If u and v are positive real numbers, is u>v?

[Mo2men]

If u and v are positive real numbers, is u>v?

1. u^3/v < 1

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

OA: C
Source: Manhattan

[spoiler]Any short cut when combine both statements?[/spoiler]

[GMATGuruNY]

If u and v are positive real numbers, is u>v?

1. u^3/v < 1

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

Since u and v are POSITIVE, the inequalities in the statements can be simplified by multiplying each side by v.

Statement 1, rephrased: u³ < v
Case 1: u=1 and v=2
In this case, u < v, so the answer to the question stem is NO.
Case 2: u=1/2 and v=1/3
In this case, u > v, so the answer to the question stem is YES.
INSUFFICIENT.

Statement 2, rephrased: ∛u < v
Case 1: u=1 and v=2
In this case, u < v, so the answer to the question stem is NO.
Case 3: u=8 and y=7
In this case, u > v, so the answer to the question stem is YES.
INSUFFICIENT.

Statements combined:
Test whether it's possible for both statements to be satisfied if v < u.
Adding v < u to Statement 1 yields the following:
u³ + v < u + v
u³ < u.
Here, u must be a FRACTION.
Adding v < u to Statement 2 yields the following:
∛u + v < u + v
∛u < u.
Here, u must be GREATER THAN 1.
Since it is not possible for u simultaneously to be both a fraction and a value greater than 1, the two statements cannot both be satisfied if v < u.
Implication:
For both statements to be satisfied, u must NOT be greater than v.
Thus. the answer to the question stem is NO.
SUFFICIENT.

The correct answer is C.

[Mo2men]

Statements combined:
Test whether it's possible for both statements to be satisfied if v < u.
Adding v < u to Statement 1 yields the following:
u³ + v < u + v
u³ < u.
Here, u must be a FRACTION.
Adding v < u to Statement 2 yields the following:
∛u + v < u + v
∛u < u.
Here, u must be GREATER THAN 1.
Since it is not possible for u to be both a fraction and a value greater than 1, the two statements cannot both be satisfied if v < u.
Implication:
For both statements to be satisfied, u must NOT be greater than v.
Thus. the answer to the question stem is NO.
SUFFICIENT.
The correct answer is C.

Thanks Mitch for you support,

I have general question to understand better the method that you used to solve the problem.

1- is not it incorrect to jump to the conclusion based on testing one condition ( v < u)?

2-You have test that v < u , what if the result of your test proved that v < u? Should I test if v > u to cover all situations? or can I conclude directly that u >v?

Thanks

[GMATGuruNY]

Thanks Mitch for you support,

I have general question to understand better the method that you used to solve the problem.

1- is not it incorrect to jump to the conclusion based on testing one condition ( v < u)?

The question stem asks whether v < u.
As shown in my solution above, v < u would require that u simultaneously be both a fraction and a value greater than 1.
Since it is not possible for u to be simultaneously both a fraction and a value greater than 1, we can conclude that v is NOT less than u.
Thus, the answer to the question stem is NO.

2-You have test that v < u , what if the result of your test proved that v < u? Should I test if v > u to cover all situations? or can I conclude directly that u >v?

If we were able to show that v < u is possible, we would then test whether u < v is also possible.
If both cases were possible, then the correct answer would be E.