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# If x, y, and z are consecutive integers, and x < y <

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Intern
Joined: 19 Nov 2004
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If x, y, and z are consecutive integers, and x < y < [#permalink]

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19 Dec 2004, 19:05
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12. If x, y, and z are consecutive integers, and x < y < z, is x even?
(1) x + y = odd
(2) x + z is even

I sort of got confused along my solution to this problem.
Director
Joined: 07 Nov 2004
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21 Dec 2004, 07:22
Pick E

Take two sets of (x,y,z) that ae consecutive integers were x<y<z
a = (1, 2, 3)
b = (2, 3, 4)

s1: x+y = odd
In set a, x=1 (= odd) and x+y= 1+2 = 3 (=odd)
In set b, x=2 (= even) and x+y= 2+3 = 5 (=odd)
So, x can be odd or even and still satisfy the condition
Insufficient

s2: x+z = even
In set a, x=1 (= odd) and x+z= 1+3 = 4 (=even)
In set b, x=2 (= even) and x+z= 2+4 = 6 (=even)
So, x can be odd or even and still satisfy the condition
Insufficient

s1+s2: As you can see both sets a and b satisfy s1 and s2.
Insufficient
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21 Dec 2004, 08:47
E. There is even no need in calculations
ANY 3 consecutive integers satisfy (1)and (2)
21 Dec 2004, 08:47
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