The position of how many digits in the number 726801 will remain unchanged after the digits within the number are rearranged in descending order (from left to right)?
One
Analyzing Digit Positions After Rearrangement
The question asks us to determine how many digits in a given number maintain their original position after the digits are rearranged in descending order from left to right. The given number is 726801.
Step-by-Step Solution
Let's break down the process:
- Identify the digits in the original number.
- Arrange these digits in descending order.
- Compare the position of each digit in the original number with its position in the rearranged number.
- Count the number of positions where the digit is the same in both the original and rearranged numbers.
Original Number and Its Digits
The original number is 726801.
The digits in the number are: 7, 2, 6, 8, 0, 1.
Rearranging Digits in Descending Order
Arranging the digits (8, 7, 6, 2, 1, 0) in descending order (from largest to smallest) gives us:
876210
Comparing Positions
Now, let's compare the original number and the rearranged number position by position:
| Position | Original Digit | Rearranged Digit | Position Changed? |
|---|---|---|---|
| 1st | 7 | 8 | Yes |
| 2nd | 2 | 7 | Yes |
| 3rd | 6 | 6 | No |
| 4th | 8 | 2 | Yes |
| 5th | 0 | 1 | Yes |
| 6th | 1 | 0 | Yes |
By comparing the original digit and the rearranged digit at each position, we can see which positions have remained unchanged.
Identifying Unchanged Positions
Looking at the table, the digit at the 3rd position is 6 in both the original number (726601) and the rearranged number (876210). This is the only position where the digit has not changed.
Conclusion on Unchanged Digits
Only one digit, the digit '6' at the 3rd position, remains in the same position after the digits of the number 726801 are rearranged in descending order.
Therefore, the number of digits whose position remains unchanged is one.
Revision Table: Number Rearrangement Concepts
| Concept | Description | Example |
|---|---|---|
| Descending Order | Arranging numbers or digits from the largest value to the smallest value. | Digits 5, 1, 9 arranged in descending order: 9, 5, 1 |
| Ascending Order | Arranging numbers or digits from the smallest value to the largest value. | Digits 5, 1, 9 arranged in ascending order: 1, 5, 9 |
| Position of a Digit | The place value or location of a digit within a number (e.g., units, tens, hundreds, or simply 1st, 2nd, 3rd position from left). | In 726, the digit 7 is at the 1st position (hundreds place). |
| Rearranging Digits | Forming a new number or sequence using the same digits as an original number, but in a different order. | Rearranging digits of 123 could give 321, 132, 213, etc. |
Additional Information: Logical Reasoning with Numbers
Questions like this test your ability to follow instructions and compare sequential data. They are common in logical reasoning sections of various tests. Here are some related concepts:
- Sequence Analysis: Identifying patterns or properties in a sequence of numbers or items.
- Comparison Tasks: Directly comparing two sets of data based on given criteria.
- Ordering: Arranging items based on specific rules (ascending, descending, alphabetical, etc.).
- Position-Based Problems: Questions that focus on the location of elements within a sequence or structure.
When tackling these problems, it's helpful to write down the steps clearly, as shown in the solution, especially when comparing positions. This reduces the chance of making errors.
Important Questions from Number System
Find the length of the longest rod which can be used to measure exactly the lengths 5 m 13 cm, 11 m 34 cm, and 12 m 15 cm.
In a 2-digit number, the tens digit is two times its unit digit, and the number is 12 less than two times the number obtained by interchanging its digits. Find the original number.
Find the sum of the smallest and the greatest 3-digit numbers formed by using the digits 0, 1, 2, 3, 4 without any repetition of digits.
By knowing the pH value of a liquid, we can find the:
If a 10-digit number M30348462N is divisible by both 8 and 11, then what is the value of M² + N² - 18?
