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Question

If 16902608+26081690 is divided by 7, then the remainder is

A
5
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B
2
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C
0
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D
1
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Solution

The correct option is D 1
We know that,
1690=7×241+3,2608=7×372+4

Now, let
A=16902608+26081690=(7×241+3)2608+(7×372+4)1690=7k1+32608+7k2+41690, k1,k2N=7k+32608+41690, kN

B=32608+41690
Remainder of A and B are same, so
B=3×33×869+4×43×563=3×27869+4×64563=3(281)869+4(63+1)563=3(28k31)+4(63k4+1), k3,k4Z=7m+1, mZ

Hence, the remainder is 1.

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