NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 23:53 It is currently 24 Apr 2024, 23:53
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If (x # y) represents the remainder that results when the po

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
jokkemauritzen
Intern
Intern
Joined: 18 Oct 2013
Posts: 1
Own Kudos [?]: 54 [54]
Given Kudos: 0
Send PM
If (x # y) represents the remainder that results when the po [#permalink] New post   Updated on: 29 Mar 2014, 14:55
54
Bookmarks
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

73% (01:35) correct 27% (01:48) wrong based on 898 sessions
Hide Show timer Statistics
If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1?

A. 8
B. 9
C. 16
D. 23
E. 24

Is there a quick and easy way to find divisors to an integer/expression when we are looking for a distinct remainders?

correct answer is
Show Spoiler
23
, I found the answer by calculating and doing several divisions, is there an easier way?
ShowHide Answer
Official Answer
D

Originally posted by jokkemauritzen on 29 Mar 2014, 14:23.
Last edited by Bunuel on 29 Mar 2014, 14:55, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92901
Own Kudos [?]: 618865 [16]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: If (x # y) represents the remainder that results when the po [#permalink] New post   29 Mar 2014, 15:02
6
Kudos
10
Bookmarks
Expert Reply
jokkemauritzen wrote:
If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1?

A. 8
B. 9
C. 16
D. 23
E. 24

Is there a quick and easy way to find divisors to an integer/expression when we are looking for a distinct remainders?

correct answer is
Show Spoiler
23
, I found the answer by calculating and doing several divisions, is there an easier way?


(x # y) represents the remainder that results when the positive integer x is divided by the positive integer y.

Thus (16 # y) = 1 implies that \(16=yq+1\) --> \(15=yq\) --> y is a factor of 15. The factors of 15 are 1, 3, 5, and 15. Now, y cannot be 1, since 16 divided by 1 yields the remainder of 0 not 1.

Therefore the sum of all the possible values of y is 3+5+15=23.

Answer: D.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 3, and 8. Thank you.
General Discussion
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6821
Own Kudos [?]: 29918 [4]
Given Kudos: 799
Location: Canada
Send PM
If (x # y) represents the remainder that results when the po [#permalink] New post   Updated on: 17 May 2021, 07:16
3
Kudos
1
Bookmarks
Expert Reply
Top Contributor
jokkemauritzen wrote:
If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1?

A. 8
B. 9
C. 16
D. 23
E. 24


If y > 16, (16 # y) = 16, so we need only check the values from 1 to 15
Also, we need not check the FACTORS of 16, since they will all yield a remainder of 0
We're left with:
(16 # 3) = 1 KEEP!
(16 # 5) = 1 KEEP
(16 # 7) = 2
(16 # 9) = 7
(16 # 10) = 6
(16 # 11) = 5
(16 # 12) = 4
(16 # 13) = 3
(16 # 14) = 2
(16 # 15) = 1 KEEP

3 + 5 + 15 = 23

Answer: D

RELATED VIDEO

Originally posted by BrentGMATPrepNow on 19 Apr 2019, 06:07.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:16, edited 1 time in total.
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18756
Own Kudos [?]: 22049 [2]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: If (x # y) represents the remainder that results when the po [#permalink] New post   26 Apr 2019, 15:39
2
Bookmarks
Expert Reply
jokkemauritzen wrote:
If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1?

A. 8
B. 9
C. 16
D. 23
E. 24


16/15 has a remainder of 1.

16/5 has a remainder of 1.

16/3 has a remainder of 1.

So the sum of all possible values of y is 15 + 5 + 3 = 23.

Alternate Solution:

We are looking for all values of y such that 16 divided by y produces a remainder of 1. Then, 16 - 1 = 15 must be divisible by y. Excluding y = 1 (which produces a remainder of 0); the possibilities for y are 15, 5 and 3. Thus, the sum of all possible values of y is 15 + 5 + 3 = 23.

Answer: D
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5343
Own Kudos [?]: 3964 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: If (x # y) represents the remainder that results when the po [#permalink] New post   13 Oct 2021, 11:05
Asked: If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1?

16 # 3 = 1
16 # 5 = 1
16 # 15 = 1

The sum of all the possible values of y such that {(16 # y) = 1} = 3 + 5 + 15 = 23

IMO D
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14819
Own Kudos [?]: 64906 [1]
Given Kudos: 426
Location: Pune, India
Send PM
Re: If (x # y) represents the remainder that results when the po [#permalink] New post   25 Oct 2023, 23:21
1
Kudos
Expert Reply
jokkemauritzen wrote:
If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1?

A. 8
B. 9
C. 16
D. 23
E. 24

Is there a quick and easy way to find divisors to an integer/expression when we are looking for a distinct remainders?

correct answer is
Show Spoiler
23
, I found the answer by calculating and doing several divisions, is there an easier way?


First check this video that discusses Division and Remainders basics: https://youtu.be/A5abKfUBFSc

Now we just visualise: 16 divided by y leaves remainder 1. It means that 15 balls were evenly distributed into groups and 1 was leftover. Then we are looking for factors of 15.
We could have had groups of 3 balls each or 5 balls each or 15 balls each.
Hence, y could be 3 or 5 or 15 - in each case the remainder is 1.

Sum of 3 + 5 + 15 = 23

Answer (D)
GMAT Club Bot
gmatclubot
Re: If (x # y) represents the remainder that results when the po [#permalink]
25 Oct 2023, 23:21
Moderators:
Bunuel
Math Expert
92900 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions