When 28 is divided by the positive integer x, the remainder is 1. What is the sum of all the possible values of x for which this is true? A. 2 B. 3 C. 9 D. 30 E. 39

(E) First, we must find which numbers leave a remainder of 1. These numbers must be divisors of 27 (which is 1 less than 28) greater than 1. Such divisors of 27 are 3, 9, 27.

The first number is 3: 28/3 = 9, remainder 1. The next number after that is 9: 28/9 = 3, remainder 1. 27 also gives a remainder of 1, giving 3 possible values for x.

Adding these three values, we get 3 + 9 + 27 = 39.

The correct answer is choice (E). -------------

Why we need to add all the three possible divident for this question?

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