Data Sufficiency

VJesus12 wrote: ↑

Sun Apr 25, 2021 11:06 am

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.

Answer: C

Source: Official Guide

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