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# When 28 is divided by the positive integer x, the remainder is 1. What

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Math Expert
Joined: 02 Sep 2009
Posts: 51073
When 28 is divided by the positive integer x, the remainder is 1. What  [#permalink]

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22 Jul 2015, 01:12
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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

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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, 03:08
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 only possible values of the form 28=xp+1 are 3,9 or 27

The sum = 3+9+27 =39. E is the correct answer. We dont need to look for values >28 as all these values will leave a remainder of 28 and not 1.
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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, 03:25
The values x can hold such that the given conditions are met would be 3, 9 and 27. Sum (3+9+27) = 39. Ans (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, 04:19
2
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 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, 04:59
2
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, 05:18
2
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

So sum = 27+9+3 = 39
So 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, 11:32
1
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.

28 - 27 = 1;

Hence x can be factors of 27 => 1, 3, 9, 27
1 cannot be used here, since 1 divides all integers evenly.

Hence the sum of the no.s = 3+9+27 = 39

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, 16:28
1
A quick scan will give us 3 and 9 as the desired numbers that leave 1 as remainder.

But before jumping to options - there is also 27 that will give 1 as a remainder.

So the answer is 3+9+27 = 39.

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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26 Jul 2015, 11:04
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.

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

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14 Nov 2017, 10:24
can anybody please explain why are we leaving 1 from the factors of 27?
Math Expert
Joined: 02 Sep 2009
Posts: 51073
Re: When 28 is divided by the positive integer x, the remainder is 1. What  [#permalink]

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14 Nov 2017, 10:45
Psk13 wrote:
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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Re: When 28 is divided by the positive integer x, the remainder is 1. What  [#permalink]

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14 Nov 2017, 11:03
Bunuel
thanks
Re: When 28 is divided by the positive integer x, the remainder is 1. What &nbs [#permalink] 14 Nov 2017, 11:03
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# When 28 is divided by the positive integer x, the remainder is 1. What

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