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Q.
In the number 46723598 how many such digits will be as far away from the beginning of the number if arranged in ascending order from right to left ?
- a)One
- b)Two
- c)Three
- d)Four
- e)None
Correct answer is option 'A'. Can you explain this answer?
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Understanding the Problem
To determine how many digits in the number 46723598 are farther away from the beginning when arranged in ascending order from right to left, we first need to sort the digits.
Step 1: Arrange the Digits in Ascending Order
- The digits of the number 46723598 are:
4, 6, 7, 2, 3, 5, 9, 8.
- Arranging these digits in ascending order gives us:
2, 3, 4, 5, 6, 7, 8, 9.
Step 2: Reverse the Order
- Now, reversing this order to get it from right to left yields:
9, 8, 7, 6, 5, 4, 3, 2.
Step 3: Analyze the Original Position
- Next, we will compare the original positions of the digits 2, 3, 4, 5, 6, 7, 8, and 9 against their new positions in the sorted order.
- Original positions in 46723598:
4(1), 6(2), 7(3), 2(4), 3(5), 5(6), 9(7), 8(8).
- New positions in 98765432:
9(1), 8(2), 7(3), 6(4), 5(5), 4(6), 3(7), 2(8).
Step 4: Count the Digits Farther from the Beginning
- In the sorted list, only the digit '2' from the original number remains in the last position (8th) of the new arrangement.
- All other digits (3, 4, 5, 6, 7, 8, 9) are now positioned closer to the start than their original positions.
Conclusion
- Thus, only one digit (the '2') is farther away from the beginning in the new arrangement.
Therefore, the correct answer is option 'A' - One.
To determine how many digits in the number 46723598 are farther away from the beginning when arranged in ascending order from right to left, we first need to sort the digits.
Step 1: Arrange the Digits in Ascending Order
- The digits of the number 46723598 are:
4, 6, 7, 2, 3, 5, 9, 8.
- Arranging these digits in ascending order gives us:
2, 3, 4, 5, 6, 7, 8, 9.
Step 2: Reverse the Order
- Now, reversing this order to get it from right to left yields:
9, 8, 7, 6, 5, 4, 3, 2.
Step 3: Analyze the Original Position
- Next, we will compare the original positions of the digits 2, 3, 4, 5, 6, 7, 8, and 9 against their new positions in the sorted order.
- Original positions in 46723598:
4(1), 6(2), 7(3), 2(4), 3(5), 5(6), 9(7), 8(8).
- New positions in 98765432:
9(1), 8(2), 7(3), 6(4), 5(5), 4(6), 3(7), 2(8).
Step 4: Count the Digits Farther from the Beginning
- In the sorted list, only the digit '2' from the original number remains in the last position (8th) of the new arrangement.
- All other digits (3, 4, 5, 6, 7, 8, 9) are now positioned closer to the start than their original positions.
Conclusion
- Thus, only one digit (the '2') is farther away from the beginning in the new arrangement.
Therefore, the correct answer is option 'A' - One.
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