Question
Find the number of solutions of 13A-18B=2 where A and B are natural numbers between 1 and 100.
Answer: Option B
:
B
option (b)
Based on Chinese Remainder theorem
The number can be re-written as 13A=18B+2-------(1)
Reduce the number to 13A=5B+2 (removing 13 from RHS)
Now find the first value of B for which A is an integer. In this case, B=10 is the first value for which A is also an integer.
B=10 and A=14 are the first integer solutions.
A will follow the AP 14 + 18d; d can take values 0 to 4 B will follow the AP 10 + 13d; d can take values 0 to 6A will be the limiting value and hence the solution is 5 and the answer option b)
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:
B
option (b)
Based on Chinese Remainder theorem
The number can be re-written as 13A=18B+2-------(1)
Reduce the number to 13A=5B+2 (removing 13 from RHS)
Now find the first value of B for which A is an integer. In this case, B=10 is the first value for which A is also an integer.
B=10 and A=14 are the first integer solutions.
A will follow the AP 14 + 18d; d can take values 0 to 4 B will follow the AP 10 + 13d; d can take values 0 to 6A will be the limiting value and hence the solution is 5 and the answer option b)
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