NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 10:51 It is currently 23 Apr 2024, 10:51
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 S is a set of integers and 5 is in S, is every multiple

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
tingjojo
Intern
Intern
Joined: 25 May 2010
Posts: 36
Own Kudos [?]: 32 [9]
Given Kudos: 22
Location: Taiwan
Concentration: Operations, International Business
Schools: Booth PT '18 (D) Anderson '18 (A) Sloan '18 (D) CBS '18 (D) Ross '18 (A) Kellogg '18 (M)
GMAT 1: 720 Q50 V38
GPA: 3.59
WE:Supply Chain Management (Manufacturing)
Send PM
If S is a set of integers and 5 is in S, is every multiple [#permalink] New post   17 May 2011, 06:59
2
Kudos
7
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

48% (01:19) correct 52% (01:18) wrong based on 198 sessions
Hide Show timer Statistics
If S is a set of integers and 5 is in S, is every multiple of 5 in S?

(1) If x is in S, then x+5 is in S
(2) If x is in S, then x-5 is in S
ShowHide Answer
Official Answer
C
User avatar
agdimple333
Manager
Manager
Joined: 24 Mar 2011
Posts: 229
Own Kudos [?]: 724 [1]
Given Kudos: 20
Location: Texas
Send PM
Re: If S is a set of integers and 5 is in S, is every multiple [#permalink] New post   17 May 2011, 17:12
1
Kudos
St - 1 ==> if X is in S, then X + 5 is in S, meaning X is in S then X + 5 is in S, if X+5 is in S then (X+5)+5 is in S and so on.. So if 5 is in S then 10 is in S, if 10 is in S, then 15 is in S.. and so on.
But see that questions ask you every multiple of 5 means even -ve.
So st 1 is not sufficient.

St - 2==> Same story as above... but other way. .. 0, -5, -10... are in S.

If you combine I and II than ....-10, -5, 0, 5, 10,... are in S i.e. every multiple of 5 is in S.

So C.

I came across this yesterday in knewton (i think) and found it little weird. :(
User avatar
amit2k9
Director
Director
Joined: 08 May 2009
Status:There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Posts: 552
Own Kudos [?]: 588 [0]
Given Kudos: 10
Send PM
Re: If S is a set of integers and 5 is in S, is every multiple [#permalink] New post   18 May 2011, 02:55
a 0 is a multiple of 5 too. If first element is 5 means 5,10,15. Hence not sufficient.

b takes into account negative elements. Not sufficient.

a+b considers -5k<= multiple <=5k

hence C.
User avatar
hussi9
Manager
Manager
Joined: 28 Mar 2010
Status:GMAT in 4 weeks
Posts: 128
Own Kudos [?]: 453 [0]
Given Kudos: 25
GPA: 3.89
Send PM
Re: If S is a set of integers and 5 is in S, is every multiple [#permalink] New post   18 May 2011, 10:48
S=[.....5....]

Statment 1:
5+5,
=>5+5+5 and so on for all =ve multiples of 5
S=[5,10,15,.........] Not all multiples of 5 but have no clue of other components of S so insuff

stament 2:
5-5
S=[....10,-5,0,5] Not all multiples of 5 but have no clue of other components of S so insuff


Combining both S= [10,-5,0,5,10,15]

==> AND is C
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92875
Own Kudos [?]: 618555 [3]
Given Kudos: 81561
Send PM
CAT Tests Forum Quiz Mode
Re: If S is a set of integers and 5 is in S, is every multiple [#permalink] New post   10 Jun 2013, 05:58
3
Kudos
Expert Reply
If S is a set of integers and 5 is in S, is every multiple of 5 in S?

(1) If x is in S, then x+5 is in S. Since 5 is in the set, then 5+5=10, 10+5=15, 15+5=20, ... are also in the set. So, every multiple of 5 more than or equal to 5 are in the set. Though we cannot be sure about the multiples of 5 less than 5 (0, -5, ...). Not sufficient.

(2) If x is in S, then x-5 is in S. The same here: 5, 0, -5, -10, are also in the set. We don't know whether the multiples of 5 which are greater thatn 5 are also in the set. Not sufficient.

(1)+(2) All multiples of 5 are in the set. Sufficient.

Answer: C.

