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Please help me out with this question.

by aman88 » Wed Dec 12, 2012 3:17 am
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

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by Brent@GMATPrepNow » Wed Dec 12, 2012 8:17 am
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
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by Jim@StratusPrep » Wed Dec 12, 2012 8:22 am
Yes, you can factor as you did, but you cannot divide it and take it to the other side of the equation, because you do not know if it is positive or negative. However, you can evaluate it from your first step and make sure your two expressions (x^3 and x^8 -1) are both the same sign, giving you a positive number.
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by aman88 » Wed Dec 12, 2012 9:22 am
Thank you so much Brent and Jim. You guys are great!
Bow! :)
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by puneetkhurana2000 » Wed Dec 12, 2012 9:41 am
x^3(x^8-1)>0 can be written as x^3(x^4-1)(x^4+1)>0 ...a^2 - b^2 = (a-b)(a+b)

Further written as x^3(x^2-1)(x^2+1)(x^4+1)>0

Further written as x^3(x-1)(x+1)(x^2+1)(x^4+1)>0

Now (x^2+1) and (x^4+1) will always be positive...so we need to take into account the 3 terms only.
The critical points are -1, 0 and +1.

The equation satisfies only when the range is x > 1 and -1 < x < 0 .

The only option that satisfies this is C
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by eski » Thu Dec 13, 2012 5:45 am
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
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by Brent@GMATPrepNow » Thu Dec 13, 2012 9:29 am
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
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