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

(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

I guess by mistake you have chosen C = 6.. it shud be c = 5 and NOT c= -6 (C^2 + C - 30 = 0)

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

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

Answer: C

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

Answer: C

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