Digit-rearrangement difference: Arrange the digits of 92581473 in ascending order to form a new number. What is the difference between the digit that is fourth from the right and the digit that is third from the left in this new arrangement?
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AOne
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BTwo
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CThree
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DFour
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EZero
Answer
Correct Answer: Two
Explanation
Introduction / Context:Ordering digits and picking positional values is a staple reasoning task. Here, you form a strictly ascending sequence, then index from different ends and compute a numeric difference.
Given Data / Assumptions:
- Original digits: 9, 2, 5, 8, 1, 4, 7, 3.
- New arrangement: ascending order.
- Positions requested: 4th from right, 3rd from left.
Concept / Approach:Ascending order for the digits yields a unique sequence. Convert “k-th from right” to an index from the left if helpful (for an 8-digit number, 4th from right = 5th from left).
Step-by-Step Solution:
Step 1: Sort digits ⇒ 1, 2, 3, 4, 5, 7, 8, 9.Step 2: 4th from right ⇒ position 8 - 4 + 1 = 5th from left ⇒ digit 5.Step 3: 3rd from left ⇒ digit 3.Step 4: Difference ⇒ 5 - 3 = 2.Verification / Alternative check:Visual scan from the right: rightmost digits are 9(1st), 8(2nd), 7(3rd), 5(4th) ⇒ still 5. Third from left remains 3.
Why Other Options Are Wrong:
- One/Three/Four/Zero: Not equal to 2; arise from index miscounts.
Common Pitfalls:Forgetting that “from right” reverses the direction; mis-sorting (placing 7 before 5), or missing that there are eight digits.
Final Answer:Two