Question 1040775
<font color=black size=3>
Draw points X and Y 10 units apart. Then draw a circle with center point X and radius 3. P is some point on this circle. Imagine P can slide around freely on the circle but must stay on the circle.


Draw another circle with center Y and radius 4. Q will be stuck to the second circle. 


Let d = distance from P to Q


If you imagine P and Q getting as far apart as possible, then the value of d would be maxed out. This only happens if P and Q lie on the line XY (extend out segment XY to get line XY). This max value of d is 3+10+4 = 17 units. I'm adding the distance from X to Y (10) to the two radii (3 and 4). 
P and Q can't get any further than 17 units apart.



---------------------------------------------------------------



The smallest value of d is d = 3. This can be found by computing 10-3-4 = 3. Basically take the distance of X to Y (10) and subtract off the two radii (3 and 4)



---------------------------------------------------------------


So to summarize, the smallest value of d is d = 3 and the largest is d = 17. We can have distances between those two values. We cannot have any distance smaller than 3 or larger than 17.


<font color=red>Choice A</font> is the answer because d = 2 is smaller than d = 3. We cannot have P and Q be 2 units apart. 
</font>