document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=995336>Question 995336</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the correct addition shown at the right, A,B, and C are different non-zero digits. What is the value of C?<BR>\n" );
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document.write( "A)0<BR>\n" );
document.write( "B)6<BR>\n" );
document.write( "C)8<BR>\n" );
document.write( "D)9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #614088 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=614088\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's go through all the choices\r<BR>\n" );
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document.write( "A) 0\r<BR>\n" );
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document.write( "If C = 0, then B+B ends with a zero and this is only possible if B = 0 or B = 5. \r<BR>\n" );
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document.write( "if B = 0, then A,B,C all must be 0 but they are all different and nonzero\r<BR>\n" );
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document.write( "if B = 5, then it's not possible that B+B yields the same digit as B. So C = 0 is not possible. \r<BR>\n" );
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document.write( "This rules out choice A.\r<BR>\n" );
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document.write( "B) 6\r<BR>\n" );
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document.write( "If C = 6, then B has to be 3 or 8. \r<BR>\n" );
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document.write( "If B = 3, then B+B=3+3 = 6 but that's not equal to B = 3. So B can't be 3.<BR>\n" );
document.write( "If B = 8, then B+B=8+8 = 16. The units digit 6 is not equal to B = 8 (even with a carry). So B can't be 8.\r<BR>\n" );
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document.write( "This rules out choice B\r<BR>\n" );
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document.write( "C) 8\r<BR>\n" );
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document.write( "If C = 8, then B has to be 4 or 9\r<BR>\n" );
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document.write( "If B = 4, then B+B doesn't have the units digit of B. So B = 4 is eliminated in this sub-case.<BR>\n" );
document.write( "If B = 9, then B+B adds to 9+9 = 18 and we have a carry of 1 from the previous addition. So we really have 19. This makes B+B have a units digit of B. So it fits\r<BR>\n" );
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document.write( "So far, we see that it's possible for C = 8 and B = 9\r<BR>\n" );
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document.write( "That would make A = 1\r<BR>\n" );
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document.write( "Summary:<BR>\n" );
document.write( "A = 1<BR>\n" );
document.write( "B = 9<BR>\n" );
document.write( "C = 8\r<BR>\n" );
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document.write( "Notice how BB+BB = ABC turns into 99+99 = 198 which fits the summary shown above. \r<BR>\n" );
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document.write( "Final Answer: <font color=\"red\">C) 8</font>\r<BR>\n" );
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document.write( "Note: we don't need to check D) 9 since we found the answer in choice C.\r<BR>\n" );
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