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Any number with an even exponent is \(>0\), but I wanna give you an alternative solution: 1. \(x^6>x^7\) so \(0>x^7-x^6, 0>x^6(x-1)\) at this point we can divide by x^6 because we know that does not equal 0(otherwise x^6=x^7 and not >) \(0>x-1\) and finally \(1>x\). Is x positive? it could be(0,5) or not (-1)

2.\(x^7>x^8\) becomes \(0>x^6(x^2-x)\) divide \(0>x^2-x\) so \(x(x-1)<0\) and \(0<x<1\). Is x positive? yes B _________________

It is beyond a doubt that all our knowledge that begins with experience.

1. x^6 > x^7 This option is only possible either when 1>x>0 or x<0 Like if x is <1 but >0 then the values will keep on decreasing with every increasing exponent and if x<0 then the even powers will be positive and odd ones would be -ve therefore irrespective of the value of |x| the even exponents will always be greater

2. x^7 > x^8 This is only possible when 1>x>0, as the situation would be as in case 1 but when X<0 the even exponents will always be greater

Only 2 is sufficient but 1 is not B _________________

When you feel like giving up, remember why you held on for so long in the first place.

Sorry this is probably as silly as it gets but i need help in understanding the below

In x^7 > x^8, say we divide by x^6, x> x^2 0>x(x-1) Now 0>x and 0>(x-1) for 0>x-1 ==> x <1, till here i am fine but how do we get x>0 to make 0<x<1 ?? _________________

Sorry this is probably as silly as it gets but i need help in understanding the below

In x^7 > x^8, say we divide by x^6, x> x^2 0>x(x-1) Now 0>x and 0>(x-1) for 0>x-1 ==> x <1, till here i am fine but how do we get x>0 to make 0<x<1 ??

Till here you are fine x> x^2 so \(x^2-x<0\) we have to solve this, and to solve let me use an old trick. Lets solve \(x^2-x=0,x(x-1)=0\) so x=1 or x=0. Now because the sign of x^2 is + and the operator is < we take the INTERNAL values: \(0<x<1\). Remember: to solve inequalities like this (x^2) treat them like equations (replace <,> with = ) then, once you have the results take a look at the sign of x^2 an the operator. (<,-) or (>,+) take ESTERNAL values. (if they are the "same") (>,-) or (<,+) take INTERNAL values(like this case).

Let me know if it's clear now _________________

It is beyond a doubt that all our knowledge that begins with experience.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Post your Blog on GMATClub We would like to invite all applicants who are applying to BSchools this year and are documenting their application experiences on their blogs to...

HBS alum talks about effective altruism and founding and ultimately closing MBAs Across America at TED: Casey Gerald speaks at TED2016 – Dream, February 15-19, 2016, Vancouver Convention Center...