Is x > 0?
1) x^6>x^7
2) x^7>x^8
OAB[/b]
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x>0
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j_shreyans
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GMATGuruNY
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Each statement implies that x≠0.j_shreyans wrote:Is x > 0?
1) x^6>x^7
2) x^7>x^8
Implication:
Raising x to an EVEN POWER will yield a POSITIVE value.
As a result, each statement can safely be simplified by dividing by an even power of x.
Statement 1:
Dividing each side by x�, we get:
x�/x� > x�/x�
1 > x.
If x=1/2, then x>0.
If x=-1, then x<0.
INSUFFICIENT.
Statement 2:
Dividing each side by x�, we get:
x�/x� > x�/x�
1/x > 1.
The resulting inequality holds true only if x>0.
SUFFICIENT.
The correct answer is B.
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ceilidh.erickson
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Without doing algebra, we can think conceptually about the ways that even and odd exponents behave:
x > 0?
1) x� > x�
Ask yourself - what kinds of numbers are larger to the 6th power than to the 7th power?
- If x were a negative number, then x� would be positive and x� would be negative, so that fits.
or...
- If x were a positive fraction, then x� would be a smaller fraction than x�, so that would also fit.
This statement tells us that either x is negative, or x is a positive fraction. Insufficient.
2) x� > x�
Here, if x were negative, x� would be positive, so there's no way it could be less than x�. The only kind of number for which the 7th power is greater than the 8th power is a positive fraction. Sufficient.
x > 0?
1) x� > x�
Ask yourself - what kinds of numbers are larger to the 6th power than to the 7th power?
- If x were a negative number, then x� would be positive and x� would be negative, so that fits.
or...
- If x were a positive fraction, then x� would be a smaller fraction than x�, so that would also fit.
This statement tells us that either x is negative, or x is a positive fraction. Insufficient.
2) x� > x�
Here, if x were negative, x� would be positive, so there's no way it could be less than x�. The only kind of number for which the 7th power is greater than the 8th power is a positive fraction. Sufficient.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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Hi j_shreyans,
This DS questions serves as a great example of how Number Properties can appear on the GMAT. Number Properties are the "little rules" behind how math "works." Typically, when a question refers to positive, negative, 0, odd, even (among other things), you're facing a question that has at least one built-in Number Property.
Most Number Property questions can be solved in a variety of ways: TESTing VALUES, Algebra, or just knowing the Number Properties and how they "relate" to the given question. Since Number Properties will show up on a bunch of questions on Test Day (including a number of DS questions), knowing more than one approach to dealing with these types of prompts can give you the flexibility to find the "fast and easy" way to the correct answer.
GMAT assassins aren't born, they're made,
Rich
This DS questions serves as a great example of how Number Properties can appear on the GMAT. Number Properties are the "little rules" behind how math "works." Typically, when a question refers to positive, negative, 0, odd, even (among other things), you're facing a question that has at least one built-in Number Property.
Most Number Property questions can be solved in a variety of ways: TESTing VALUES, Algebra, or just knowing the Number Properties and how they "relate" to the given question. Since Number Properties will show up on a bunch of questions on Test Day (including a number of DS questions), knowing more than one approach to dealing with these types of prompts can give you the flexibility to find the "fast and easy" way to the correct answer.
GMAT assassins aren't born, they're made,
Rich
