If x < y < z and y-x > 7, where x is an even integer and y and z are odd integers, what is the least possible value of z - x? Choose the correct choice from the following answers
A) 6
B) 7
C) 11
D) 8
E) 10
We have:   1) x<y<z 2)="" y-x="">5   3) x</y<z>=2k (x is an even number)   4) y=2n+1 (y is an odd number)   5) z=2p+1 (z is an odd number)   6) z-x=? least value   z-x=2p+1-2k=2p-2k+1=2(p-k)+1 - that means that z-x must be an ODD number. We can eliminate answer choices A, C and E   we are asked to find the least value, so we have to pick the least numbers   since y is odd and x is even, y-x must be odd. since y-x&gt;7 the least value for y-x must be 11, the least value for x must be 2, and, thus, the least possible value for y must be 11 (y-2=9, y=11)   2&lt;11&lt;z, since z is odd, the least possible value for z is 13   z-x=13-2= 
<gadget id="calculator">13-2</gadget>
<output>11</output>
11   Answer 11
<result>C</result>
If x < y < z and y-x > 7, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?