If x < y < z and y-x > 9, 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) 7 C) 8 D) 13 E) 10
We have:   1) x<y<z 2)="" y-x="">9   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;9, 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 13 (y-2=11, y=13)   2&lt;13&lt;z, since z is odd, the least possible value for z is 15   z-x=15-2= 
<gadget id="calculator">15-2</gadget>
<output>13</output>
13   Answer 13
<result>D</result>
If x < y < z and y-x > 9, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?