document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=298192>Question 298192</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Maurice wants to multiply together two numbers composed of two digits each. Unfortunately, he reverses the digits of one of the numbers and obtains a result which is greater than the exact result by 3015. Which of the following could be one of the numbers?\r<BR>\n" );
document.write( "\n" );
document.write( "(A) 23 (B) 38 (C) 45 (D) 62 (E) 81 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #214572 by </B><A HREF=/tutors/aboutme.mpl?userid=amoati><B>amoati(11)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=amoati><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=214572\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's assume that the numbers are A & B and it was B that Maurice reverses.\r<BR>\n" );
document.write( "\n" );
document.write( "Since B is 2 digits number we can say that B = W + 10 Y\r<BR>\n" );
document.write( "\n" );
document.write( "So the exact result would be A * (W + 10 Y) and when he reserves the digits of the B number, the result would be A * (Y + 10 W)\r<BR>\n" );
document.write( "\n" );
document.write( "So the difference would be A * (Y + 10 W) - A * (W + 10 Y) = 3015\r<BR>\n" );
document.write( "\n" );
document.write( "So A * (Y + 10 W - W -10 Y) = 3015\r<BR>\n" );
document.write( "\n" );
document.write( "A * (9 W - 9 Y) = 3015\r<BR>\n" );
document.write( "\n" );
document.write( "dividing by 9\r<BR>\n" );
document.write( "\n" );
document.write( "A * (W - Y) = 335\r<BR>\n" );
document.write( "\n" );
document.write( "335 is the multiplication of 5 * 67 (67 is a prime number)\r<BR>\n" );
document.write( "\n" );
document.write( "So the difference between the two digits of the B number is 5\r<BR>\n" );
document.write( "\n" );
document.write( "then the correct answer would be (B) 38\r<BR>\n" );
document.write( "\n" );
document.write( "In fact we can verify our answer since now we know both numbers A = 67, B = 38\r<BR>\n" );
document.write( "\n" );
document.write( "So A * B = 67 * 38 = 2546 and when B is reserved 67 * 83 = 5561 and the difference 5561 - 2546 = 3015 :) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );