M is the largest three digits number which divided by 6and 5 leaves reminder 5 and 3 respectively .what will be the reminder when M is divided by 11 ?
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Since M is the largest 3 digit number with certain conditions to be satisfied let us start with
Largest 3 digit number is 999.
999÷6 = 166 and reminder 3. If the reminder is to be 5 the number has to be 165*6+5=995
999÷5 = 199 and reminder is 4. If the reminder is to be 3 the number has to be 998.
If we reduce 6 from 995 continuously and reduce 5 from 998 both had to become same at some point. Thus
995–6=991; 991–6=983; 983–6=977
998–5=993; 993–5=988; 988–5=983
Therefore M=983
This 983÷11=89 and reminder is 4.
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