If 204=8, 503=13, 305=11 and 907=25, what is 705?

To solve this, let's analyze the given equations:

1. 204 = 8
2. 503 = 13
3. 305 = 11
4. 907 = 25

Looking at these equations, it seems like the numbers on the right side are not directly related to the numbers on the left through simple arithmetic operations like addition or multiplication. However, if we consider the positions of the digits and their possible manipulation, one pattern could be that each number on the right is derived by adding the digits of the number on the left and then possibly applying another operation.

Let's try adding the digits of each number on the left:

1. 204: (2 + 0 + 4 = 6)
2. 503: (5 + 0 + 3 = 8)
3. 305: (3 + 0 + 5 = 8)
4. 907: (9 + 0 + 7 = 16)

However, these sums do not directly match the numbers on the right. Let's explore another possibility: perhaps the numbers on the right are derived by some other pattern or operation involving the digits.

Another possible pattern could involve the positions of the digits or their manipulation in a different way. For example, if we consider the first and last digits of each number and add them, then multiply by the middle digit (if it exists), we still don't get a clear pattern.

Given the provided examples, let's consider a different approach:

• 204 = 8: Could be (2 + 0 + 4 = 6), but this doesn't match. Maybe it involves the positions or another operation.
• 503 = 13: Similarly, (5 + 0 + 3 = 8), which doesn't match.
• 305 = 11: Again, (3 + 0 + 5 = 8), not matching.
• 907 = 25: Here, (9 + 0 + 7 = 16), still not matching.

Let's consider a pattern where we square the digits and then sum them:

1. 204: (2^2 + 0^2 + 4^2 = 4 + 0 + 16 = 20), which doesn't match.
2. 503: (5^2 + 0^2 + 3^2 = 25 + 0 + 9 = 34), which doesn't match.
3. 305: (3^2 + 0^2 + 5^2 = 9 + 0 + 25 = 34), which doesn't match.
4. 907: (9^2 + 0^2 + 7^2 = 81 + 0 + 49 = 130), which doesn't match.

Since none of these patterns directly apply, let's consider another possibility:

If we look at the numbers again, there might be a simpler pattern or a trick question. However, without a clear pattern from the given examples, we can't accurately determine the value for 705 using the provided information.

If there's a specific rule or pattern that isn't immediately apparent from the examples given, it would be necessary to know that rule to solve for 705.

For instance, if the rule was something like "take the first digit, add the second digit, and then multiply by the third digit," we would need to know that to apply it correctly. Without such a rule, we can only speculate on possible patterns.

Given the examples, there doesn't seem to be a straightforward mathematical operation (like addition, multiplication, or exponentiation of digits) that consistently applies to yield the results on the right side. Therefore, without more information or a clear pattern, it's challenging to determine what 705 would equal based on the provided examples.