Q. 44

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

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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