Data Sufficiency

Vincen wrote:What is the value of x?

(1) 3x² + 8x + 16/3 = 0
(2) 15x² + 80/3 = -40x

This question tests our knowledge of SPECIAL PRODUCTS:
a² + 2ab + b² = (a + b)(a + b)
a² - 2ab + b² = (a - b)(a - b)

Target question: What is the value of x?

Statement 1: 3x² + 8x + 16/3 = 0
Let's first eliminate the fractions by multiplying both sides of the equation by 3
When we do this, we get: 9x² + 24x + 16 = 0
Factor to get: (3x + 4)(3x + 4) = 0
So, it must be the case that 3x + 4 = 0
So, 3x = -4
x = -4/3
So, the answer to the target question is x = -4/3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 15x² + 80/3 = -40x
Let's first eliminate the fractions by multiplying both sides of the equation by 3
When we do this, we get: 45x² + 80 = -120x
Add 120x to both sides: 45x² + 120x + 80 =0
Divide both sides by 5 to get: When we do this, we get: 9x² + 24x + 16 = 0
This is the same equation we had in statement 1
So, the answer to the target question is x = -4/3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent