In the number analogy 381 is to 160 as 478 is to which of the following numbers.

Introduction / Context:
This is a numerical analogy that tests pattern recognition between pairs of numbers. We are given 381 : 160 and asked to find the corresponding number paired with 478. The key to such questions is to look for consistent arithmetic operations, such as addition, subtraction or multiplication, that link the first number to the second. Once the rule is found, we apply it to the new number to get the correct answer.

Given Data / Assumptions:

• First numerical pair: 381 and 160.
• Second numerical pair: 478 and an unknown number from the options.
• Options: 347, 357, 247, 257.
• We assume a simple operation or fixed relationship applies to both pairs.

Concept / Approach:
A good starting point is to check the difference between numbers in the first pair. Calculate 381 minus 160, which is 221. If we suppose that the pattern is “subtract 221,” then the second pair should also differ by exactly 221, meaning 478 minus 221 should equal the unknown number. Computing this gives 478 minus 221 equals 257. We then check whether 257 appears among the options, which it does. This shows a consistent and simple arithmetic relationship working across both pairs.

Step-by-Step Solution:
Step 1: Subtract 160 from 381 to find the difference: 381 - 160 = 221. Step 2: Assume that the pattern is “subtract 221” to move from the first to the second number. Step 3: Apply this assumed rule to the second left hand number 478. Step 4: Compute 478 - 221 = 257. Step 5: Confirm that 257 is present as an option and that no other simple rule fits the given data as nicely.

Verification / Alternative check:
We can test for alternative explanations, such as operations on digits, but they are less neat. For instance, trying to combine digit sums or products does not yield 160 from 381 in a straightforward way. The constant difference of 221 between the first pair and the same difference between 478 and 257 is a much more natural pattern for exam based analogies. Therefore, applying the same fixed subtraction gives a strong consistent rule. Because 478 - 257 is also 221, the relationship 381 : 160 :: 478 : 257 holds in both directions.

Why Other Options Are Wrong:

• 347: 478 - 347 = 131, which does not match the difference of 221.
• 357: 478 - 357 = 121, again not consistent with the first pair difference.
• 247: 478 - 247 = 231, also different from 221, so it breaks the pattern.

Common Pitfalls:
Many students immediately focus on complex manipulations of digits instead of checking simple operations. Exam setters often prefer a single clear rule, such as a fixed difference or ratio, because it can be quickly applied. If a consistent subtraction or addition works neatly for the first pair, it is wise to test it on the second before trying more complicated ideas. This saves time and reduces confusion.

Final Answer:
The correct completion of the number analogy is 478 : 257, following the rule “subtract 221” used in the first pair.