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What is the value of x?

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What is the value of x?

by Vincen » Tue Nov 28, 2017 6:28 am
What is the value of x?

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

The OA is D .

Experts, may you clarify this DS question? I don't know how to solve it. Thanks in advance.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Nov 28, 2017 6:47 am
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
Brent Hanneson - Creator of GMATPrepNow.com
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by GMATGuruNY » Tue Nov 28, 2017 6:49 am
Vincen wrote:What is the value of x?

(1) 3x^2 + 8x + 16/3 = 0
(2) 15x^2 + 80/3 = -40x
Statement 1:
Multiplying the equation by 3, we get:
9x² + 24x + 16 = 0
(3x + 4)(3x + 4) = 0.
The equation above is valid only if 3x+4 = 0:
3x + 4 = 0
3x = -4
x = -4/3.
SUFFICIENT.

Statement 2:
Multiplying the equation by 3, we get:
45x² + 80 = -120x

Dividing the equation by 5, we get:
9x² + 16 = -24x
9x² + 24x + 16 = 0.
Same equation as in Statement 1.
SUFFICIENT.

The correct answer is D.
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