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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

Kudos for a correct solution.

The number that divide 28 completely will be the factors of 28

The Numbers which leave remainder 1 when divide 28 will be Dividing 27 perfectly i.e. Factors of 27

Factors of 27 = {1, 3, 9, 27}

But 1 is not acceptable as it divides each integer completely

So Sum of all numbers satisfying the required condition = 3+9+27 = 39

Answer: Option E
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Re: When 28 is divided by the positive integer x, the remainder is 1. What [#permalink]

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22 Jul 2015, 05:59

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First we have to check what number will give a reminder of 1 when 28 is divided by that number we know that

Dividend/Divisor = Quotient + Reminder/Divisor

28/x = Q + 1/x or 28 = xQ + 1

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.

so add all 3+9+27 = 39

So E is the correct Answer Choice
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Re: When 28 is divided by the positive integer x, the remainder is 1. What [#permalink]

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22 Jul 2015, 06:18

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Bunuel wrote:

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

Kudos for a correct solution.

The biggest integer x which will give remainder 1 when 28 is divided by it is 27 so 28= 27*Q + 1 Now 27 can be divided by 3 and 9 only ( excluding 1 ) Thus 3 and 9 will also give remainder 1

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

Kudos for a correct solution.

800score Official Solution:

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). _________________

can anybody please explain why are we leaving 1 from the factors of 27?

We are told that when 28 is divided by the positive integer x, the remainder is 1. Though 1 is in fact a factor of 27, it does not satisfy the given condition: 28 divided by 1 gives the remainder of 0, not 1.
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