<p><span style="font-size:22px"><a href="https://www.prepswift.com/quizzes/quiz/prepswift-three-overlapping-sets" target="_blank">Three Overlapping Sets Exercise</a></span></p><p>There is a <u><strong>small</strong></u> possibility you will encounter a <strong><span style="color:#8e44ad;">Three Overlapping Sets</span></strong> problem on the GRE. If you're interested, please keep reading. However, if you're finding it a bit too esoteric for your liking, this is a topic you can most likely safely skip.</p>
<p><strong><span style="color:#2980b9;">The Formula to Remember </span></strong></p>
<p><span style="font-size:18px;">$$total = A + B + C - (exactly \ two) - 2(all \ three) + none$$</span></p>
<p><strong><span style="color:#e74c3c;">Example</span></strong></p>
<p>In a neighborhood containing $235$ houses, $77$ have a swimming pool, $100$ have a garage, and $156$ have a yard. If every house has at least one of these elements, and if $14$ houses have all three, how many houses have exactly two?</p>
<p>$$235 = 77 + 100 + 156 - (exactly \ two) - 2(14)$$</p>
<p>$$235 = 305 - (exactly \ two)$$</p>
<p><strong><span style="color:#27ae60;">$$exactly \ two = 70$$</span></strong></p>