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# u=?

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Math Revolution GMAT Instructor
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25 Jul 2016, 19:40
Expert's post
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Question Stats:

69% (00:30) correct 31% (00:43) wrong based on 114 sessions

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u=?
1) |u|+|v|=0
2) u^2+v^2=0

*An answer will be posted in 2 days
[Reveal] Spoiler: OA

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26 Jul 2016, 11:12
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MathRevolution wrote:
u=?

$$\textbf{1) }\vert u \vert +\vert v\vert =0$$

The minimum result of the absolute value operator is 0. There is a single input for this: 0.

$$u = v = 0$$

Sufficient

$$\textbf{2) }u^2+v^2=0$$

The minimum result of squaring a number is 0 (barring complex numbers). There is a single input for this: 0.

$$u = v = 0$$

Sufficient

[Reveal] Spoiler:
(D) each statement alone is sufficient

Note that the answer would change if negative values could be obtained from either function.
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27 Jul 2016, 04:13
MathRevolution wrote:
u=?
1) |u|+|v|=0
2) u^2+v^2=0

*An answer will be posted in 2 days

1) |u|+|v|=0
same as
(+ve value) + ( +ve value) = 0
only possible
when u and v are 0
therefore sufficient.

2) u^2+v^2=0
same as above
+ve + +ve = 0
sufficient.

D

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27 Jul 2016, 18:01
1
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MathRevolution wrote:
u=?
1) |u|+|v|=0
2) u^2+v^2=0

*An answer will be posted in 2 days

1) |u|+|v|=0
|u|=-|v|

how can a positive value be equal to -ve value. Only when u=v=0
Sufficient.

2) u^2+v^2=0
u^2= -v^2

u^2 will always be +ve and it can not be equal to -ve value. Its possible only when u=v=0
Sufficient

Both statements are sufficient independently.

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28 Jul 2016, 07:51
Top Contributor
MathRevolution wrote:
u = ?

1) |u| + |v| = 0
2) u² + v² = 0

Target question: What is the value of u?

Statement 1: |u| + |v| = 0
IMPORTANT: |k| is always greater than or equal to 0

So, |u| = some number greater than or equal to 0 AND |v| = some number greater than or equal to 0
So, statement 1 basically says: (some number greater than or equal to 0) + (some number greater than or equal to 0) = 0
This is possible ONLY IF each value is equal to zero.
So, |v| = 0 and |u| = 0, which means u = 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: u² + v² = 0
IMPORTANT: k² is always greater than or equal to 0

So, u² = some number greater than or equal to 0 AND v² = some number greater than or equal to 0
So, statement 2 basically says: (some number greater than or equal to 0) + (some number greater than or equal to 0) = 0
This is possible ONLY IF each value is equal to zero.
So, v² = 0 and u² = 0, which means u = 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

[Reveal] Spoiler:
D

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31 Jul 2016, 08:46
There are 2 variables in the original condition and there is a high chance that C is the correct answer. Using con 1) and con 2), we get u=v=0. Hence the correct answer is D.
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17 Aug 2017, 08:25
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Re: u=?   [#permalink] 17 Aug 2017, 08:25
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