The digits of a three-digit number A are written in reverse order to form another three digit number B. If B > A and B – A is perfectly divisible by 7, then which of the following is necessarily true?
The digits of a three-digit number A are written in reverse order to form another three digit number B. If B > A and B – A is perfectly divisible by 7, then which of the following is necessarily true?
Option 1 -
112 < A < 311
Option 2 -
100 < A < 299
Option 3 -
106 < A < 305
Option 4 -
118 < A < 317
Asked by Shiksha User
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1 Answer
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Correct Option - 3
Detailed Solution:Let A = abc and B = cba
Therefore, B – A = 100c + 10b + a – (100a + 10b + c) = 99 (c – a). B – A is a multiple of 7.
Therefore, c – a = 7 (a, c) (1, 8) or (2, 9).
Hence, number is between 108 to 198 or 209 to 299.
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