All questions of Practice Test: Pedagogy for CTET & State TET Exam

Understanding Divisibility by 45
To determine the value of 'a' in the number 82a58b, we first need to ensure that it is divisible by 45. A number is divisible by 45 if it is divisible by both 5 and 9.
Step 1: Check divisibility by 5
- A number is divisible by 5 if its last digit is either 0 or 5.
- Therefore, 'b' must be 0 or 5 for 82a58b to be divisible by 5.
Step 2: Check divisibility by 9
- A number is divisible by 9 if the sum of its digits is divisible by 9.
- The sum of the digits in 82a58b is: 8 + 2 + a + 5 + 8 + b = 23 + a + b.
Step 3: Evaluating possible values of 'b'
- If b = 0: Sum = 23 + a which must be divisible by 9.
- If b = 5: Sum = 28 + a which must also be divisible by 9.
Calculating for b = 0
- 23 + a divisible by 9 gives possible values of a as 4 (since 27 is the nearest multiple of 9).
Calculating for b = 5
- 28 + a divisible by 9 gives possible values of a as 7 (since 36 is the nearest multiple of 9).
Step 4: Ensuring not divisible by 20
- A number is not divisible by 20 if it does not end with 0.
- Therefore, if b = 0, 82a580 is divisible by 20. Thus, we discard this case.
Final Conclusion
- The only valid case is when b = 5 and a = 7.
- Hence, the value of 'a' is 7, confirming option 'A' as the correct answer.