BTGmoderatorDC wrote:If a certain vase contains only roses and tulips, how many tulips are there in the vase?
(1) The number of roses in the vase is 4 times the number of tulips in the vase.
(2) There is a total of 20 flowers in the vase.
Here's a solution that uses
2 variables
Let R = number of roses in the vase
Let T = number of tulips in the vase
Target question: What is the value of T?
Statement 1: The number of roses in the vase is 4 times the number of tulips in the vase.
We can write:
R = 4T
As we can see, there are infinitely many different values of R and T that satisfy this equation. For example...
Case a: T = 3 and R = 12. In this case, the answer to the target question is
T = 3
Case b: T = 4 and R = 16. In this case, the answer to the target question is
T = 4
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: There is a total of 20 flowers in the vase.
We can write:
R + T = 20
As we can see, there are many different values of R and T that satisfy this equation. For example...
Case a: T = 3 and R = 17. In this case, the answer to the target question is
T = 3
Case b: T = 4 and R = 16. In this case, the answer to the target question is
T = 4
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that
R = 4T
Statement 2 tells us that
R + T = 20
At this point, we should recognize that we have a system of 2 linear equations with 2 variables. As such, we COULD solve this system for R and T, which means we COULD answer the
target question.
ASIDE: Although we COULD solve the system of equations, we would never waste valuable time on test day doing so. We need only determine that we COULD answer the target question.
Since we COULD answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
