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The ratio of cats to dogs to birds to fish is 4:5:2:10. Ther

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The ratio of cats to dogs to birds to fish is 4:5:2:10. Ther  [#permalink]

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New post 14 Dec 2013, 14:25
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The ratio of cats to dogs to birds to fish is 4:5:2:10. There are no other types of animals in the pet store. If there are 20 of one type of animal at the store then which of the following cannot be the total number of animals in the store?

A) 42
B) 63
C) 84
D) 105
E) 210

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Magoosh GMAT Instructor
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Re: The ratio of cats to dogs to birds to fish is 4:5:2:10. Ther  [#permalink]

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New post 14 Dec 2013, 14:36
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3
enigma123 wrote:
The ratio of cats to dogs to birds to fish is 4:5:2:10. There are no other types of animals in the pet store. If there are 20 of one type of animal at the store then which of the following cannot be the total number of animals in the store?

A) 42
B) 63
C) 84
D) 105
E) 210

Dear enigma123,
I'm happy to help. :-) This is a good question on ratio and proportions. See:
http://magoosh.com/gmat/2013/gmat-quant ... oportions/

The parts add up to 4 + 5 + 2 + 10 = 21, so we know that any possible number of total answers must be a multiple of 21. All five answer choices are multiples of 21:
(A) 42 = 21*2
(B) 63 = 21*3
(C) 84 = 21*4
(D) 105 = 21*5
(E) 210 = 21*10

The second stipulation is that the factor by which we are multiplying must bring one of the four numbers to 20.
4 time 5 is 20, so 5 is a possible multiple, and (D) is a possible total number.
5 time 4 is 20, so 4 is a possible multiple, and (C) is a possible total number.
2 time 10 is 20, so 10 is a possible multiple, and (E) is a possible total number.
10 time 2 is 20, so 2 is a possible multiple, and (A) is a possible total number.

By contrast, if we multiply everything by 3, none of the individual numbers becomes 20. Therefore, (B) is not a possible total number of animals, and this is the answer. OA = (B).

Does this make sense?
Mike :-)
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Re: The ratio of cats to dogs to birds to fish is 4:5:2:10. Ther  [#permalink]

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New post 11 Sep 2014, 03:31
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enigma123 wrote:
The ratio of cats to dogs to birds to fish is 4:5:2:10. There are no other types of animals in the pet store. If there are 20 of one type of animal at the store then which of the following cannot be the total number of animals in the store?

A) 42
B) 63
C) 84
D) 105
E) 210


Let the animal = x

4x + 5x + 2x + 10x = 21x

All options are already multiples of 21, so nothing can be ignored

Ratio is 4:5:2:10 >>> Note that the LCM of ratio's = 20. Already given that 20 animals are any of one type, so again all options have to be worked out.

Refer sheet below:
Attachment:
sap.png
sap.png [ 5.13 KiB | Viewed 8408 times ]


63 does not come up in calculation

Answer = B
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New post 10 Jun 2016, 13:49
The ratio of cats to dogs to birds to fish in a pet store is 4:5:2:10. There are no other types of animals in the pet store. If there are 20 of one type of animal the store then which of the following cannot be the total number of animals in the store?

a) 42
b) 63
c) 84
d) 105
e) 210
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Re: The ratio of cats to dogs to birds to fish is 4:5:2:10. Ther  [#permalink]

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New post 10 Jun 2016, 13:55
sabrina3509 wrote:
The ratio of cats to dogs to birds to fish in a pet store is 4:5:2:10. There are no other types of animals in the pet store. If there are 20 of one type of animal the store then which of the following cannot be the total number of animals in the store?

a) 42
b) 63
c) 84
d) 105
e) 210


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Re: The ratio of cats to dogs to birds to fish is 4:5:2:10. Ther  [#permalink]

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New post 19 Jun 2017, 11:03
enigma123 wrote:
The ratio of cats to dogs to birds to fish is 4:5:2:10. There are no other types of animals in the pet store. If there are 20 of one type of animal at the store then which of the following cannot be the total number of animals in the store?

A) 42
B) 63
C) 84
D) 105
E) 210

Total no of animals must be a multiple of \(4+5+2+10 = 21\) , all the options satisfies the conditions...

If the total no of cats is 20 , total no of animals is 105 ( Option D )
If the total no of dogs is 20 , total no of animals is 84 ( Option C )
If the total no of birds is 20 , total no of animals is 210 ( Option E )
If the total no of fist is 20 , total no of animals is 42 ( Option A )

So, the correct answer will be (B)
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Re: The ratio of cats to dogs to birds to fish is 4:5:2:10. Ther  [#permalink]

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New post 06 Jul 2017, 17:45
enigma123 wrote:
The ratio of cats to dogs to birds to fish is 4:5:2:10. There are no other types of animals in the pet store. If there are 20 of one type of animal at the store then which of the following cannot be the total number of animals in the store?

A) 42
B) 63
C) 84
D) 105
E) 210


We are given that the ratio of cats to dogs to birds to fish is 4 : 5 : 2 : 10 = 4x : 5x : 2x : 10x.

Thus, the total number of animals is 21x.

Let’s analyze each answer choice:

A) 42

21x = 42

x = 2

Since 20 is a multiple of 2 and, in particular, the number of fish = 10x = 10(2) = 20, there can be 42 animals in the store.

B) 63

21x = 63

x = 3

Since 20 is not a multiple of 3, there cannot be 63 animals in the store.

Alternate solution:

We are given that the ratio of cats to dogs to birds to fish is 4 : 5 : 2 : 10 = 4x : 5x : 2x : 10x.

Thus, the total number of animals is 21x.

Since the number of one type of animal is 20, we can see that x could be 5, 4, 10, and 2, respectively, for the number of cats, dogs, birds, and fish to be 20.

Since the total number of animals is 21x, the total number of animals could be 105, 84, 210, and 42. We see that all of these 4 numbers are in the given answer choices. However, the answer choice of 63 is not one of these 4 numbers, so it can’t be the total number of animals.

Answer: B
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Re: The ratio of cats to dogs to birds to fish is 4:5:2:10. Ther  [#permalink]

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New post 06 Jul 2017, 18:43
If 4 corresponds to 20: 20+25+10+50 = 105.

If 5 corresponds to 20: 16+20+8+40 = 84.

If 2 corresponds to 20: 40+50+20+100 = 210.

If 10 corresponds to 20: 8+10+4+20 = 42.

Ans - B.
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Re: The ratio of cats to dogs to birds to fish is 4:5:2:10. Ther  [#permalink]

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