If y is the sum of x consecutive positive integers, and x>3, is y odd?
(1) x is odd.
(2) The largest number among the x consecutive integers is odd.
OE:
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(1) x is odd.
(2) The largest number among the x consecutive integers is odd.
OE:
[Reveal] Spoiler:
(1): plug in x=5 and y=1+2+3+4+5=15 -> y = odd
But, we can also plug in y=2+3+4+5+6=20 -> y = even
IS
(2): Make sure the largest number is odd
Plug in y=1+2+3+4+5=15 -> y = odd
But, we can also plug in y=2+3+4+5 -> y = even
IS
Combined: Plug in x=5 and make sure the largest number is odd:
y=1+2+3+4+5=15 -> y = odd
But, Plug in x=7 y=1+2+3+4+5+6+7=28 -> y = even
IS
But, we can also plug in y=2+3+4+5+6=20 -> y = even
IS
(2): Make sure the largest number is odd
Plug in y=1+2+3+4+5=15 -> y = odd
But, we can also plug in y=2+3+4+5 -> y = even
IS
Combined: Plug in x=5 and make sure the largest number is odd:
y=1+2+3+4+5=15 -> y = odd
But, Plug in x=7 y=1+2+3+4+5+6+7=28 -> y = even
IS