document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1016747>Question 1016747</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A number when divided by 7 leaves a remainder 3 & the resulting quotient when divided by 11 leaves remainer 6.If the same number when divided by 11 leaves remainer m and resulting quotient when divided by 7 leaves a remainder n.What are the values of m & n respectively? </SPAN>\n" );
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document.write( "Question:<BR>\n" );
document.write( "A number when divided by 7 leaves a remainder 3 & the resulting quotient when divided by 11 leaves remainer 6.If the same number when divided by 11 leaves remainer m and resulting quotient when divided by 7 leaves a remainder n.What are the values of m & n respectively?<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "It will be assumed that we work with only positive integers.<BR>\n" );
document.write( "\"A number when divided by 7 leaves a remainder 3 & the resulting quotient when divided by 11 leaves remainer 6.\"<BR>\n" );
document.write( "Let the number be N=7x+3, then when N is divided by 7, it leaves a remainder of 3.<BR>\n" );
document.write( "The resulting quotient (integer part) equals (7x+3)/7=x.<BR>\n" );
document.write( "If x/11 leaves a remainder of 6, the smallest value of x is 6, although x could equal 6,17,28,....<BR>\n" );
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document.write( "If x=6, then N=7*6+3=45.<BR>\n" );
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document.write( "\"If the same number when divided by 11 leaves remainer m and resulting quotient when divided by 7 leaves a remainder n.What are the values of m & n respectively?\"<BR>\n" );
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document.write( "N/11=45/11=4 R1, so m=1.<BR>\n" );
document.write( "Quotient=4,<BR>\n" );
document.write( "Quotient/7=4/7=0 R4, so n=4<BR>\n" );
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document.write( "Answer: m=1, n=4  assuming N is the smallest positive value of N=45.<BR>\n" );
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