Data Sufficiency

BTGmoderatorDC wrote: ↑

Thu Feb 24, 2022 4:53 pm

What is the value of x?

(1) 4x = 2y − 6
(2) (y - 3)/2 = x


OA E

Source: Veritas Prep

Target question: What is the value of x?

Key concept #1: It's impossible to solve a linear equation with two variables (with no restrictions on the values of the variables) for one of the variables.

Statement 1: 4x = 2y − 6
Since this is a linear equation with two variables, we can't solve it for x
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (y - 3)/2 = x
Since this is a linear equation with two variables, we can't solve it for x
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Key concept #2: We can solve a system of two linear equations with two variables as long as the two equations are different
In this case, the two equations given in statements 1 and 2 are equivalent. Here's why:
Take the equation from statement 2: (y - 3)/2 = x
Multiply both sides of the equation by 2 to get: y - 3 = 2x
Multiply both sides of the equation by 2 to get: 2y - 6 = 4x, which is identical to the equation given and statement 1.

So, we basically have just 1 unique linear equation with two variables, which means we can't solve it for x.
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent