document.write( "Question 1201991: In a class, 85% of the students passed a test. 40% of the students who failed the test received a grade lower then 30. 20% of the students who passed the test received a grade higher than 90. Then, what percent of students scored between 30 and 90, inclusive?\r
\n" ); document.write( "\n" ); document.write( "(A) 68%
\n" ); document.write( "(B) 71%
\n" ); document.write( "(C) 74%
\n" ); document.write( "(D) 77%
\n" ); document.write( "(E) 80% \n" ); document.write( "

Algebra.Com's Answer #836627 by ikleyn(52778) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "In a class, 85% of the students passed a test. 40% of the students who failed the test
\n" ); document.write( "received a grade lower then 30. 20% of the students who passed the test
\n" ); document.write( "received a grade higher than 90. Then, what percent of students scored between 30 and 90, inclusive?
\n" ); document.write( "(A) 68%
\n" ); document.write( "(B) 71%
\n" ); document.write( "(C) 74%
\n" ); document.write( "(D) 77%
\n" ); document.write( "(E) 80%
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " This problem admits short, clear and strightforward solution, as shown below.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "85% of the students passed a test; hence, 15% failed.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "40% of these 15% received a grade lower then 30.\r\n" );
document.write( "\r\n" );
document.write( "Hence, 0.4*0.15 = 0.06, or 6%, are out of our consideration.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "20% of 85%, or 0.2*0.85 = 0.17 = 17%, received a grade higher than 90.\r\n" );
document.write( "\r\n" );
document.write( "These 17% also are out of our consideration.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is clear that these 6% set and 17% set are disjoint, since they are on opposite ends of the 100% set.\r\n" );
document.write( "\r\n" );
document.write( "Hence and therefore, the ANSWER to the problem's question is  100% - 6% - 17% = 77%.   \r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );