What is the value of x? (1) 2x – 5y + 6 = 12

[ruben]

Hi,

I was wondering why the answer to this question is E. Even if we obtain the same equations when we isulate de x, we can still do:

2x - 5y + 6 = 12
2x - 5y = 12 - 6
2x - 5y = 6
2x = 6 + 5y
x = (6 + 5y)/2

Then solve for the y 8x - (4x + 10y) + 27 = 39 that equals to y=(12-4x)/2 .
Finally we can substitute y in the equation x = (6 + 5y)/2
=(6+5(12-4x)/2)/2 that gives us the x. Can anyone help?

Thanks :D


What is the value of x?

(1) 2x - 5y + 6 = 12

(2) 8x - (4x + 10y) + 27 = 39

When a data sufficiency question provides equations or algebraic expressions that can be simplified, make sure to do so before drawing any conclusions.

(1) INSUFFICIENT: After simplifying the equation, the value of x still cannot be determined without knowing the value of y:

2x - 5y + 6 = 12
2x - 5y = 12 - 6
2x - 5y = 6
2x = 6 + 5y
x = (6 + 5y)/2

(2) INSUFFICIENT: After simplifying the equation, the value of x still cannot be determined without knowing the value of y:

8x - (4x + 10y) + 27 = 39
8x - 4x - 10y = 39 - 27
4x - 10y = 12
2x - 5y = 6
2x = 6 + 5y
x = (6 + 5y)/2

(1) AND (2) INSUFFICIENT: Note that we ended up with the same equation from both statements. Therefore, we cannot solve for the value of x. On data sufficiency problems involving systems of equations, be aware of duplicates and always simplify the equations before making the final decision.

The correct answer is E.

[StaceyKoprince]

Hey, ruben, I think you might have made a little math error in there that messed things up.

You said

Then solve for the y 8x - (4x + 10y) + 27 = 39 that equals to y=(12-4x)/2

Here's a step-by-step process for solving for y
8x - (4x + 10y) + 27 = 39 distribute the negative sign into the parentheses
8x - 4x - 10y + 27 = 39 combine the x's and the pure numbers
4x - 10y = 12 move x to right
-10y = -4x+12 divide by -10
y = 2x/5 - 6/5

If you manipulate that, you get 5y = 2x-6 => 5y+6 = 2x => (5y+6)/2 = x, which is still the same equation from statement 1.

[Guest]

THANK YOU SO MUCH FOR THE HELP!!!

RUBEN