2:
No. of dogs that have been microchipped that are also either spayed or neutered = 37.5% of 0.4x = 0.15x
x<50
x should be an integer (and so should 0.15x)
But we cannot get a unique value for 0.15 x (consider the following 2 cases)
If x=40, 0.15x=6
If x=20, 0.15x=3
Not sufficient.

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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19 Jul 2019, 03:49
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

Solution:

Question Stem analysis:

If there are 40 % of dogs who have been micro chipped in a set, the rest 60 % aren't.
we need a specified value for the number of dogs

Statement One Alone:

37.5% of the dogs that have been micro chipped are also either spayed or neutered. This statement does not tell us any information about the dogs who have not been micro-chipped or the total number of dogs.
Hence statement one alone is insufficient. We can eliminate A & D

Statement two alone:

Total number of dogs is less than 50. this does not gives us a specified number but this gives us a range.

Statement one & two together

We know that , the number of dogs is less than 50 and that 40 % of them are micro chipped , considering the numbers less than 50, we can test some values , for eg, 49 now 40 % of 49 is surely not an integer, we can try 40, we see that the total number of micro-chipped dogs is 16. so we have a number, but can it satisfy the first condition and be an integer? Yes. it does. 37.5 % of 16 is 6 and hence it can be the total number of dogs, but testing some further values, we notice that 40 % of 20 is 8 & 37.5 % of 8 is 3. So we are getting two different values satisfying both the conditions and hence there isn't a specific answer or value.
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Re: 40% of the dogs at a certain animal shelter have been microchipped. Ho  [#permalink]

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19 Jul 2019, 04:43
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.
Give nothing. INSUFFICIENT

(2) There are less than 50 dogs at the animal shelter
n - number of dogs
n<50
If 40% of the dogs at a certain animal shelter have been microchipped, 0,4*n = integer (must be)
Possible variants:
5,10,15...45
INSUFFICIENT

(1) and (2) If 37.5% of the dogs that have been microchipped are also either spayed or neutered, than 0,4*0,375*n = integer (must be)
0,4*0,375 = 0,15
0,15*n = integer
n<50
Possible variants:
20 and 40
INSUFFICIENT

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

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19 Jul 2019, 04:44
1
40% of the dogs have been microchipped---->60% of the dogs haven't been microchipped., how many of the dogs account for 60%?????
So, we need to know the total of the dogs in a real number in that shelter

ST1: We know the percentage of the dogs regarding to its types.---->Obviously not helpful to answer the question----->NS

ST2: total of the dogs < 50
--->the number of the dogs with microchip + the number of the dogs without microchip < 50------>This piece of info looks like a condition for an equation; however, we couldn't get anything from this statement to answer the question---->NS

ST1 + ST2: Still couldn't answer the question, as the we need at least 1 real number to form an equation; meanwhile, we don't have any after combining all the given info.------>My 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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19 Jul 2019, 05:02
1
The number of total dogs is 'a'
--> a*40%=a*40/100=2/5*a(microchipped dogs--it should be integer)

Statement1:

"37.5% of microchipped dogs":
--> 37.5%*(2/5*a)= (37.5/100) *(2/5*a)=3/20*a
That means 3/20*a must be integer.
Still no info about how many dogs there are. Any multiples of 20 could help to find the solution.

--> (if a=20, then 20*2/5=8 microchipped ones. 20-8 =12(not been microchipped)
--> (if a=60, then 60*2/5=24 microchipped ones. 60-24 =36(not been microchipped)
....
Insufficient.

Statement2: a<50
Also, the solution depends on 'a'
if a=45, then 45-(45*40/100)=27 (not been microchipped)
if a=35, then 35-(35*40/100)=19 (not been microchipped)
....
Insufficient

Taken together 1 and 2:
---> '3/20*a' and a<50
There are 2 multiples of 20 between 1 and 50,(not inclusive): (20 and 40) --> that means two different solutions

Insufficient

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

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19 Jul 2019, 05:20
1
40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?
As we are talking about alive beings, their number always has to be an integer

(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
Not sufficient, as 37.5% could of 100 or 200 or ...1000 of dogs

(2) There are less than 50 dogs at the animal shelter
Not sufficient, as 40% could of 10, 20,30,40 (multiple of 10<50) dogs

Combined, we get that 37,5% spayed of 40% chipped of X dogs needs to be an integer less than 50. Is there is such unique integer?
$$0.375 *0.40*X = 0.15*X$$, then to be an integer X must be multiple of 20 less than 50: 20, 40
Back-test :
$$40*.4*.375 = 6$$
$$20*.4*.375 = 3$$

So, since there are 2 possibilities of X, then insufficient, answer is E.
Re: 40% of the dogs at a certain animal shelter have been microchipped. Ho   [#permalink] 19 Jul 2019, 05:20

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