What is the value of x?

1. xy-4=2y

Not Sufficient

2. x+2y=8
2y=8-x
Not Sufficient

1 and 2:
xy-4=8-x
xy+x=12
x(y+1)=12

Not Sufficient

Answer: E

#1 and #2 separately are obviously insufficient coz we can't determine the value of a single variable from just one equation with 2 variables.

#1 + #2 gives us a system of 2 equations and the solutions are 2 pairs of (x,y): (6,1) and (4,2). This result prevents us from explicitly answering the question.

Answer is E

(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.
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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.
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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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