Question

Find the number of solutions of 13A-18B=2 where A and B are natural numbers between 1 and 100.

• A. 6
• B. 5
• C. 3
• D. 1
• E. 7

Answer 1

The correct option is B 5

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)