document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161905>Question 1161905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose your textbook is opened at random and the product of the facing page numbers is 71556. To what page is the textbook opened? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #785542 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13215)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=785542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The two pages have consecutive page numbers.<br><BR>\n" );
document.write( "We can find the page numbers using estimation and logical reasoning.<br><BR>\n" );
document.write( "(1) Looking at the first three digits \"715\", we can see that they lie between 26^2=676 and 27^2 = 729.  So the two page numbers are in the 260's.<br><BR>\n" );
document.write( "(2) The units digit of the product is 6.  The product of two consecutive integers has units digit 6 if the two units digits are either 2 and 3 or 7 and 8.<br><BR>\n" );
document.write( "(3) Since 715 is closer to 729 than to 676, the two page numbers must be 627 and 628.<br><BR>\n" );
document.write( "The answer is verified by multiplying those two numbers and seeing that the product is indeed 71556.<br><BR>\n" );
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document.write( "Comments added after seeing three responses to your question made after I made mine....<br><BR>\n" );
document.write( "In terms of efficiency, if you have a calculator, the quickest way to find the answer is as shown by tutor @ikleyn: take the square root of 71556 to find that it is about 627.5, making the two page numbers 627 and 628.<br><BR>\n" );
document.write( "If you do not have a calculator, then estimation and logical reasoning will get you to the answer in far less time than the method shown by the other two tutors.<br><BR>\n" );
document.write( "Finding the answer by finding the prime factorization of 71556 and then finding how to combine those factors to get two consecutive integers takes a lot of work.  An average person will get the final answer to the problem in less time than it takes an average person to find the prime factorization -- not to mention the time it takes to play with that prime factorization to find the two page numbers.<br>\r<BR>\n" );
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