Is x > 3? (1) The sum of x and the square of x is 12 (2) x^2 > 9

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No. This question asks: “Is x > 3?”

Given information in question stem or diagram: No important information is given in the question stem.

Statement 1: The first step in this statement is to translate the wording into the following equation: x + x^2 = 12. Since this is a quadratic equation, you should set everything equal to zero so that x^2 + x – 12 = 0. Factoring this, you see that (x + 4)(x - 3) = 0 and x would be -4 or 3. The difficulty in this statement is that many people assume that this information is not sufficient because there are two values, one negative and one positive. However, remember that to prove sufficiency in a yes or no question requires only a definitive answer, not one value. Since each of these values (-4 and 3) gives a “no” answer to the question, this statement is sufficient. The answer is either A or D.

Statement 2: x^2 > 9. If x^2 > 9 then either x > 3, which gives you a “yes” answer, or x < 3, which gives you a “no” answer. For example x could be -5 (which when squared is > 9) or 5 (which when squared is also > 9). This statement is thus not sufficient, and the correct answer is A.

Note: This question is created to prey on two common mistakes, one relating to Data Sufficiency itself and one relating to algebra: 1.) People (even those who have done lots of data sufficiency) tend to forget to look for the “no” answer in Yes/No questions and they often make mistakes about what is really required for sufficiency on Yes/No questions. 2.) People forget about the negative possibilities when dealing with squared variables in inequalities.

Bunuel
It seems that statement 1 does not make any sense-it's just combination of some words. Here, my thinking says: \(x+x^2=12\) is not same as what statement 1 says!
Thanks__

The sum of x and the square of x is 12 is exactly the same as x + x^2 = 12.

(1) The sum of x and the square of x is 12.
\(x^2+x=12\)
Since we have a quadratic equation, we will get two values of x. Also the question asked has a specific range, so chances are that we get our answer here.
\(x(x+1)=12=3*4=-4*-3\)
So, x is 3 or -4. In both cases, the answer is NO for ' Is x>3?'
Sufficient.

(2) x^2 > 9
\(x^2>9...........|x|>3......x>3 \ \ or \ \ x<-3\)
Both yes and no possible.
Insufficient


A

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