In the following number analogy, 563 is related to 635. Using the same rearrangement pattern, 894 will be related to which of the following numbers?

Introduction / Context:
This is a number analogy involving rearrangement of digits. The pair 563 : 635 suggests that the digits of the first number have been permuted to obtain the second. The question is to identify the same pattern and apply it to 894 to determine the correct related number. Such questions test observation of position changes rather than arithmetic operations like addition or multiplication.

Given Data / Assumptions:
- First pair is 563 and 635, written as 563 : 635.
- Second pair begins with 894 and needs to be completed as 894 : ?.
- Each number has three digits, so patterns may involve rotation or rearrangement of these digits.
- The correct option must be obtainable by applying the same positional change to 894 that turns 563 into 635.

Concept / Approach:
First, analyse how the digits move in the pair 563 to 635. The digits of 563 are 5, 6, and 3. The digits of 635 are 6, 3, and 5. The hundreds digit 5 has moved to the units place, the tens digit 6 has moved to the hundreds place, and the units digit 3 has moved to the tens place. This is equivalent to a left rotation of the digits, where each digit moves one place left and the leftmost digit wraps around to the right. Once this pattern is recognised, apply the same left rotation to 8, 9, and 4 in 894.

Step-by-Step Solution:
Step 1: Write down 563 as 5, 6, 3 and its partner 635 as 6, 3, 5. Step 2: Observe that 5 moves from first to third position, 6 moves from second to first, and 3 moves from third to second. Step 3: Recognise this as a left rotation: 5, 6, 3 becomes 6, 3, 5. Step 4: Now write 894 as 8, 9, 4. Step 5: Apply the same left rotation. The first digit 8 goes to the end, the second digit 9 moves to the first position, and the third digit 4 moves to the second position. Step 6: The new order is 9, 4, 8, which forms the number 948. Step 7: Check options and confirm that 948 is offered as option D.

Verification / Alternative check:
To verify, test the identified rule again on the original pair. Rotating 5, 6, 3 left gives 6, 3, 5, which matches 635 exactly. No arithmetic adjustment is required, so the rule is purely positional. Applying any different rearrangement to 894, such as reversing digits or rotating right, produces results like 498 or 489, which do not follow the same pattern. Therefore only 948 is consistent with the given example.

Why Other Options Are Wrong:
Option A, 849, corresponds to moving the last digit to the first position and shifting others right, which is a different rotation. Option B, 489, is a more complex rearrangement that does not match the original pattern. Option C, 498, appears to be a reversal of 894 with an additional change. None of these transitions reflect the simple left rotation that transforms 563 into 635. Hence they must be rejected.

Common Pitfalls:
Some learners immediately apply arithmetic operations such as adding or subtracting fixed values between numbers, overlooking that the digits have simply been rearranged. Others may detect a rotation but apply it in the wrong direction. To avoid these mistakes, always compare each digit position in both numbers and look for a consistent positional mapping before attempting more complex operations. This reduces confusion and leads quickly to the correct answer in this type of question.

Final Answer:
Following the same left rotation of digits that maps 563 to 635, the number 894 is mapped to 948, so option D is correct.