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CAT 2024 Slot 1 QA Question 4

Type-in-the-answer (no negative marking) · Modern Math · Permutation & Combination · Try it, then check the answer and solution below.

CAT 2024 Slot 1QAModern Math • Permutation & CombinationModerate
The sum of all four-digit numbers that can be formed with the distinct non-zero digits a,b,c,a, b, c,and $d , with each digit appearing exactly once in every number, is $153310 + n , where nn is a single digit natural number. Then, the value of (a+b+c+d+n)(a + b + c + d + n) is
TITA Answer:
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Answer and solution

Answer: 31

📌 Core Concept
The sum of all permutations of distinct digits can be calculated by considering each digit's contribution to each place value. Each digit appears in each position an equal number of times, leading to the formula:
Total Sum=(a+b+c+d)×6×1111\text{Total Sum} = (a + b + c + d) \times 6 \times 1111
🔢 Step-by-Step Solution
1
Determine the number of permutations:
Since there are 4 distinct digits, the number of four-digit numbers formed is 4!=244! = 24.
2
Calculate

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