Last visit was: 19 Jul 2024, 04:36 It is currently 19 Jul 2024, 04:36
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# If K is a positive integer such that the remainder when 17 is divided

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94411
Own Kudos [?]: 642227 [6]
Given Kudos: 86282
CEO
Joined: 26 Feb 2016
Posts: 2865
Own Kudos [?]: 5324 [0]
Given Kudos: 47
Location: India
GPA: 3.12
examPAL Representative
Joined: 07 Dec 2017
Posts: 1048
Own Kudos [?]: 1799 [1]
Given Kudos: 26
Senior Manager
Joined: 21 Jan 2015
Posts: 422
Own Kudos [?]: 359 [0]
Given Kudos: 82
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28
GMAT 2: 690 Q49 V35
WE:Sales (Consumer Products)
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
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19172
Own Kudos [?]: 22673 [1]
Given Kudos: 286
Location: United States (CA)
Re: If K is a positive integer such that the remainder when 17 is divided [#permalink]
1
Bookmarks
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.

Intern
Joined: 05 Aug 2016
Posts: 13
Own Kudos [?]: 9 [1]
Given Kudos: 2
Location: United States
Concentration: General Management
GMAT 1: 730 Q50 V40
Re: If K is a positive integer such that the remainder when 17 is divided [#permalink]
1
Kudos
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.
Re: If K is a positive integer such that the remainder when 17 is divided [#permalink]
Moderator:
Math Expert
94411 posts