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03 May 2023, 23:50
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
33% (01:52) correct
67%
(01:24)
wrong
based on 46
sessions
History
Date
Time
Result
Not Attempted Yet
If x and y are positive integers and x is even, is \(x^a + y^b\) = even
1) y is odd
2) a! = b!
1) y is odd
2) a! = b!
06 May 2023, 03:38
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question stem says x=even and statement 1 says y=odd.
So, x^a+y^b will be even^anything+odd^anything=even+odd= odd
x^a+y^b=odd, always.
Statement 1 is sufficient. So A.
But the answer is E. Where am I going wrong?
So, x^a+y^b will be even^anything+odd^anything=even+odd= odd
x^a+y^b=odd, always.
Statement 1 is sufficient. So A.
But the answer is E. Where am I going wrong?
06 May 2023, 04:30
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cottonmouth
cottonmouth - You've made an incorrect assumption in concluding the highlighted portion of your explanation. You've assumed that a and b are both positive integers, however, the question doesn't state anything on the positive-negative nature of 'a' and 'b' either in the premise or in statement 1. Hence, assuming that is incorrect.
Example:
\(2 ^ 0\) = Is it even? No, because \(2^0 = 1\), and 1 is odd.
\(3 ^ {-1}\) = Is it odd? No, because \(3^{-1} = \frac{1}{3}\), and fractions are neither even nor odd.
So 'even^anything' is not always even and 'odd^anything' is not always odd.
With this information now known, would you like to retry the question? If you're still not able to arrive at the correct answer, do let me know. I am happy to share a solution.
P.S. The answer indicated is correct.
