To find the sum of all positive integers up to 990 that are divisible by 7 and not by 2, we need to follow a step-by-step approach.

Step 1: Find the first number that satisfies the given conditions.
- The first positive integer that is divisible by 7 and not by 2 is 7 itself.

Step 2: Find the last number that satisfies the given conditions.
- We need to find the largest positive integer less than or equal to 990 that satisfies the given conditions.
- To find this, we divide 990 by 7 and take the integer part: 990 ÷ 7 = 141.
- Therefore, the largest positive integer less than or equal to 990 that is divisible by 7 is 141 x 7 = 987.

Step 3: Find the number of terms that satisfy the given conditions.
- To find the number of terms, we divide the last number (987) by the common difference (7) and add 1: (987 - 7) ÷ 7 + 1 = 141.

Step 4: Calculate the sum using the arithmetic progression formula.
- The sum of an arithmetic progression can be calculated using the formula: sum = (n/2)(2a + (n-1)d), where n is the number of terms, a is the first term, and d is the common difference.
- In this case, n = 141, a = 7, and d = 7.
- Substituting these values into the formula, we get: sum = (141/2)(2(7) + (141-1)(7)) = 71(14 + 140(7)) = 71(14 + 980) = 71(994) = 70,274.

Therefore, the sum of all positive integers up to 990 that are divisible by 7 and not by 2 is 70,274.

The correct answer is option C) 35,287.