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# How many more dogs than cats are in the veterinarian’s office?

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Math Expert
Joined: 02 Sep 2009
Posts: 44629
How many more dogs than cats are in the veterinarian’s office? [#permalink]

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23 Aug 2016, 02:46
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5% (low)

Question Stats:

86% (00:32) correct 14% (00:24) wrong based on 58 sessions

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How many more dogs than cats are in the veterinarian’s office?

(1) There is a total of 30 dogs and cats in the office.
(2) The number of cats is the square root of the number of dogs.
[Reveal] Spoiler: OA

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Posts: 600
Re: How many more dogs than cats are in the veterinarian’s office? [#permalink]

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23 Aug 2016, 05:14
Bunuel wrote:
How many more dogs than cats are in the veterinarian’s office?

(1) There is a total of 30 dogs and cats in the office.
(2) The number of cats is the square root of the number of dogs.

Stat 1: D+C = 30...Insufficient

Stat 2: C = sqr(D) => C^2= D...Insufficient.

Stat 1+Stat 2: C^2+C = 30 => C = 6 and -5...only positive value is considered.

then C = 6 and D = 36.

IMO option C is the correct answer..
Intern
Joined: 21 Apr 2016
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Re: How many more dogs than cats are in the veterinarian’s office? [#permalink]

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23 Aug 2016, 05:21
A insufficient b insufficient c is the option 25 dogs 5 cats

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Joined: 18 Aug 2013
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Re: How many more dogs than cats are in the veterinarian’s office? [#permalink]

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23 Aug 2016, 06:09
(1) C + D = 30 ---> Insufficient

(2) C = sqrt (D) ---> Insufficient

Both (1) and (2) => D = 30 - C

C = sqrt (30-C) => C^2 = 30 - C => C^2 + C - 30 = 0 => (C+6) (C-5) = 0

C = -6 ( we can ignore the -ve value. since the no. of cats cant be -ve), 5 --> C = 5

D = 30 - 5 = 25 .. So together (1) and (2) --> conditions are sufficient --> Option C
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Re: How many more dogs than cats are in the veterinarian’s office? [#permalink]

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23 Aug 2016, 06:12
msk0657 wrote:
Bunuel wrote:
How many more dogs than cats are in the veterinarian’s office?

(1) There is a total of 30 dogs and cats in the office.
(2) The number of cats is the square root of the number of dogs.

Stat 1: D+C = 30...Insufficient

Stat 2: C = sqr(D) => C^2= D...Insufficient.

Stat 1+Stat 2: C^2+C = 30 => C = 6 and -5...only positive value is considered.

then C = 6 and D = 36.

IMO option C is the correct answer..

I guess by mistake you have chosen C = 6.. it shud be c = 5 and NOT c= -6 (C^2 + C - 30 = 0)
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Re: How many more dogs than cats are in the veterinarian’s office? [#permalink]

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23 Aug 2016, 11:14
Bunuel wrote:
How many more dogs than cats are in the veterinarian’s office?

(1) There is a total of 30 dogs and cats in the office.
(2) The number of cats is the square root of the number of dogs.

Let D denote Dogs and C denote Cats, question is what's D-C ?

1) D + C = 30 , not sufficient , Eliminate A and D
2) C = $$\sqrt{D}$$ or $$D = C^2$$. Not sufficient, Eliminate B

1) + 2) , $$C^2 + C - 30 =0$$ and (C+6)(C-5) = 0
C has a positive root and Hence answer is C

+1 for Kudos
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How many more dogs than cats are in the veterinarian’s office? [#permalink]

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01 Jan 2018, 08:46
Expert's post
Top Contributor
Bunuel wrote:
How many more dogs than cats are in the veterinarian’s office?

(1) There is a total of 30 dogs and cats in the office.
(2) The number of cats is the square root of the number of dogs.

Let D = # of dogs
Let C = # of cats

Target question: What is the value of D - C?

Statement 1: There is a total of 30 dogs and cats in the office
In other words, D + C = 30
There are several scenarios that satisfy statement 1. Here are two:
Case a: D = 29 and C = 1. In this case, the answer to the target question is D - C = 29 - 1 = 28
Case b: D = 20 and C = 10. In this case, the answer to the target question is D - C = 20 - 10 = 10
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The number of cats is the square root of the number of dogs.
In other words, C = √D
There are several scenarios that satisfy statement 1. Here are two:
Case a: D = 9 and C = 3. In this case, the answer to the target question is D - C = 9 - 3 = 6
Case b: D = 25 and C = 5. In this case, the answer to the target question is D - C = 25 - 5 = 20
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
From both statements, we get the following system:
D + C = 30
C = √D

Take top equation and replace C with √D to get: D + √D = 30
Subtract D from both sides: √D = 30 - D
Square both sides: (√D)² = (30 - D)²
Expand: D = 900 - 60D + D²
Rearrange to get: D² - 61D + 900 = 0
Factor to get: (D - 25)(D - 36) = 0
So, EITHER D = 25 OR D = 36
From statement 1, we can see that there CANNOT be more than 30 dogs, so we can ignore the solution D = 36
So, it must be the case that D = 25
If D = 25, then C = 5
So, the answer to the target question is D - C = 25 - 5 = 20
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

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How many more dogs than cats are in the veterinarian’s office? [#permalink]

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02 Jan 2018, 05:10
Bunuel wrote:
How many more dogs than cats are in the veterinarian’s office?

(1) There is a total of 30 dogs and cats in the office.
(2) The number of cats is the square root of the number of dogs.

Let the number of dogs = d & number of cats = c

1) d + c = 30
We can have many combinations

Insufficient

2) c = $$\sqrt{d}$$

Any perfect square can work. We can have many combinations

Insufficient

Combine 1 & 2

d + c = 30

d + $$\sqrt{d}$$ = 30

here we can start with plug in values starting with perfect square close to 30

Check d =25........5 + 25 = 30,,,bingo

Any other perfect square less than 25 won't make total 30

Sufficient

How many more dogs than cats are in the veterinarian’s office?   [#permalink] 02 Jan 2018, 05:10
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# How many more dogs than cats are in the veterinarian’s office?

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