Data Sufficiency

BTGModeratorVI wrote: ↑

Tue Feb 16, 2021 8:15 am

What was the discounted price of a certain television set?

(1) The original price of the television set was $50 more than the discounted price.
(2) The original price of the television set was 110 percent of the discounted price.

Answer: C
Source: official guide

Target question: What was the discounted price of a certain television set?
Let D = the discounted price of the television set

Statement 1: The original price of the television set was $50 more than the discounted price.
Let R = the original price of the television set
We can write: R - D = 50
Since there are infinitely many solutions to this equation, we can’t answer the target question with certainty.
Statement 1 is NOT SUFFICIENT

Statement 2: The original price of the television set was 110 percent of the discounted price
We can write: R = 1.1D
Since there are infinitely many solutions to this equation, we can’t answer the target question with certainty.
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that R - D = 50
Statement 2 tells us that R = 1.1D
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 D, 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 can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent