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When 28 is divided by the positive integer x, the remainder is 1. What [#permalink]
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22 Jul 2015, 02:12
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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, 04:08
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, 04:25
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, 05:19
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, 05:59
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
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, 12:32
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, 17:28
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, 12:04
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, 11:24
can anybody please explain why are we leaving 1 from the factors of 27?



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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, 11:45



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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, 12:03




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