The correct option is B
This question can be solved using Chinese Remainder theorem.
Suppose the no. of chairs is N. It is also known that 600<N<700.
Suppose the quotients when N is divided by 5, 7 and 8 and leaves the remainders 3, 2 and 5 be A, B
and C respectively.
Then, N = 5A+3 = 7B+2 = 8C+5.......................(1)
Solving first for
We get the first integral solution for (A,B) at (4,3).
The first solution for the above pair of equations = 23.
This increases in an Arithmetic Progression of 35 (LCM of 7 and 5)
Thus the general form of the above equation = 23+35k
Let us equate this to the last part of eqn (1).
The first integral solution for this occurs at C=11 and K=2
Thus the first number which when divided by 5, 7 and 8; leaves the remainders 3, 2 and 5 is 93.
This number is the first term of an AP with a common difference of 280 (LCM of 7, 5 and 8)
Thus, the number which will lie in the range of 600-700 is 653.
653 when divided by 13 leaves a remainder of 3; which is option (b).