document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081543>Question 1081543</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The president just recently appointed 25 generals of the army, of these, 14 have already served in Gulf War, 12 in the cold war of Russia, and 10 in war in Syria. Therefore 4 who have served both in Gulf War and Syria, 6 served both in Gulf War and Russia, and 3 have served both Russia and Syria. How many generals who had served both Gulf War, Russia, and Syria. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695595 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=695595\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Make a Venn diagram with 3 overlapping circles.<BR>\n" );
document.write( "You should be able to count 7 distinct regions.<BR>\n" );
document.write( "The region in the center is the generals who<BR>\n" );
document.write( "served in G, R, and S. Call that region X.<BR>\n" );
document.write( "G = 14<BR>\n" );
document.write( "R = 12<BR>\n" );
document.write( "S = 10<BR>\n" );
document.write( "G AND R = 6<BR>\n" );
document.write( "G AND S = 4<BR>\n" );
document.write( "R AND S = 3<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "The trick now is to identify each of the 7 distinct regions<BR>\n" );
document.write( "so that you have eliminated all the overlaps.<BR>\n" );
document.write( "-----------------------------------------<BR>\n" );
document.write( "A little shortcut is to lump together the 4 regions that make<BR>\n" );
document.write( "up G. That gives you 14.<BR>\n" );
document.write( "Then I get 2 more regions from R minus overlap with G<BR>\n" );
document.write( "Then I get 1 more which is S and ONLY S ( no overlaps )<BR>\n" );
document.write( "4 + 2 + 1 = 7<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "14 +<BR>\n" );
document.write( "12 - 6 <BR>\n" );
document.write( "10 - 4 - ( 3-x )<BR>\n" );
document.write( "This should add up to 25<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "14 + 12 - 6 + 10 - 4 - 3 + x = 25 <BR>\n" );
document.write( "23 + x = 25 <BR>\n" );
document.write( "x = 2 <BR>\n" );
document.write( "That means there are 2 generals who seved in<BR>\n" );
document.write( "Gulf War, Russia, and Syria.<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Hope this helps. The key is to add up the 7 regions<BR>\n" );
document.write( "without overlaps to find x<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "Now you can check by adding up each of the 7<BR>\n" );
document.write( "(1) 14 - 4 - ( 6-2 )<BR>\n" );
document.write( "(2) 12 - 6 - ( 3-2 )<BR>\n" );
document.write( "(3) 10 - 4 - ( 3-2 )<BR>\n" );
document.write( "(4) 4 - 2<BR>\n" );
document.write( "(5) 6 - 2<BR>\n" );
document.write( "(6) 3 - 2<BR>\n" );
document.write( "(7) 2<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Add them up<BR>\n" );
document.write( "(1) 6<BR>\n" );
document.write( "(2) 5<BR>\n" );
document.write( "(3) 5<BR>\n" );
document.write( "(4) 2<BR>\n" );
document.write( "(5) 4<BR>\n" );
document.write( "(6) 1<BR>\n" );
document.write( "(7) 2<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "25 total\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );