document.write( "Question 622674: A survey among 370 4th year students conducted to know in which private university do they want to apply for college. The results of the survey are:
\n" ); document.write( "64 like ateneo only
\n" ); document.write( "108 like ateneo and ust
\n" ); document.write( "190 like ust
\n" ); document.write( "86 like ateneo and lasalle
\n" ); document.write( "51 like ateneo and lasalle but not ust
\n" ); document.write( "164 like lasalle
\n" ); document.write( "42 like lasalle and ust but not ateneo
\n" ); document.write( "Questions:
\n" ); document.write( "1. how many students like ateneo?
\n" ); document.write( "2. how many like lasalle and ust?
\n" ); document.write( "3. how many like all 3 universities?
\n" ); document.write( "4. how many do not like lasalle?
\n" ); document.write( "5. how many do not like any of the 3 universities? \n" ); document.write( "
Algebra.Com's Answer #391522 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
A survey among 370 4th year students conducted to know in which private university do they want to apply for college. The results of the survey are:
\n" ); document.write( "64 like ateneo only
\n" ); document.write( "108 like ateneo and ust
\n" ); document.write( "190 like ust
\n" ); document.write( "86 like ateneo and lasalle
\n" ); document.write( "51 like ateneo and lasalle but not ust
\n" ); document.write( "164 like lasalle
\n" ); document.write( "42 like lasalle and ust but not ateneo
\n" ); document.write( "Questions:
\n" ); document.write( "1. how many students like ateneo?
\n" ); document.write( "number of students that like ateneo is 223
\n" ); document.write( "2. how many like lasalle and ust?
\n" ); document.write( "number of students that like lasalle and ust is 277
\n" ); document.write( "3. how many like all 3 universities?
\n" ); document.write( "number of students that like all 3 universities is 35
\n" ); document.write( "4. how many do not like lasalle?
\n" ); document.write( "number of students that do not like lasalle is 205
\n" ); document.write( "5. how many do not like any of the 3 universities?
\n" ); document.write( "number of students that do not like all 3 universities is 29
\n" ); document.write( "you can make a table as follows:
\n" ); document.write( "
\r\n" );
document.write( "                                  ateneo       ust          lasalle       none\r\n" );
document.write( "none                                                                      29\r\n" );
document.write( "ateneo only                       64\r\n" );
document.write( "ust only                                       40\r\n" );
document.write( "lasalle only                                                36\r\n" );
document.write( "ateneo and ust only               73           73\r\n" );
document.write( "ateneo and lasalle only           51                        51\r\n" );
document.write( "ust and lasalle only                           42           42\r\n" );
document.write( "ateneo and ust and lasalle only   35           35           35\r\n" );
document.write( "\r\n" );
document.write( "total                             223          190          164           29\r\n" );
document.write( "

\n" ); document.write( "your venn diagram would look like this:
\n" ); document.write( "\"$$$\"
\n" ); document.write( "the intersection of ateneo and lasalle is 51
\n" ); document.write( "the intersection of ateneo and ust is 73
\n" ); document.write( "the intersection of ust and lasalle is 42
\n" ); document.write( "the intersection of all 3 is 35
\n" ); document.write( "the breakdown of the analysis is as follows:
\n" ); document.write( "ateneo only is 64 (given)
\n" ); document.write( "86 like ateneo and lasalle but 51 like ateneo and lasalle only.
\n" ); document.write( "this means that the 86 includes students that like all 3.
\n" ); document.write( "strip that out and you get 35 students like all 3 (86 - 51).
\n" ); document.write( "108 like ateneo and ust.
\n" ); document.write( "strip out 35 that like all 3 and you get 73.
\n" ); document.write( "42 like lasalle and ust but not ateneo (given)
\n" ); document.write( "since 164 like lasalle and 42 like lasalle and ust only and 35 like all 3 and 51 like lasalle and ateneo only, this leaves 164 - 42 - 35 - 51 = 36 that like lasalle only.
\n" ); document.write( "since 190 like ust and 73 like ust and ateneo only and 35 like all 3 only 42 like ust and lasalle only, this leaves 190 - 73 - 35 - 42 = 40 tht like ust only.
\n" ); document.write( "that totals up to 341 that like ateneo or ust or lasalle or a combination of them.
\n" ); document.write( "since total students are 370, then the number of students that don't like any of them is equal to 370 - 341 = 29.
\n" ); document.write( " \n" ); document.write( "
\n" );