A four digit number abcd where a is greater than b and none of the digits are repeated,is divisible by 11. The sum of the digits at hundreds place and thousand place is 17.What is the possible tens place digit if the sum of unit place and tens place digits is a multiple of 9?

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A four digit number abcd where a is greater than b and none of the dig...

Since A+B=17 and A is greater than B, so A=9 and B=8. Here the maximum possible multiple of 9 can be 9 itself. According to the question none of the digits repeat, so C =7,2,5,4,3&6 and D =2,7,4,5,6&3 So the numbers can be formed are•9872•9827•9854•9845•9836•9863Already mentioned that ABCD is divisible by 11So 9845 is completely divisible by 11.And hence the digit at tens place ie C = 4

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A four digit number abcd where a is greater than b and none of the dig...

Given Conditions
- We have a four-digit number represented as abcd.
- The digits are a, b, c, d, where a > b and all digits are unique.
- The sum of the digits in the thousands (a) and hundreds (b) places equals 17.
- The number is divisible by 11.
- The sum of the tens (c) and units (d) places is a multiple of 9.
Step 1: Find Possible Values for a and b
- Since a + b = 17 and a > b, the possible pairs (a, b) are:
- (9, 8)
- (8, 7)
- (7, 6)
- (6, 5)
Step 2: Check Divisibility by 11
- For a number to be divisible by 11, the difference between the sum of the digits in odd positions and even positions must be a multiple of 11.
- The odd positions are a and c, while the even positions are b and d:
- |(a + c) - (b + d)| must be a multiple of 11.
Step 3: Explore Values for c and d
- Since d + c must be a multiple of 9, we can explore combinations based on the previous pairs of (a, b).
Step 4: Analyze Possible Combinations
- Let's take (9, 8):
- Then, c + d must be a multiple of 9.
- Possible pairs: (0, 9), (1, 8), (2, 7), (3, 6), (4, 5), (5, 4), (6, 3), (7, 2), (8, 1), (9, 0).
- However, since we already have used 8 and 9, c and d must be among (0, 1, 2, 3, 4, 5, 6, 7).
Conclusion
- After checking for valid combinations, the only possible tens place digit c that satisfies these conditions while ensuring no digit repetition is 0.
- Thus, the possible tens place digit is 0.

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A four digit number abcd where a is greater than b and none of the digits are repeated,is divisible by 11. The sum of the digits at hundreds place and thousand place is 17.What is the possible tens place digit if the sum of unit place and tens place digits is a multiple of 9? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about A four digit number abcd where a is greater than b and none of the digits are repeated,is divisible by 11. The sum of the digits at hundreds place and thousand place is 17.What is the possible tens place digit if the sum of unit place and tens place digits is a multiple of 9? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A four digit number abcd where a is greater than b and none of the digits are repeated,is divisible by 11. The sum of the digits at hundreds place and thousand place is 17.What is the possible tens place digit if the sum of unit place and tens place digits is a multiple of 9?.

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