Q. 44

If N ÷ 5 leaves remainder 3 and N ÷ 2 leaves remainder 0, then N ÷ 10 leaves remainder 4.

Answer :

False(F)

Here it’s given N ÷ 5 leaves remainder 3


N = 5n + 3,where n = 0,1,2,3,..


and N ÷ 2 leaves remainder 0


N is an even number


But N = 5n + 3,it’s sum of two terms whose second term is odd.


Therefore,5n should be an odd number.


5n can be odd when n = 1,3,5,…


So, in this case when N = 5n + 3


N = 5(1) + 3 = 8 when(n = 1)


Hence when we substitute n = 1,3,5,.. in N = 5n + 3,we get 8,18,28 etc


Now, when we divide N by 10 ,N can be written as


N = 10×n + 8,when n = 0,1,2,3,..


Therefore, when N ÷ 10 ,always leaves remainder 8.


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