<p>Can anyone give me a clear explanation for how to solve this problem? Not understanding the Collegeboard solution explanation.... For all numbers x and y, let the operation # be defined by x # y = xy - y. If a an b are positive integers, which of the following can be equal to zero? </p>
<p>I. a # b
II. (a + b) # b
III. a # ( a + b )</p>
<p>(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III</p>
<p>Thanks in advance!</p>
<p>Haven’t seen the CB solution, but here goes.</p>
<p>Note that x#y = y(x-1).</p>
<p>Positive integers means: 1, 2, etc.</p>
<p>Whatever is on the left hand side of # gets plugged into x and whatever is on the right hand side gets plugged into y. So, this expression will be zero only if the stuff on the left hand side of the # is 1, or the stuff on the right hand side is 0.</p>
<p>Since a#b = b(a-1), item I can be zero if a=1.</p>
<p>Since (a+b)#b = b(a+b-1), item II can never be zero (b>0 and a+b > 1).</p>
<p>Finally, a#(a+b) = (a+b)*(a-1), so item III can be zero if a=1.</p>
<p>So, E is the answer.</p>
<p>Fignewton: I will pass that on to my daughter. Thanks so much for your help!</p>