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]
If u and v are positive real numbers, is u>v?
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- GMATGuruNY
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Since u and v are POSITIVE, the inequalities in the statements can be simplified by multiplying each side by v.Mo2men wrote:If u and v are positive real numbers, is u>v?
1. u^3/v < 1
2. (u^1/3) /v < 1
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.
Last edited by GMATGuruNY on Mon Mar 26, 2018 12:05 pm, edited 1 time in total.
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Thanks Mitch for you support,GMATGuruNY wrote:
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.
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
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The question stem asks whether v < u.Mo2men wrote: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)?
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.
If we were able to show that v < u is possible, we would then test whether u < v is also possible.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 both cases were possible, then the correct answer would be E.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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