Given two rows of numbers, apply the following rules to find the resultant of each pair (first number followed by second number):

- **Step 1:** If an even number is followed by an odd prime number, the resultant is the sum of both numbers.
- **Step 2:** If an odd number is followed by a perfect square, the resultant is the odd number minus the perfect square.
- **Step 3:** If an odd number is followed by another odd number, the resultant is the sum of both numbers.
- **Step 4:** If an even number is followed by an odd non-prime number, the resultant is the even number minus the odd number.
- **Step 5:** If an odd number is followed by an even number, the resultant is the product of the two numbers.

Find the difference between the resultant of the first row and the second row.

First row: 5 4 15

Second row: 21 16 4

Question

Given two rows of numbers, apply the following rules to find the resultant of each pair (first number followed by second number):

- **Step 1:** If an even number is followed by an odd prime number, the resultant is the sum of both numbers.
- **Step 2:** If an odd number is followed by a perfect square, the resultant is the odd number minus the perfect square.
- **Step 3:** If an odd number is followed by another odd number, the resultant is the sum of both numbers.
- **Step 4:** If an even number is followed by an odd non-prime number, the resultant is the even number minus the odd number.
- **Step 5:** If an odd number is followed by an even number, the resultant is the product of the two numbers.

Find the difference between the resultant of the first row and the second row.

First row: 5 4 15

Second row: 21 16 4

Accepted Answer

**Solution:**

1. Analyze the first row pairs:
   - Pair (5, 4): 5 is odd, 4 is a perfect square.
     According to Step 2, resultant = 5 - 4 = 1

- Pair (4, 15): 4 is even, 15 is odd non-prime.
     According to Step 4, resultant = 4 - 15 = -11

- Pair (15, _): Since the third number has no pair following it, consider only pairs as given (assumed pairs are (5,4), (4,15) for first row).

Sum of first row resultants = 1 + (-11) = -10

2. Analyze the second row pairs:
   - Pair (21, 16): 21 is odd, 16 is a perfect square.
     According to Step 2, resultant = 21 - 16 = 5

- Pair (16, 4): 16 is even, 4 is even (not odd), so no rule applies directly; however, since 16 is even and 4 is even, none of the steps match exactly. Assuming no resultant for this pair or zero.

Sum of second row resultants = 5 + 0 = 5

3. Find the difference between the sums:
   $$	ext{Difference} = |(-10) - 5| = |-15| = 15$$

**Note:** The original question's explanation seems to consider pairs differently. Let's re-examine pairs as per the question's format:

Given rows:
- First row: 5 4 15
- Second row: 21 16 4

Pairs are formed vertically:
- Pair 1: (5, 21)
- Pair 2: (4, 16)
- Pair 3: (15, 4)

Calculate resultants for each pair:

- Pair 1: 5 (odd) followed by 21 (odd)
  Step 3 applies: sum = 5 + 21 = 26

- Pair 2: 4 (even) followed by 16 (even)
  No rule for even followed by even, so resultant = 0

- Pair 3: 15 (odd) followed by 4 (even)
  Step 5 applies: product = 15 × 4 = 60

Sum of first row resultants = 26 + 0 + 60 = 86

Sum of second row resultants is not applicable here as pairs are vertical.

Since the question asks for difference between the resultant of first and second row, it likely means sum of resultants of each row considered horizontally:

First row pairs:
- (5,4): 5 odd, 4 perfect square → Step 2: 5 - 4 = 1
- (4,15): 4 even, 15 odd non-prime → Step 4: 4 - 15 = -11
Sum = 1 + (-11) = -10

Second row pairs:
- (21,16): 21 odd, 16 perfect square → Step 2: 21 - 16 = 5
- (16,4): 16 even, 4 even → no rule, resultant = 0
Sum = 5 + 0 = 5

Difference = |-10 - 5| = 15

**Answer:** 15

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