Short answer:
If n > 0, yes.
If n < 0, no.
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question on inequalities
Source: Beat The GMAT — Problem Solving |
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albatross86
- Master | Next Rank: 500 Posts
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albatross86
- Master | Next Rank: 500 Posts
- Posts: 392
- Location: Bangalore, India
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Sure sorry, didn't mean to be abrupt - thought you were looking for confirmation rather than explanationel_torero wrote:can you please elaborate why? thanks so much!
In general, exponent inequalities like this one depend on more than just the value of n; they also depend on the values of x and y. In this case it only depends on n, as you can see in the examples below:
YES and NO are the answers to the question, Is x^(1/n) < y^(1/n)?
CASE 1: 0< x < y < 1; n > 0
eg. x = 0.1; y = 0.2; n = 0.5
=> x^(1/n) = 0.01; y^(1/n) = 0.04 => YES
eg. x = 0.01; y = 0.04; n = 2
=> x^(1/n) = 0.1; y^(1/n) = 0.2 => YES
CASE 2: 0 < x < y < 1; n < 0
eg. x = 0.01, y = 0.04, n = -2
=> x^(1/n) = 10; y^(1/n) = 5 => NO
eg. x = 0.1, y = 0.2, n = -0.5
=> x^(1/n) = 100; y^(1/n) = 50 => NO
CASE 3: 1 < x < y ; n > 0
eg. x = 2, y = 3, n = 0.5
=> x^(1/n) = 4; y^(1/n) = 9 => YES
eg. x = 4, y = 9; n = 2
=> x^(1/n) = 2; y^(1/n) = 3 => YES
CASE 4: 1 < x < y; n < 0
eg. x = 2, y = 3, n = -1
=> x^(1/n) = 1/2 ; y^(1/n) = 1/3 => NO
eg. x = 2, y = 3, n = -0.5
=> x^(1/n) = 1/4; y^(1/n) = 1/9 => NO
~Abhay
Believe those who are seeking the truth. Doubt those who find it. -- Andre Gide
Believe those who are seeking the truth. Doubt those who find it. -- Andre Gide
Abhay,
I've been reading a lot of your answers in different threads, and they are always very clear and elaborate; I'm learning a ton from reading them, so thanks a lot.
I see that your exam date is coming up. Good luck with that. I think you're aiming a little low relative to your skill level, but you're probably just being modest.
I've been reading a lot of your answers in different threads, and they are always very clear and elaborate; I'm learning a ton from reading them, so thanks a lot.
I see that your exam date is coming up. Good luck with that. I think you're aiming a little low relative to your skill level, but you're probably just being modest.
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albatross86
- Master | Next Rank: 500 Posts
- Posts: 392
- Location: Bangalore, India
- Thanked: 116 times
- GMAT Score:770
Thanks a lot Jeremy!jeremy8 wrote:Abhay,
I've been reading a lot of your answers in different threads, and they are always very clear and elaborate; I'm learning a ton from reading them, so thanks a lot.
I see that your exam date is coming up. Good luck with that. I think you're aiming a little low relative to your skill level, but you're probably just being modest.
Lol @ the target score - I always aim way high; that way I might just hit something decent
~Abhay
Believe those who are seeking the truth. Doubt those who find it. -- Andre Gide
Believe those who are seeking the truth. Doubt those who find it. -- Andre Gide
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nikhilkatira
- Master | Next Rank: 500 Posts
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- Thanked: 12 times
I AGREEjeremy8 wrote:Abhay,
I've been reading a lot of your answers in different threads, and they are always very clear and elaborate; I'm learning a ton from reading them, so thanks a lot.
I see that your exam date is coming up. Good luck with that. I think you're aiming a little low relative to your skill level, but you're probably just being modest.
Best,
Nikhil H. Katira
Nikhil H. Katira
If n is positive x < y = YESel_torero wrote:if you know 0< x < y, then is x^(1/n) < y^(1/n) for any number n?
If n is negative y < x = NO
