If x < y < z and y-x > 3, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?  Choose one.
A) 7 B) 6 C) 8 D) 9 E) 10
We have:   1) x<y<z 2)="" y-x="">3   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;3, the least value for y-x must be 5, the least value for x must be 2, and, thus, the least possible value for y must be 7 (y-2=5, y=7)   2&lt;7&lt;z, since z is odd, the least possible value for z is 9   z-x=9-2= 
<gadget id="calculator">9-2</gadget>
<output>7</output>
7   7nswer 7
<result>A</result>
If x < y < z and y-x > 3, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?