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by Max@Math Revolution » Mon Aug 22, 2016 3:14 am
u=?
1) |u|+|v|=0
2) u^2+v^2=0

*An answer will be posted in 2 days.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Aug 22, 2016 5:09 am
Max@Math Revolution wrote: What is the value of u?

1) |u| + |v| = 0
2) u² + v² = 0
Target question: What is the value of u?

Statement 1: |u| + |v| = 0
Since the ABSOLUTE VALUE of a number is always greater than or equal to zero, the ONLY way that two absolute values can add to be zero is when each absolute value evaluates to be zero.
That is |u|= 0 AND |v| = 0
If |u|= 0, then u = 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Statement 2: u² + v² = 0
Since the SQUARE of a number is always greater than or equal to zero, the ONLY way that two squares can add to be zero is when each square evaluates to be zero.
That is u² = 0 AND v² = 0
If u² = 0, then u = 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT


Answer = D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Wed Aug 24, 2016 4:39 am
Since there are 2 variables in the original condition, there is a high chance that C is the correct answer. Using 1) & 2), we get 1)=2). Then, u=v=0. Hence, the correct answer is D.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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