What is x? (1) x = 4y - 4 (2) xy = 8 GMAT Data Sufficiency

Question- What is x?

(1) x = 4y - 4
(2) xy = 8

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“What is x?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. 
Data sufficiency questions are usually refined questions for GMAT. Candidates while solving these questions do not actually understand the hints and find the questions complex. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

There is only one approach to solve the problem

We will take both the statements separately to check if they are sufficient.

Let us start with statement 1:
x = 4y − 4
1 equation with 2 variables means there are infinitely many possible values for x.
In such cases, we can test with some values..
There are multiple values of x and y that satisfy the statement.
Case a: x = 0 and y = 1.
x = 4y − 4
Now, if we put the values, we get:
0=4*1-4
0=4-4
Hence, in this case x = 0
Case b: x = 4 and y = 2.
x = 4y − 4
Now, if we put the values, we get:
4=4*2-4
4=8-4
Hence, in this case x = 4
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Now, we will consider Statement 2:
xy = 8
In this statement also there are infinitely many possible values for x.
If we're uncertain, we can TEST some values.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 8.
Considering the equation: xy = 8
Now, we will put the values, we get:
1*8 = 8
Hence, in this case x = 1
Case b: x = 4 and y = 2.
Considering the equation: xy = 8
Now, we will put the values, we get:
4*2 = 8
Hence, in this case x = 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Now, we will combine Statements 1 and 2
Statement 1 tells us that x = 4y − 4
Statement 2 tells us that xy = 8
Let us take x = 4y − 4, and solve for y.
So, add 4 to both sides to get: x + 4 = 4y
Divide both sides by 4 to get: (x + 4)/4 = y
Now, we will take xy = 8 and replace y with (x + 4)/4 to get…
(x)(x + 4)/4 = 8
Multiply both sides by 4 to get: (x)(x + 4) = 32
Expand: x² + 4x = 32
Set equal to zero to get: x² + 4x - 32 = 0
Factor: (x + 8)(x - 4) = 0
So, EITHER x = -8 OR x = 4
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT.

Correct Answer: E

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