Question:

The sum of all four-digit numbers that can be formed with the distinct non-zero digits aa, bb, cc, and dd, with each digit appearing exactly once in every number, is 153310+n153310 + n, where nn is a single digit natural number. Then, the value of (a+b+c+d)(a + b + c + d) is ?

Updated On: Nov 29, 2024
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Correct Answer: 31

Solution and Explanation

There are 24 distinct four-digit numbers that can be formed with the digits aa, bb, cc, and dd (since there are 4!=244! = 24 possible permutations). The sum of all these numbers is:

24×(a+b+c+d)×111124 \times (a + b + c + d) \times 1111.

We are given that this sum is 153310+n153310 + n, where nn is a single digit. By equating, we have:

24×(a+b+c+d)×1111=153310+n24 \times (a + b + c + d) \times 1111 = 153310 + n.

From this equation, solve for a+b+c+d+na + b + c + d + n.

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