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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

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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