What is the value of \(x?\)

[M7MBA]

What is the value of \(x?\)

(1) \(x^2+x+10=16\)

(2) \(x=4y^4+2y^2+3\)

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

[Jay@ManhattanReview]

What is the value of \(x?\)

(1) \(x^2+x+10=16\)

(2) \(x=4y^4+2y^2+3\)

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

Let's take each statement one by one.

(1) \(x^2+x+10=16\)

=> x^2 + x - 6 = 0 => x = -3 or 2. No unique value of x. Insufficient

(2) \(x=4y^4+2y^2+3\)

Since we do not have the unique value y, we can't get the unique value of x. Insufficient.

(1) and (2) together

From (2) \(x=4y^4+2y^2+3\), note that \(4y^4+2y^2+3\) is a positive value, irrespective of the value of y. Thus, from (1), one of the values of x = - 3 is ruled out. Thus x = 2. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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[Brent@GMATPrepNow]

What is the value of \(x?\)

(1) \(x^2+x+10=16\)

(2) \(x=4y^4+2y^2+3\)

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

Target question: What is the value of x?

Statement 1: x² + x + 10 = 16
Subtract 16 from both sides to get: x² + x - 6 = 0
Factor: (x + 3)(x - 2) = 0
This means EITHER x = -3 OR x = 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x = 4y� + 2y² +3
x can have infinitely many values, depending on the value of y.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that EITHER x = -3 OR x = 2

Statement 2 tells us that x must be a POSITIVE number. We know this because 4y� and 2y² are always greater than or equal to 0.
So, when we add 3 to 4y� + 2y², it is guaranteed that 4y� + 2y² + 3 is POSITIVE, which means x is positive

So when we combine both statements we can be certain that x = 2

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent