souvonik2k wrote:
What is the value of x?
(1) x² + x + 10 = 16
(2) x = 4y⁴ + 2y² +2
Target question: What is the value of x? Statement 1: x² + x + 10 = 16 Given: x² + x + 10 = 16
Subtract 16 from both sides: x² + x - 6 = 0
Factor: (x + 3)(x - 2) = 0
So,
EITHER x = -3 OR x = 2Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x = 4y⁴ + 2y² +2 Since we don't know anything about the value of y, there are many possible values of x. Here are two:
Case a: if y = 0, then
x = 4(0)⁴ + 2(0)² +2 = 2 Case b: if y = 1, then
x = 4(1)⁴ + 2(1)² +2 = 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 tells us that x is POSITIVE.
How do we know that x is POSITIVE?
Well, 4y⁴ ≥ 0 and 2y² ≥ 0 for all values of y. So, the SUM 4y⁴ + 2y² +2 MUST BE POSITIVE.
Since x = 4y⁴ + 2y² +2, we know that x is POSITIVE.
If x is positive, then x cannot equal -3, which means
x must equal 2Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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