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mingshum 
Posted  02/24/2009 : 11:39:08 What is the fastest way to solve this SAT prep problem?
If x, y, and z are positive integers such that the value of x+y is even and the value of (x + y) + x + z is odd, which of the following must be true?
A) x is odd B) x is even C) If z is even, then x is odd. D) If z is even, then xy is even. E) xy is even.
I eliminated choices A,B and E.
Answer is C. 
2 L A T E S T R E P L I E S (Newest First) 
mingshum 
Posted  02/24/2009 : 13:42:08 very clear explanation...thanks 
Haven 
Posted  02/24/2009 : 12:56:58 On way of looking at this problem is to substitute letters for number values "O" for odd and "E" for even.
The problem tells you that the value of x + y = a even number. So that means that x and y must both be odd or x and y must both be even.
The problem also tells you that (x + y) is squared. Since (x + y) is an even number it can be reasoned that (x + y) will be an even number also.
Now with this information you can write an equation substituting possible number values with letters
(x + y)+ x + z = odd
even + odd + z = odd In this case z must be even when x is odd
or
even + even + z = odd In this case z must be odd when x is even
I hope that this explanation was of some help to you. 


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