NIMCET 2009 — Reasoning PYQ

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Question

NIMCET 2009 — Reasoning PYQ

NIMCET | Reasoning | 2009

Using the digits 1, 5, 2, 8 all possible four digit numbers are formed and the sum of all such numbers is between:

Choose the correct answer:

Explanation

To find the sum of all $n$ -digit numbers formed using $n$ distinct digits, we use a standard mathematical formula.

1. Identify the given values:

Given digits: $1, 2, 5, 8$
Number of digits ( $n$ ): $4$
Sum of the given digits: $1 + 2 + 5 + 8 = 16$

2. Formula for the sum of all possible numbers:

The sum of all numbers formed by using $n$ non-zero distinct digits is:

\text{Sum} = (\text{Sum of digits}) \times (n-1)! \times (111\dots n \text{ times})

3. Apply the formula:

For $n = 4$ , the formula becomes:

\text{Sum} = (1 + 2 + 5 + 8) \times (4 - 1)! \times (1111)

\text{Sum} = 16 \times 3! \times 1111

Since $3! = 3 \times 2 \times 1 = 6$ :

\text{Sum} = 16 \times 6 \times 1111

\text{Sum} = 96 \times 1111

4. Final Calculation:

\text{Sum} = 106,656

Conclusion:

The calculated sum, 106,656, falls clearly between 100,000 and 150,000.

Correct Option:

(d) 100000 and 150000