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01 Mar 2023, 23:52
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
64% (01:50) correct
36%
(02:01)
wrong
based on 47
sessions
History
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Time
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Not Attempted Yet
If x and y are positive integers, is x even?
(1) \(x^y + y^x \)is even.
(2) \(y^x\)+ 4x is odd.
(1) \(x^y + y^x \)is even.
(2) \(y^x\)+ 4x is odd.
02 Mar 2023, 00:22
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TBT
Pretty straightforward ques!
Question: Is x even ?
Statement 1
(1) \(x^y + y^x \)is even.
As the sum of two terms is even, each term can be even or each term can be odd.
Hence, x and y both can be even or both x and y can be odd.
As we have two contradicting answers, we can eliminate A and D.
Statement 2
(2) \(y^x\)+ 4x is odd.
\(y^x\) = odd - even
So \(y^x\) = odd.
As x is a positive integer, we can conclude that y is odd.
However, we don't have any information on x.
Hence the statement is not sufficient and we can eliminate B.
Combined
From Statement 1, we concluded that x and y follow the same even-odd nature.
From Statement 2, we know that y is odd.
Hence, we can conclude that x is odd.
The statements combined help answer the question.
Option C
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