mgmt_gmat wrote:which of the following is a value of X
for which X^11-X^3>0
A. -2
B. -1
C. -1/2
D. 1/2
E. 1

We see that all the answers have different properties:

A) negative number smaller than -1
B) -1
C) negative fraction
D) positive fraction
E) 1

So, we can answer the question either using those properties or we can simply backsolve, i.e. plug in the choices until one works.

Backsolving with such simple numbers should be very quick, so there's absolutely no reason not to do so if a more "elegant" solution doesn't immediately jump out at you.

Plugging in:

E) 1 - 1 = 0.. wrong
D) 1/2^11 - 1/2^3... second term is bigger, so < 0.. wrong.
C) -(1/2^11) - (-1/2^3) = -(1/2^11) + (1/2^3)... second term is bigger, so > 0.. correct!

Note that we dno't need to actually solve D or E, we just need to determine which term is bigger so we can identify the sign of the final answer.

mgmt_gmat wrote:which of the following is a value of X
for which X^11-X^3>0
A. -2
B. -1
C. -1/2
D. 1/2
E. 1

X^11 - X^3 = X^3 (X^8 - 1) > 0 is possible only when -1 < X < 0, because in that case only, each of the two factors of X^11 - X^3 is negative. Only [spoiler]C[/spoiler] fits in the rut. See how [spoiler]C[/spoiler] works

When X = [spoiler]-½[/spoiler], then X^3 = -1/8 < 0 and (X^8 - 1) = (a positive proper fraction - 1) < 0 and (a < 0) × (b < 0) > 0.

[spoiler]C[/spoiler]