700plus2010 Posted March 12, 2010 Share Posted March 12, 2010 Find the smallest number which when divided by 2, 4, 6 and 8 leaves 1 as a remainder in each case, but divides evenly when divided by 7? I approached this question by multiplying 6*8 and 7*7 so I got 49 as a result. Is my reasoning correct? Quote Link to comment Share on other sites More sharing options...
Abhishek009 Posted March 12, 2010 Share Posted March 12, 2010 Approaching these prob is easy if options are given, Neways: Consider the multiple of 7 in each case. 7 wil not leave 1 as rem when divided by 8 14 wil not leave rem 1 when divided by 2 21 wil not leave rem 1 when divided by 6 28 wil not give rem 1 when divided by 2 and 4 35 wil not give rem 1 when divided by 4 42 is divisible by 2 and 6 , hence not possible. 49 leaves rem 1 in all cases hence the smallest number is 49. Its a bit lengthy method........ Quote Link to comment Share on other sites More sharing options...
700plus2010 Posted March 12, 2010 Author Share Posted March 12, 2010 Thanks for your help. I just had the question not the choices... Quote Link to comment Share on other sites More sharing options...
Fiver Posted March 13, 2010 Share Posted March 13, 2010 but divides evenly when divided by 7?[/font] This essentially means that the number in question is an even multiple of 7 and thus is contradictory to what is presented earlier in the question (as the number will have to be divisible by 2); i guess the question intends to say that the number is perfectly divisible by 7. Another way is to take the LCM of all divisors to which the number yeilds a remiander and add the remainder to this LCM or to any multiple of this LCM, depending on what the question demands. e.g. the LCM of 2, 4, 6 & 8 is as good as the LCM of 6 & 8 = 24 add 1 = 25, but 25 is not a multiple of 7; hence choose 2*24=48+1 = 49 (correct as it is a multiple of 7) Quote Link to comment Share on other sites More sharing options...
700plus2010 Posted March 13, 2010 Author Share Posted March 13, 2010 Fiver, good explanation! Thanks Quote Link to comment Share on other sites More sharing options...
meticulousboy Posted March 19, 2010 Share Posted March 19, 2010 LCM (2,4,6,8) = 24. So, the numbers of interest would be 25, 49, 73... Choose the one which is divisible by 7. Quote Link to comment Share on other sites More sharing options...
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