GMAT Data Sufficiency- What is the Value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2

Question: What is the value of x?
1) x^2 + x + 10 = 16
2) x = 4y^4+2y^2+2

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 the value of x? If 1)x^2 + x + 10 = 16 2)x = 4y^4+2y^2+2”- 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. GMAT data sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Approach Solution 1:
There is only one approach to solve the problem
We will check each statement separately.
Statement 1:
x² + x + 10 = 16
We will rewrite as: x² + x - 6 = 0
The Factors are: (x + 3)(x - 2) = 0
So, x = -3 OR x = 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2:
x = 4y⁴ + 2y² + 2
As you can see, the value of x depends on the value of y.
Now, we will consider these two cases:
Case a:
y = 0, in which case
x = 4(0⁴) + 2(0²) + 2.
On evaluation we see that x = 2
Case b:
y = 1, in which case
x = 4(1⁴) + 2(1²) + 2.
On evaluation we see that x = 8
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that x = -3 OR x = 2
Statement 2: Since y⁴ and 2y² are greater than or equal to zero FOR ANY value of y, we can see that 4y⁴ + 2y² + 2 must be positive. In other words, x must be POSITIVE.
If x must be positive, then x MUST equal 2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT.
Correct Answer: C

Some suggested GMAT Data Sufficiency Questions

• GMAT Data Sufficiency- Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is 5 units
• GMAT Data Sufficiency- If each side of parallelogram P has length 1, what is the area of P ?
• GMAT Data Sufficiency- Is the positive integer n a multiple of 24?
• GMAT Data Sufficiency- Did Insurance Company K have More than $300 Million in Total Net Profits Last Year?
• GMAT Data Sufficiency- Is 1/(a - b) > b - a ?
• GMAT Data Sufficiency-  Is |x-10| > |x-30|
• GMAT Data Sufficiency- If J≠0, What Is The Value Of J?
• GMAT Data Sufficiency- Paint X Costs $15 per Gallon, and Paint Y Costs $20 per Gallon
• GMAT Data Sufficiency- What is the total value of Company H's stock?
• GMAT Data Sufficiency- Is PQ > 1?
• GMAT Data Sufficiency- How Many of the Students in a Certain Class are Taking Both a History and a Science Course?
• GMAT Data Sufficiency- The Set S of Numbers has the following Properties
• GMAT data Sufficiency- A Contractor Combined x Tons of a Gravel Mixture that Contained 10 percent Gravel G
• GMAT Data Sufficiency- If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies
• GMAT Data Sufficiency- From a Group of M Employees, N Will be Selected, at Random
• GMAT Data Sufficiency- Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)?
• GMAT Data Sufficiency- Juan Bought Some Paperback Books That Cost $8
• GMAT Data Sufficiency- The symbol ∆ Denotes One of The Four Arithmetic Operations
• GMAT Data Sufficiency- X is Older Than Y, Z Is Younger Than W, And V is Older Than Y. Is Z Younger Than X?
• GMAT Data Sufficiency- 2x+3y