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Which of the following is true about the absolute difference between a two- digit number and the number obtained by reversing its digits?
- a)It is divisible by 11.
- b)It is divisible by 6.
- c)It is divisible by 9.
- d)It is divisible by 7.
Correct answer is option 'C'. Can you explain this answer?
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Which of the following is true about the absolute difference between a...
Let the units digit and tens digit be 'a' and 'b' respectively.
The number = 10b + a
Required difference = |(10b + a) - (10a +b)|= |9b - 9a| = 9 x |b - a|
The difference will always be divisible by 9.
Hence, option 3.
Hence, option 3.
Most Upvoted Answer
Which of the following is true about the absolute difference between a...
If I reverse 9 then its become absolute difference between a two- digit number. right ?
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Which of the following is true about the absolute difference between a...
The absolute difference between a two-digit number and the number obtained by reversing its digits can be found by subtracting the two numbers. Let's consider a two-digit number AB, where A represents the tens digit and B represents the units digit.
To reverse the digits, we obtain the number BA. The absolute difference between AB and BA can be calculated as follows:
AB - BA = 10A + B - (10B + A) = 9A - 9B = 9(A - B)
From this expression, we can see that the absolute difference is always divisible by 9, regardless of the values of A and B. This means that option c) is true.
Explanation:
To understand why the absolute difference is always divisible by 9, let's consider a few examples:
1) If we take the number 23, its reverse is 32. The absolute difference is 23 - 32 = -9, which is divisible by 9.
2) If we take the number 78, its reverse is 87. The absolute difference is 78 - 87 = -9, which is again divisible by 9.
3) If we take the number 36, its reverse is 63. The absolute difference is 36 - 63 = -27, which is divisible by 9.
We can observe that the absolute difference is always a multiple of 9. This is because when we subtract the two numbers, we are effectively subtracting the sum of their digits. The difference will always be a multiple of 9 because the digits vary by a multiple of 9. For example, in the number 23, the difference between the tens digit (2) and the units digit (3) is 1, which is a multiple of 9.
In conclusion, the absolute difference between a two-digit number and the number obtained by reversing its digits is always divisible by 9.
To reverse the digits, we obtain the number BA. The absolute difference between AB and BA can be calculated as follows:
AB - BA = 10A + B - (10B + A) = 9A - 9B = 9(A - B)
From this expression, we can see that the absolute difference is always divisible by 9, regardless of the values of A and B. This means that option c) is true.
Explanation:
To understand why the absolute difference is always divisible by 9, let's consider a few examples:
1) If we take the number 23, its reverse is 32. The absolute difference is 23 - 32 = -9, which is divisible by 9.
2) If we take the number 78, its reverse is 87. The absolute difference is 78 - 87 = -9, which is again divisible by 9.
3) If we take the number 36, its reverse is 63. The absolute difference is 36 - 63 = -27, which is divisible by 9.
We can observe that the absolute difference is always a multiple of 9. This is because when we subtract the two numbers, we are effectively subtracting the sum of their digits. The difference will always be a multiple of 9 because the digits vary by a multiple of 9. For example, in the number 23, the difference between the tens digit (2) and the units digit (3) is 1, which is a multiple of 9.
In conclusion, the absolute difference between a two-digit number and the number obtained by reversing its digits is always divisible by 9.
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Which of the following is true about the absolute difference between a two- digit number and the number obtained by reversing its digits?a)It is divisible by 11.b)It is divisible by 6.c)It is divisible by 9.d)It is divisible by 7.Correct answer is option 'C'. Can you explain this answer?
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Which of the following is true about the absolute difference between a two- digit number and the number obtained by reversing its digits?a)It is divisible by 11.b)It is divisible by 6.c)It is divisible by 9.d)It is divisible by 7.Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Which of the following is true about the absolute difference between a two- digit number and the number obtained by reversing its digits?a)It is divisible by 11.b)It is divisible by 6.c)It is divisible by 9.d)It is divisible by 7.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is true about the absolute difference between a two- digit number and the number obtained by reversing its digits?a)It is divisible by 11.b)It is divisible by 6.c)It is divisible by 9.d)It is divisible by 7.Correct answer is option 'C'. Can you explain this answer?.
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Which of the following is true about the absolute difference between a two- digit number and the number obtained by reversing its digits?a)It is divisible by 11.b)It is divisible by 6.c)It is divisible by 9.d)It is divisible by 7.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Which of the following is true about the absolute difference between a two- digit number and the number obtained by reversing its digits?a)It is divisible by 11.b)It is divisible by 6.c)It is divisible by 9.d)It is divisible by 7.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Which of the following is true about the absolute difference between a two- digit number and the number obtained by reversing its digits?a)It is divisible by 11.b)It is divisible by 6.c)It is divisible by 9.d)It is divisible by 7.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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