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30 Jan 2023, 07:50
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D
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Difficulty:
15%
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Question Stats:
82% (00:46) correct
18%
(01:14)
wrong
based on 66
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What is the value of \(𝑥 + 𝑦\)?
(1) \(|𝑥| + |𝑦| = 0\)
(2) \(𝑥^2 + 𝑦^2 = 0\)
(1) \(|𝑥| + |𝑦| = 0\)
(2) \(𝑥^2 + 𝑦^2 = 0\)
RohitKakkar
30 Jan 2023, 08:05
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Statement A
Two positive quantities can only be 0 when both are zero, hence A is true. Eliminated B,C and E
Statement B
Square of two numbers can never be negetive which implies if addition of squares of two number is 0, then numbers are itself 0, so B is also must be true
Hence the answer is D Both numbers are 0, x+y=0
Posted from my mobile device
Two positive quantities can only be 0 when both are zero, hence A is true. Eliminated B,C and E
Statement B
Square of two numbers can never be negetive which implies if addition of squares of two number is 0, then numbers are itself 0, so B is also must be true
Hence the answer is D Both numbers are 0, x+y=0
Posted from my mobile device
30 Jan 2023, 09:07
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Kushchokhani
What is the value of \(𝑥 + 𝑦\)?
(1) \(|𝑥| + |𝑦| = 0\)
(2) \(𝑥^2 + 𝑦^2 = 0\)
(1) \(|𝑥| + |𝑦| = 0\)
(2) \(𝑥^2 + 𝑦^2 = 0\)
Solution:
Pre Analysis:
- We are asked the value of \(x+y\)
- Nature of x and y is not given thus we have to assume that they are real numbers
Statement 1: \(|𝑥| + |𝑦| = 0\)
- We know \(|x|\ge 0\) and \(|y|\ge 0\)
- So, if \(|x|+|y|=0\), then we can be sure that \(x=y=0\) and \(x+y=0+0=0\)
- Thus, statement 1 alone is sufficient and we can eliminate options B, C and E
Statement 2: \(x^2 + y^2 = 0\)
- Using the same logic as above, we can be sure that \(x=y=0\) and \(x+y=0+0=0\)
- Thus, statement 2 alone is also sufficient
Hence the right answer is Option D
