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Thu Sep 02, 2021 3:03 am

Princeton Review

If 2a + 3b = 7, what is the value of b?

1) a − b = − 4
2) 4a = 14 − 6b

OA A

Given: 2a + 3b = 7

Target question: What is the value of b ?

Key property: If we have a system of 2 different linear equations with two variables, then we can solve that system for each variable

Statement 1: a − b = − 4
Since this linear equation is different from the given linear equation (2a + 3b = 7), we have a system of two different linear equations with two variables, which means we COULD solve that system for a and b (although we would never waste valuable time on test day doing so)
Since we could answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 4a = 14 − 6b
This equation seems similar to the given equation (2a + 3b = 7). So let's investigate further....
Take: 4a = 14 − 6b
Divide both sides by 2 to get: 2a = 7 - 3b
Add 3b to both sides to get: 2a + 3b + 7
Since statement 2 provides us with an equation that is equivalent to the given equation (2a + 3b = 7), we DON'T have a system of two different linear equations.
As such, we can't solve that system for a and b.
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent