NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 03:07 It is currently 26 Apr 2024, 03:07
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 41 is a factor of positive integer y, which of the following MUST

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92929
Own Kudos [?]: 619101 [2]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
If 41 is a factor of positive integer y, which of the following MUST [#permalink] New post   02 Jul 2020, 01:48
2
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

52% (01:27) correct 48% (01:24) wrong based on 47 sessions
Hide Show timer Statistics
If 41 is a factor of positive integer y, which of the following MUST be divisible by y[?

I. \(82y+82\)
II. \(41y\)
III. \(41+y\)

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
ShowHide Answer
Official Answer
B
User avatar
L
nick1816
Retired Moderator
Joined: 19 Oct 2018
Posts: 1878
Own Kudos [?]: 6296 [0]
Given Kudos: 704
Location: India
Send PM
Re: If 41 is a factor of positive integer y, which of the following MUST [#permalink] New post   02 Jul 2020, 04:44
1. 82(y+1)

y and y+1 are coprimes and y is a factor of 41. Hence, y+1 can never be divisible by y.

hence if y=41 or 82, only in that case 82(y+1) divisible by y

2. 41*y is definitely divisible by y.

3. 41+y

suppose y= 41k

41+y = 41(k+1)

k+1 is divisible by k, only when k=1

B




Bunuel wrote:
If 41 is a factor of positive integer y, which of the following MUST be divisible by y[?

I. \(82y+82\)
II. \(41y\)
III. \(41+y\)

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
User avatar
S
dimri10
Manager
Manager
Joined: 16 May 2011
Posts: 240
Own Kudos [?]: 308 [0]
Given Kudos: 64
Concentration: Finance, Real Estate
GMAT Date: 12-27-2011
WE:Law (Law)
Send PM
GMAT ToolKit User
Re: If 41 is a factor of positive integer y, which of the following MUST [#permalink] New post   02 Jul 2020, 05:11
Y is in the form of 41k .
1. 82(41k+1) will not necessarily be divisible by 41k
2. 41*41k will always divide 41k
3. 41(1+k) will not necessarily be divisible by 41k

Posted from my mobile device
User avatar
G
raunakd11
Manager
Manager
Joined: 30 Jan 2020
Posts: 143
Own Kudos [?]: 144 [0]
Given Kudos: 143
Location: India
Schools: ISB YLP 2020 NUS '23
GPA: 4
Send PM
Re: If 41 is a factor of positive integer y, which of the following MUST [#permalink] New post   02 Jul 2020, 05:31
Bunuel wrote:
If 41 is a factor of positive integer y, which of the following MUST be divisible by y[?

I. \(82y+82\)
II. \(41y\)
III. \(41+y\)

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III


Hello!
I) has 82y+ 82, which is nothing but 82(y+1),
There is no assurance that the number can be divisible by y. There can be multiple solutions.

II) is clearly evident, since, 41 x 41 or any other number related should be divisible.

III) Adding a number 41k or any other cannot guarantee that it is divisible by y.

Hence, only II) suffices the criteria.

IMO, Option B goes up.

Thank you!

Regards,
Raunak Damle :thumbsup:
GMAT Club Bot
gmatclubot
Re: If 41 is a factor of positive integer y, which of the following MUST [#permalink]
02 Jul 2020, 05:31
Moderators:
Bunuel
Math Expert
92929 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