lheiannie07 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
Answer: C
Cheers,
Brent
