The string/regex you compare to should encompass as much as possible of the whole output string:

# need to chomp the file input before testing
$found = 1 if /^$student\t$studentAge$/;
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Personally, I would suggest using eq because this isn't really a regex problem. You are searching the file for an exact match to a string which is completely known. A regex might be suitable if you were looking for, say, a name followed by an age: /^\s*\w+\s+\d+\s*$. But testing for string equality fits what you are doing, and is faster than a regex.

my $text = "$student\t $studentAge\n";
my $found = 0;
while (<$fh>) {
   $found = 1 if $_ eq $text;
}
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Your example here deals with the input of a single name and age. If you're dealing with homework, that might be all you need. Or, if you're writing a web interface to soemthing, you'll obtain your information one at a time. In other cases, however, you would receive many names, many ages. In that case, I would suggest reading the file into a hash, so you can quickly and easily test each new value.

# Read the file into a hash
#
my %dataFileContains;
open my $fh, 'students.dat' or die "open failed: $!";
my $line;
while  ($line = <$fh>) {
   chomp $line;
   $dataFileContains{$line}++;
}
close $fh;
#
# Read in and test each value, caching those which 
# will be output.
#
my @output;
my ( $name, $age );

while ( ($name, $age ) = getStudentData() ) {
    my $outLine = "$name\t$age";
    push @output, $outLine unless $dataFileContains{$outLine};
}
#
# Output the data.
#
if ( scalar @output ) {
    open my $fh, '>>students.dat' or die "open failed: $!";
    foreach ( @output ) {
       print $fh, "$output\n";
    }
}
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