CTET & State TET Exam > CTET & State TET Questions > If the number 82a58b is completely divisible ...
Start Learning for Free
If the number 82a58b is completely divisible by 45 but not by 20, then find the value of ‘a’?
- a)9
- b)8
- c)7
- d)12
Correct answer is option 'A'. Can you explain this answer?
?
Most Upvoted Answer
If the number 82a58b is completely divisible by 45 but not by 20, then...
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.
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.
|
Explore Courses for CTET & State TET exam
|
|
Top Courses for CTET & State TETView all
Question Description
If the number 82a58b is completely divisible by 45 but not by 20, then find the value of ‘a’?a)9b)8c)7d)12Correct answer is option 'A'. Can you explain this answer?? for CTET & State TET 2025 is part of CTET & State TET preparation. The Question and answers have been prepared according to the CTET & State TET exam syllabus. Information about If the number 82a58b is completely divisible by 45 but not by 20, then find the value of ‘a’?a)9b)8c)7d)12Correct answer is option 'A'. Can you explain this answer?? covers all topics & solutions for CTET & State TET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the number 82a58b is completely divisible by 45 but not by 20, then find the value of ‘a’?a)9b)8c)7d)12Correct answer is option 'A'. Can you explain this answer??.
If the number 82a58b is completely divisible by 45 but not by 20, then find the value of ‘a’?a)9b)8c)7d)12Correct answer is option 'A'. Can you explain this answer?? for CTET & State TET 2025 is part of CTET & State TET preparation. The Question and answers have been prepared according to the CTET & State TET exam syllabus. Information about If the number 82a58b is completely divisible by 45 but not by 20, then find the value of ‘a’?a)9b)8c)7d)12Correct answer is option 'A'. Can you explain this answer?? covers all topics & solutions for CTET & State TET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the number 82a58b is completely divisible by 45 but not by 20, then find the value of ‘a’?a)9b)8c)7d)12Correct answer is option 'A'. Can you explain this answer??.
Solutions for If the number 82a58b is completely divisible by 45 but not by 20, then find the value of ‘a’?a)9b)8c)7d)12Correct answer is option 'A'. Can you explain this answer?? in English & in Hindi are available as part of our courses for CTET & State TET.
Download more important topics, notes, lectures and mock test series for CTET & State TET Exam by signing up for free.
Here you can find the meaning of If the number 82a58b is completely divisible by 45 but not by 20, then find the value of ‘a’?a)9b)8c)7d)12Correct answer is option 'A'. Can you explain this answer?? defined & explained in the simplest way possible. Besides giving the explanation of
If the number 82a58b is completely divisible by 45 but not by 20, then find the value of ‘a’?a)9b)8c)7d)12Correct answer is option 'A'. Can you explain this answer??, a detailed solution for If the number 82a58b is completely divisible by 45 but not by 20, then find the value of ‘a’?a)9b)8c)7d)12Correct answer is option 'A'. Can you explain this answer?? has been provided alongside types of If the number 82a58b is completely divisible by 45 but not by 20, then find the value of ‘a’?a)9b)8c)7d)12Correct answer is option 'A'. Can you explain this answer?? theory, EduRev gives you an
ample number of questions to practice If the number 82a58b is completely divisible by 45 but not by 20, then find the value of ‘a’?a)9b)8c)7d)12Correct answer is option 'A'. Can you explain this answer?? tests, examples and also practice CTET & State TET tests.
|
|
Explore Courses for CTET & State TET exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup