Is x a positive number?

x a positive number?

(1) –5x – 3 > -2x
x < -1
definitely neg
Sufficient

(2) x^2 is positive.
if x is positive or negative e the squared masks it
Insufficient

Answer: A

Is x a positive number?

(1) –5x – 3 > -2x
(2) x^2 is positive.

Kudos for a correct solution.

st 1
–5x – 3 > -2x
–5x + 2x > 3
-3x > 3
-x> 1
multiplying with -1..inequality sign changes sign

x< ( -1)

hence x is negative . Therefore A is the answer .


st . 2
x^2 is positive.

means x can positive or negative .
lets check with a value
x= 2 , x^2 = 4
x= ( -2) , x^2 = 4

hence not sufficient

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No This question asks whether x is a positive number.

Statement 1: “-5x – 3 > -2x” can be simplified by adding 3 to both sides to yield “ -5x > -2x + 3” and then adding 2x to both sides to yield “-3x > 3.” Then, to isolate x, divide both sides by 3 and –x > 1. To change the sign of x, multiply both sides by a negative 1 and the statement becomes “x < -1.” This algebraic manipulation has answered the question directly. “No, x is a not positive. x is a negative number.” This statement is sufficient. The answer is either A or D.

Statement 2: x^2 is positive allows for x to be either positive or negative. Since the answer is not consistent this statement is not sufficient.

The correct answer is A.

One important takeaway here: Even though Statement 1 provided the answer “no,” it was indeed sufficient. A definite “no” means you have sufficient information to arrive at one exact answer. So while your instincts might tell you “No --> Eliminate,” remember that “no” means “sufficient.”