If x < y < z and y-x > 1, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?  Choose the most appropriate option
A) 6  B) 3  C) 8  D) 9  E) 10
We have:   1) x<y<z 2)="" y-x="">1   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 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;1, the least value for y-x must be 3, the least value for x must be 2, and, thus, the least possible value for y must be 3 (y-2=1, y=3)   2&lt;3&lt;z, since z is odd, the least possible value for z is 5   z-x=5-2= 
<gadget id="calculator">5-2</gadget>
<output>3</output>
3   Answer 3
<result>B</result>
If x < y < z and y-x > 1, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?