UPSC Exam > UPSC Questions > If 8A5146B is divisible by 88, then what is t...
Start Learning for Free
If 8A5146B is divisible by 88, then what is the value of AxB?
- a)4
- b)16
- c)8
- d)12
- e)18
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If 8A5146B is divisible by 88, then what is the value of AxB?a)4b)16c)...
Since, the given number is divisible by 8, the last three digits should also be divisible by 8. Only when B = 4, 46B is a multiple of 8. Thus, B = 4.
As the given number is divisible by 11, the difference between the sum of its odd digits and even digits must be a multiple of 11.
Thus, (8 + 5 + 4 + 4) – (A + 1 + 6) = 14 – A should be divisible by 11. Only when A = 3, 14-A is divisible by 11.
Thus, the value of AxB = 4×3 = 12.
As the given number is divisible by 11, the difference between the sum of its odd digits and even digits must be a multiple of 11.
Thus, (8 + 5 + 4 + 4) – (A + 1 + 6) = 14 – A should be divisible by 11. Only when A = 3, 14-A is divisible by 11.
Thus, the value of AxB = 4×3 = 12.
Most Upvoted Answer
If 8A5146B is divisible by 88, then what is the value of AxB?a)4b)16c)...
Solution:
To check divisibility by 88, let's first check the divisibility by 8 and 11 separately.
Divisibility by 8:
A number is divisible by 8 if the last three digits of the number are divisible by 8.
In the given number, the last three digits are 46B.
Since 46B is not divisible by 8, the given number is not divisible by 8.
Divisibility by 11:
A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or a multiple of 11.
In the given number, the sum of digits at odd places is 5+4+6=15.
The sum of digits at even places is 8+1+4=13.
Therefore, the difference between the sum of digits at odd places and the sum of digits at even places is 15-13=2.
Since 2 is not divisible by 11, the given number is not divisible by 11.
Conclusion:
Since the given number is not divisible by either 8 or 11, it is not divisible by 88.
Hence, there is no value of AxB that satisfies the condition.
Therefore, the correct answer is option 'None of the above'.
To check divisibility by 88, let's first check the divisibility by 8 and 11 separately.
Divisibility by 8:
A number is divisible by 8 if the last three digits of the number are divisible by 8.
In the given number, the last three digits are 46B.
Since 46B is not divisible by 8, the given number is not divisible by 8.
Divisibility by 11:
A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or a multiple of 11.
In the given number, the sum of digits at odd places is 5+4+6=15.
The sum of digits at even places is 8+1+4=13.
Therefore, the difference between the sum of digits at odd places and the sum of digits at even places is 15-13=2.
Since 2 is not divisible by 11, the given number is not divisible by 11.
Conclusion:
Since the given number is not divisible by either 8 or 11, it is not divisible by 88.
Hence, there is no value of AxB that satisfies the condition.
Therefore, the correct answer is option 'None of the above'.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
If 8A5146B is divisible by 88, then what is the value of AxB?a)4b)16c)8d)12e)18Correct answer is option 'D'. Can you explain this answer?
Question Description
If 8A5146B is divisible by 88, then what is the value of AxB?a)4b)16c)8d)12e)18Correct answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If 8A5146B is divisible by 88, then what is the value of AxB?a)4b)16c)8d)12e)18Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 8A5146B is divisible by 88, then what is the value of AxB?a)4b)16c)8d)12e)18Correct answer is option 'D'. Can you explain this answer?.
If 8A5146B is divisible by 88, then what is the value of AxB?a)4b)16c)8d)12e)18Correct answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If 8A5146B is divisible by 88, then what is the value of AxB?a)4b)16c)8d)12e)18Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 8A5146B is divisible by 88, then what is the value of AxB?a)4b)16c)8d)12e)18Correct answer is option 'D'. Can you explain this answer?.
Solutions for If 8A5146B is divisible by 88, then what is the value of AxB?a)4b)16c)8d)12e)18Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of If 8A5146B is divisible by 88, then what is the value of AxB?a)4b)16c)8d)12e)18Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If 8A5146B is divisible by 88, then what is the value of AxB?a)4b)16c)8d)12e)18Correct answer is option 'D'. Can you explain this answer?, a detailed solution for If 8A5146B is divisible by 88, then what is the value of AxB?a)4b)16c)8d)12e)18Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of If 8A5146B is divisible by 88, then what is the value of AxB?a)4b)16c)8d)12e)18Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If 8A5146B is divisible by 88, then what is the value of AxB?a)4b)16c)8d)12e)18Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup