Suppose for any real number x, [x] denotes the greatest integer less than or equal to x. Let L(x,y) = [x] + [y] + [x + y] and R(x,y) = [2x] + [2y]. Then it is impossible to find any two positive real numbers x and y for which	Pick one:
A) L(x,y) = R(x,y)  B) L(x,y) ≠ R(x,y)  C) L(x,y) < R(x,y)  D) L(x,y) < R(x,y)  E) None
x – 1≤ [x] ≤ x   2x + 2y - 3 ≤ L(x,y) ≤ 2x + 2y   =&gt; a – 3 ≤ L ≤ a   2x + 2y -2 ≤ L(x,y) ≤ 2x + 2y   =&gt; a – 2 ≤ R ≤ a   Therefore, L ≤ R.   Answer : L(x,y) &lt; R(x,y)
<result>D</result>
Suppose for any real number x, [x] denotes the greatest integer less than or equal to x. Let L(x,y) = [x] + [y] + [x + y] and R(x,y) = [2x] + [2y]. Then it is impossible to find any two positive real numbers x and y for which