Can someone show how to do this algebraically?I understand the answer intuitively but want to have the algebraic way in my back pocket.
Is x > 0?
A) x^6 > x^7
B) x^7 > x^8
Answer: B
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topspin360
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GMATGuruNY
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Both statements imply that x≠0.topspin360 wrote:Can someone show how to do this algebraically?I understand the answer intuitively but want to have the algebraic way in my back pocket.
Is x > 0?
A) x^6 > x^7
B) x^7 > x^8
Answer: B
Thus, the value of x raised to ANY EVEN POWER will be POSITIVE.
As a result, we can safely simplify the statements by dividing each side by x^(even power).
Statement 1: x� > x�
Dividing each side by x�, we get:
1 > x.
Thus, x can be any nonzero value less than 1.
Since it's possible that x=1/2 or that x=-1, INSUFFICIENT.
Statement 2: x� > x�
Dividing each side by x�, we get:
1/x > 1.
Since 1/x > 0, x>0.
SUFFICIENT.
The correct answer is B.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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topspin360
- Master | Next Rank: 500 Posts
- Posts: 103
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Haha Mitch I actually remember you showing me this solution for another problem. Have to remember the methods! Thanks!GMATGuruNY wrote:Both statements imply that x≠0.topspin360 wrote:Can someone show how to do this algebraically?I understand the answer intuitively but want to have the algebraic way in my back pocket.
Is x > 0?
A) x^6 > x^7
B) x^7 > x^8
Answer: B
Thus, the value of x raised to ANY EVEN POWER will be POSITIVE.
As a result, we can safely simplify the statements by dividing each side by x^(even power).
Statement 1: x� > x�
Dividing each side by x�, we get:
1 > x.
Thus, x can be any nonzero value less than 1.
Since it's possible that x=1/2 or that x=-1, INSUFFICIENT.
Statement 2: x� > x�
Dividing each side by x�, we get:
1/x > 1.
Since 1/x > 0, x>0.
SUFFICIENT.
The correct answer is B.
