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mingshum
Senior Member

USA
29 Posts

 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 oddB) x is evenC) 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.

Haven
Senior Member

USA
28 Posts

 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 = oddeven + odd + z = odd In this case z must be even when x is oddor even + even + z = odd In this case z must be odd when x is evenI hope that this explanation was of some help to you.

mingshum
Senior Member

USA
29 Posts

 Posted - 02/24/2009 :  13:42:08 very clear explanation...thanks
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