What is the value of x?

(1) x – (4/y) = 2
x varies based on the value of y
insufficient

(2) x + 2y = 8
Same as statement 1, x varies based on the value of y
insufficient

combined, we get (y-1)(y-2)=0
X varies based on y being 1 or 2
insufficient
Answer : E

St 1) x – (4/y) = 2 -> Possible values of x and y (3,4);(6,1);(4,2) and other fraction values since its not given in the ques that x and y are int. NS
St 2) x + 2y = 8 -> Possible values of x and y (0,4);(8,0);(4,2);(2,3);(6,1) and other values+frac since its not given in the ques that x and y are int. NS
Combining St 1 and St 2 more than 1 values for both x and y
Answer E

MAGOOSH OFFICIAL SOLUTION

Because both (1) and (2) involve y as well as x, each may allow you to solve for x in terms of y, but neither by itself will yield a unique constant value for x. Eliminate A, B, and D.

Are the two statements sufficient together? Probably not, since (1) is not linear equation, and a system of a single linear equation with a single nonlinear equation doesn’t ordinarily yield a solution. Just in case this an exception, though, let’s try to solve this system for x.

(If we’re very clever we might notice that solving for y is just as good as solving for x, since it leads to a value for x. Solving for y might also be easier here. Let’s suppose that we missed that shortcut, though, and just solve for x.)

Solving the system for x begins with solving for y in terms of x in the second equation.
x + 2y = 8

Subtract x from each side.
2y = 8 – x

Divide each side by 2.
y = 4 – (x/2)

Substitute the expression 4 – (x/2) for y in the first equation.
x – 4/(4 – (x/2)) = 2

Rewrite the expression 4 – (x/2) as (8/2) – (x/2) or simply as (8 – x)/2.
x – (4/((8 – x)/2) = 2

Simplify the compound fraction.
x – (8/8 – (x)) = 2

Multiply each term by 8 – x to clear the fraction.
x(8 – x) – 8 = 2(8 – x)

Distribute to clear the parentheses.
8x – x^2 – 8 = 16 – 2x

Transpose to arrange in the usual quadratic form
-x^2 +6x – 8 = 0

Multiply through by -1.

x^2 – 6x + 8 = 0

At this point you might recognize that this is a quadratic but not a perfect quadratic square, and so must have two solutions. If you don’t recognize that, go ahead and solve it.
(x – 2)(x – 4) = 0
x = {2, 4}

Since the two statements together don’t yield a unique constant value, they are not sufficient.

The correct answer is E.

from 1) 2xy – 4y= 8
from 2) x + 2y= 8
combining:
\(\frac{6y}{(2y-1)} = x\)

since there is no restriction on value of Y , we will get numerous value of X .

Hence E

Correction:
x + 2y = 8

Subtract x from each side will become 2y = 8 - x

And the final equation after substitution is x^2-10x+24=0 and solution is x = {4, 6}

Am I correct....

Typo edited. Thank you.

Hi All,

While this prompt can certainly be solved with "System" Algebra, it can also quickly be solved by TESTing VALUES.

We're asked for the value of X.

Fact 1: X - (4/Y) = 2

IF...
Y = 1
X = 6 and the answer to the question is 6

IF...
Y = 2
X = 4 and the answer to the question is 4
Fact 1 is INSUFFICIENT

Fact 2: X + 2Y = 8

With a just a little work, you'll find that the TESTs that we used in Fact 1 ALSO fit Fact 2....

IF...
Y = 1
X = 6 and the answer to the question is 6

IF...
Y = 2
X = 4 and the answer to the question is 4
Fact 2 is INSUFFICIENT

Combined, we already have the same two (different) answers that fit BOTH Facts.
Combined, INSUFFICIENT

Final Answer:

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Rich

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