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31 Jul 2023, 07:45
Kudos
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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:
62% (01:35) correct
38%
(01:48)
wrong
based on 50
sessions
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Not Attempted Yet
If r and s are positive prime numbers, and \(n = r^a * s^b\), where a and b are positive integers, is \(\sqrt{n}\) an integer?
(1) a + b is an even number
(2) ab is an even number
(1) a + b is an even number
(2) ab is an even number
31 Jul 2023, 22:30
Kudos
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Bunuel
Question: Is \(\sqrt{n}\) an integer ?
Inference: \(\sqrt{n}\) is an integer, if a and b are even (we already know that a and b are positive integers).
Statement 1
(1) a + b is an even number
Case 1: a and b are even.
If a and b are even, \(\sqrt{n}\) is an integer
Case 2: a and b are odd.
If a and b are odd, \(\sqrt{n}\) is not an integer
Statement 2
(2) ab is an even number
Case 1: Both a and b are even.
If a and b are even, \(\sqrt{n}\) is an integer
Case 2: a or b is even, but both a and b are not even.
If a or b is even (but both a and b are not even), \(\sqrt{n}\) is not an integer
Combined
From statement 2, we know at least a or b is even.
From statement 1, we know that the sum of a and b is even.
Combined, we can conclude that both a and b are even integers.
Hence, we can conclude that \(\sqrt{n}\) is an integer.
Option C
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