BTGmoderatorDC wrote:If m and n are positive integers, is n even?
(1) m(m + 2) + 1 = mn
(2) m(m + n) is odd.
Statement 1:
Case 1: m is ODD
Plugging m=1 into m(m + 2) + 1 = mn, we get:
1(1+2) + 1 = 1(n)
4 = n
In this case, the answer to the question stem is YES.
Case 2: m is EVEN
Plugging m=2 into m(m + 2) + 1 = mn, we get:
2(2+2) + 1 = 2n
9 = 2n
n = 9/2 = ODD/EVEN
Not viable, since ODD/EVEN = noninteger, violating the condition that n must be an integer.
Since only Case 1 is viable, the answer to the question stem is YES.
Statement 2:
Case 1: m is ODD
Plugging m=1 into m(m + n) is odd, we get:
1(1+n) = ODD
1+ n = ODD
n = ODD - 1 = EVEN
In this case, the answer to the question stem is YES.
Case 2: m is EVEN
Plugging m=2 into m(m + n) is odd, we get:
2(2+n) = ODD
EVENÂ = ODD
Not viable.
Since only Case 1 is viable, the answer to the question stem is YES.
The correct answer is
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