In this number analogy, 583 is related to 293 in a particular way. Using the same pattern, 488 is related to which of the following numbers?

Introduction / Context:
This question tests numerical analogy, where a pattern connects the first pair of numbers 583 and 293, and you must apply the same rule to the new number 488. Such patterns often involve operations on digits, so the key skill is to experiment with sums and differences of digits until a consistent rule appears.

Given Data / Assumptions:
1) The first pair is 583 and 293.
2) The second pair is 488 and an unknown number chosen from the options 291, 378, 487, and 581.
3) We assume a digit based relationship, since both members of each pair are three digit numbers and the options also have three digits.
4) The pattern should be the same for both pairs, so once we find a rule that transforms 583 into 293, we must use it to transform 488 into the correct answer.

Concept / Approach:
A common approach for such problems is to look at the sum of digits in each number and compare them. For 583, the sum of digits is 5 + 8 + 3, and for 293, it is 2 + 9 + 3. If we see a consistent difference between these sums, we can check whether the same difference holds for 488 and one of the options. This avoids complicated algebra and focuses on simple arithmetic that often appears in exam style analogies.

Step-by-Step Solution:
Step 1: Compute the sum of digits of 583: 5 + 8 + 3 = 16. Step 2: Compute the sum of digits of 293: 2 + 9 + 3 = 14. Step 3: Note that the sum of digits has decreased by 2 when going from 583 to 293, that is 16 minus 14 equals 2. Step 4: Now compute the sum of digits of 488: 4 + 8 + 8 = 20. Step 5: To apply the same pattern, the related number must have a digit sum that is 2 less than 20, so the required sum is 18. Step 6: Check each option and compute its digit sum. For 291, the sum is 2 + 9 + 1 = 12. For 378, the sum is 3 + 7 + 8 = 18. For 487, the sum is 4 + 8 + 7 = 19. For 581, the sum is 5 + 8 + 1 = 14. Step 7: Only 378 has the required sum of digits equal to 18, so by the same pattern, 488 corresponds to 378.

Verification / Alternative check:
A quick verification is to restate the rule clearly: the second number in each pair must have a digit sum that is 2 less than the digit sum of the first number. The sums 16 and 14 for the first pair satisfy this rule. For 488 and 378, the sums 20 and 18 also satisfy the same rule. No other option preserves this difference of 2, so the pattern is consistent and unique.

Why Other Options Are Wrong:
Option 291 has a digit sum of 12, which is 8 less than 20, not 2 less. Option 487 has a digit sum of 19, which is only 1 less than 20. Option 581 has a sum of 14, which is 6 less than 20. None of these preserve the same difference of 2 in the digit sums, so they cannot be correct under the discovered rule.

Common Pitfalls:
A common mistake is to try to match numbers based on superficial closeness or simple subtraction of the whole three digit numbers. Another error is to assume complicated operations like squares or cubes without first checking easier patterns such as digit sums. Always test simple and symmetric rules before moving to complicated ones, especially when the exam time is limited.

Final Answer:
Therefore, the correct number that completes the analogy is 378. Thus, 583 is related to 293 in the same way that 488 is related to 378.