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Note that 104 and 52 are multiples of 13. Then
100x+50+y=(104−4)x+(52−2)+y=104x+52+(y−2−4x).
So you need y−2−4x to be a multiple of 13. That is, you need y≡2+4x(mod13). So plug each possible value of x into the congruence and see if there is a solution for y in the range needed. There are at most, then 9 solutions.
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Hey friend!
The answer is option ( B)
There are 7 three digit numbers divisible by 13 having 5 as their middle number.
156, 351, 455, 559, 650, 754, and 858.
Hope this helps!
Have a good day ahead:)
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