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DS real numbers

Expert replies
Source: — Data Sufficiency |

by kmittal82 » Mon Aug 15, 2011 5:03 am
(1)
u^3 < v (we can multiply without changing sign safely here since we know u and v are positive)

for this to be true, v is always greater than u (since u and v are both positive and real)
Sufficient

(2)
u^(1/3) < v

u = 8, v = 4 satisfies this
u = 8, v = 16 also satisfies this

Not Sufficient

Hence, (A)

OA?
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by Frankenstein » Mon Aug 15, 2011 5:15 am
GmatKiss wrote:If u and v are positive real numbers, is u > v?

(1) u^3/v < 1

(2) u^(1/3) / v < 1
Hi,
u and v are positive real numbers. We shouldn't take for granted that they are integers.
From(1):
u=0.2, v= 0.1 -> u^3/v < 1, u>v
u=2, v=9 -> u^3/v < 1, u<v
Not sufficient

From(2):
Not sufficient as shown in prev. post

Both(1) and (2):
u^3/v < 1
and u/v^3 < 1
So, (u^3/v)*(u/v^3) < 1
=> (u/v)^4<1
So, u < v. As all are positive, we can multiply and take roots this way.
Sufficient

Hence, C
Cheers!

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