Is 10–6x<0?

VERITAS PREP OFFICIAL SOLUTION:

Solution: (A)

Statement (1): 5x^2> 3x^3

Because x^2 is always positive, we can divide both sides by x2 without needing to worry about changing the inequality. In doing so, we find that:

5 > 3x

Because our goal is to determine whether 10 < 6x, we can multiply the fact above by 2:

2(5) > 2(3x)

To find that 10 > 6x. Therefore, we can prove that the answer is no; 10 is GREATER THAN 6x, and the question asks whether it’s less than 6x.

Statement (2): 4 > 3/x

We can manipulate that statement to find that:

4 – 3/x > 0

(4x – 3)/x > 0

Since both factors should either be positive or both should be negative to make the division positive, x should either be less than 0 or greater than ¾. If x is less than 0, 10 – 6x is positive but if x is greater than ¾, (10 – 6x) could be negative. Hence statement (2) alone is not sufficient to answer the question.