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Re: If K is a positive integer such that the remainder when 17 is divided [#permalink]
Bunuel wrote:
If K is a positive integer such that the remainder when 17 is divided by K is 2, what is the sum of all the possible values of K?

(A) 8
(B) 18
(C) 20
(D) 23
(E) 25


Ans: D

We are given a relation which is 17 = KI + 2 ; I and K are int Positive
so we can write it in this form K = 15/I ; as already given I and K are int I will take the values of Int which divides 15 and leaves no reminder thus those value of K are 3,5,and 15
Sum= 23

Ans D
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Re: If K is a positive integer such that the remainder when 17 is divided [#permalink]
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Expert Reply
Bunuel wrote:
If K is a positive integer such that the remainder when 17 is divided by K is 2, what is the sum of all the possible values of K?

(A) 8
(B) 18
(C) 20
(D) 23
(E) 25



We can create the equation:

17/K = Q + 2/K

17 = KQ + 2

15 = KQ

Thus, we see that K is a factor of 15. The factors of 15 are 1, 3, 5, and 15. However, K can’t be 1 since 17 is divisible by 1 (with remainder 0). On the other hand, when K is 3, 5 or 15, we do have a remainder 2 when 17 is divided by K. Thus, the sum of all possible values of K is 3 + 5 + 15 = 23.

Answer: D
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Re: If K is a positive integer such that the remainder when 17 is divided [#permalink]
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17/k gives us remainder 2. So we know that k can be divided by 15. Additionally, with prime factorization, we know 15 is broken down to 5 and 3. 15 + 3 + 5 are the only combinations for this answer and the question asks to sum possible values; therefore, the answer is 23. Answer Choice D.
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Re: If K is a positive integer such that the remainder when 17 is divided [#permalink]
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