Problem Solving

aman88 wrote:Q: 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

I am sorry if I am asking silly questions but can we take out x^3 common to deduce the left expression and take it to the right side to further deduce? (See below)

x^3(x^8-1)>0

OA C

Thanks.

Great idea. Rewriting x^11 - x^3 as x^3(x^8 - 1) will help us to quickly evaluate each answer choice.

So, we want to know which value of x makes x^3(x^8 - 1) a positive value.

IMPORTANT: Whenever a GMAT question requires us to methodically test out each of the answer choices, I always begin with E and work up. It has been my experience that the correct answer (in these circumstances) is typically near the bottom, since the test-makers want you to use up more time solving these kinds of questions.

So, beginning with E...

E) x = 1: x^3(x^8 - 1) = (1^3)(1^8 - 1) = (1)(0) = 0 (not positive, so eliminate E)
D) x = 0.5: x^3(x^8 - 1) = (0.5^3)(0.5^8 - 1) = (positive #)(negative #) = negative (not positive, so eliminate D)
C) x = -0.5: x^3(x^8 - 1) = ((-0.5)^3)((-0.5)^8 - 1) = (negative #)(negative #) = positive

Answer = C

Cheers,
Brent

eski wrote:DOUBT : Why can we simplfy the equation ? ie . make it x^11-x^3 > 0 => x^8 > 1 .
In that case any value more than 1 and less than -1 will be the right ans. In this case 2.

Thats wrong in this equation? x^8 > 1

I don't think anyone is suggesting that we rewrite x^11 - x^3 as x^8.
If so, that would be incorrect (as you suggest).

Cheers,
Brent