If x < y < z and y-x > 11, 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 options
A) 6  B) 7  C) 8  D) 9  E) 15
We have:   1) x<y<z 2)="" y-x="">11   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;11, the least value for y-x must be 13, the least value for x must be 2, and, thus, the least possible value for y must be 15 (y-2=13, y=15)   2&lt;15&lt;z, since z is odd, the least possible value for z is 17   z-x=17-2= 
<gadget id="calculator">17-2</gadget>
<output>15</output>
15   Answer 15
<result>E</result>
If x < y < z and y-x > 11, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?