Nice One : Is x negative?

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himu: Master | Next Rank: 500 Posts; Posts: 345; Joined: Sun Dec 21, 2008 10:57 pmFollowed by: 3 members; Thanked: 6 times

by himu » Sun Feb 10, 2013 9:22 pm

Is x negative?

(1) At least one of x and x2 is greater than x3.

(2) At least one of x2 and x3 is greater than x.

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Source: Beat The GMAT — Data Sufficiency | Sun Feb 10, 2013 9:22 pm

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Mon Feb 11, 2013 4:15 am

If 0 < x < 1, then x^3 < x^2 < x.

If x > 1, then x < x^2 < x^3.

So when x is positive, x^2 is never the largest of the three expressions x, x^2 and x^3. Statement 1 tells us that x^3 is not the largest of the three expressions, and Statement 2 tells us x is not the largest of the three expressions. So x^2 must be the largest, and thus x cannot be positive. So the answer is C.

Note that neither statement is sufficient alone, since while x can certainly be negative using either statement, using statement 1, x could also be positive (x could be 1/2, say), and using Statement 2 x could be positive (x could be 2, say).

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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himu: Master | Next Rank: 500 Posts; Posts: 345; Joined: Sun Dec 21, 2008 10:57 pmFollowed by: 3 members; Thanked: 6 times

by himu » Mon Feb 11, 2013 7:58 pm

Thanks Ian, that is the correct ans

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lunarpower: GMAT Instructor; Posts: 3380; Joined: Mon Mar 03, 2008 1:20 amFollowed by: 1535 members; Thanked: 2256 times; GMAT Score:800

by lunarpower » Wed Feb 13, 2013 9:38 am

hey, i wrote that problem!

--

if you ever see a problem like this -- on which you're comparing different powers of the same variable -- then, immediately, you should think about the following number properties:
* signs
* "fractions" (between 0 and 1, or between -1 and 0) vs. "non-fractions" (greater than 1 or less than -1)

for each of these ranges of numbers -- less than -1; between -1 and 0; between 0 and 1; greater than 1 -- the powers have different properties, and so the ordering of the powers is different.
it's rather pointless (and possibly confusing) to memorize what happens to the powers. instead, just throw in a few numbers of each type and watch what they do.

if the inequalities are not strict inequalities (i.e., if they are the < or > type), then you should also mess around with the numbers 0, 1, and -1.

Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions Ã Ron en franÃ§ais
Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi

--

Quand on se sent bien dans un vÃªtement, tout peut arriver. Un bon vÃªtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Wed Feb 13, 2013 10:26 am

Not to ditto everything that Ron is saying today...

I often tell my students that whenever they see a problem with exponents and inequalities, they should draw this number line, to make sure they don't forget positives/negatives or fractions/non-fractions:

If you quickly test each of these 7 numbers, you'll have considered all of the types of numbers that behave differently with inequalities and exponents.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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ani781: Master | Next Rank: 500 Posts; Posts: 141; Joined: Fri Jun 24, 2011 4:35 amFollowed by: 1 member; Location: Edison; Thanked: 12 times

by ani781 » Mon Oct 07, 2013 7:40 pm

I often tell my students that whenever they see a problem with exponents and inequalities, they should draw this number line, to make sure they don't forget positives/negatives or fractions/non-fractions:

If you quickly test each of these 7 numbers, you'll have considered all of the types of numbers that behave differently with inequalities and exponents.

Hi Ceilidh,
Can you please provide with the picture.... is the link working fine ? I am not being able to see it. Thanks in advance.

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lunarpower: GMAT Instructor; Posts: 3380; Joined: Mon Mar 03, 2008 1:20 amFollowed by: 1535 members; Thanked: 2256 times; GMAT Score:800

by lunarpower » Tue Oct 08, 2013 3:24 am

Ceilidh's picture is at https://postimg.cc/image/6wrsd3hy1/

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