Please help me out with this question.

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aman88: Master | Next Rank: 500 Posts; Posts: 142; Joined: Sat Oct 20, 2012 3:31 amFollowed by: 3 members; Location: New Delhi; Thanked: 20 times

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

Thanks.

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Source: Beat The GMAT — Problem Solving | Wed Dec 12, 2012 3:17 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

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Jim@StratusPrep: MBA Admissions Consultant; Posts: 2279; Joined: Fri Nov 11, 2011 7:51 amFollowed by: 266 members; Location: New York; Thanked: 660 times; GMAT Score:770

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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aman88: Master | Next Rank: 500 Posts; Posts: 142; Joined: Sat Oct 20, 2012 3:31 amFollowed by: 3 members; Location: New Delhi; Thanked: 20 times

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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puneetkhurana2000: Master | Next Rank: 500 Posts; Posts: 131; Joined: Wed Nov 14, 2012 2:01 pmFollowed by: 2 members; Thanked: 39 times

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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eski: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Wed Sep 05, 2012 11:36 amFollowed by: 4 members; Thanked: 2 times

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

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