Similar questions to practice:
if-p-is-a-set-of-integers-and-3-is-in-p-is-every-positive-96630.html
k-is-a-set-of-integers-such-that-if-the-integer-r-is-in-k-103005.html
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.html
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-x-136580.html
a-set-of-numbers-has-the-property-that-for-any-number-t-in-15554.html
a-set-of-numbers-has-the-property-that-for-any-number-t-in-t-98829.html

Hope it helps.
avatar
aankittcoolest
Intern
Intern
Joined: 23 Apr 2013
Posts: 2
Own Kudos [?]: 2 [1]
Given Kudos: 27
Concentration: Finance, Entrepreneurship
GMAT Date: 09-21-2013
GPA: 3.94
Send PM
GMAT ToolKit User
Re: If S is a set of integers and 5 is in S, is every multiple [#permalink] New post   18 Jun 2013, 22:49
1
Kudos
Hi ..one question..
Why can't we assume x to be any other integer such as 1,2,3,4,6...
In that case both the condtions will not suffice even after combination..
help plz..
Thanks
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92875
Own Kudos [?]: 618555 [0]
Given Kudos: 81561
Send PM
CAT Tests Forum Quiz Mode
Re: If S is a set of integers and 5 is in S, is every multiple [#permalink] New post   19 Jun 2013, 03:19
Expert Reply
aankittcoolest wrote:
Hi ..one question..
Why can't we assume x to be any other integer such as 1,2,3,4,6...
In that case both the condtions will not suffice even after combination..
help plz..
Thanks


Please check the links provided in the post above. Your doubt is answered in that threads many times.

Consider (1): we are told that if some integer (x) is in the set then that integer plus 5 is also in S. This is a property of set S.

We know that 5 is in S, which means that integers 10, 15, 20, ... are also in S. But we cannot assume that there are any other integers in the set apart from these.
User avatar
kusena
Intern
Intern
Joined: 14 Aug 2013
Posts: 23
Own Kudos [?]: 154 [0]
Given Kudos: 4
Location: United States
Concentration: Finance, Strategy
GMAT Date: 10-31-2013
GPA: 3.2
WE:Consulting (Consumer Electronics)
Send PM
GMAT ToolKit User
Re: If S is a set of integers and 5 is in S, is every multiple [#permalink] New post   08 Sep 2013, 01:22
fozzzy wrote:
If S is a set of integers 5 is in S, is every multiple of 5 in S?

1) If X is in s, then x+5 is in S.
2) if X is in S, then X-5 is in S.


Set with all multiples of 5 shld contain {....-15,-10,-5,0,5,10,15....}

From Stmt 1) 5,10,15,.... will be present in Set S, 1 Alone not sufficient
From Stmt 2) 0,-5,-10,-15....will be present in Set S, 2 Alone not sufficient
Both together can ans the question,,Hence C

Hope its clear
avatar
thapliya
Intern
Intern
Joined: 23 Apr 2016
Posts: 15
Own Kudos [?]: 17 [0]
Given Kudos: 39
Location: Finland
Concentration: General Management, International Business
GPA: 3.65
Send PM
Re: If S is a set of integers and 5 is in S, is every multiple [#permalink] New post   18 Oct 2016, 12:39
So isn't it that x can take any value,
From the first statement the constraint is 5 should be in Set and if x is in the set then x+5 should be in the set:
So x = 0 implies that 0,5,10 ... are in the set
x= -5 implies that -5, 0, 5, 10 ... are in the set
x = -10 implies that -10, -5, 0, 5 ... are in the set
x = -100 implies that -100, -95, -90, -85 ... are in the set
and I think the same logic can be extended till -infinity ... So statement 1 is sufficient.

Same logic goes for statement 2 as well...
User avatar
L
IanStewart
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4128
Own Kudos [?]: 9238 [0]
Given Kudos: 91
 Q51  V47
Send PM
Re: If S is a set of integers and 5 is in S, is every multiple [#permalink] New post   22 Jun 2021, 07:40
Expert Reply
This is not a good practice question. The GMAT doesn't test 'negative multiples' of integers, so you'd never see something like this on the real test. GMAT divisibility questions are almost always explicitly restricted to positive integers, and if they're not, you'll get the same answer whether you think about zero and negatives or don't.

A lot of prep companies design questions like this, trying to be 'tricky', but practice questions that sensitize test takers to 'traps' the GMAT would never use are doing test takers a disservice. Any time a test taker spends, during a test, thinking about the 'trap' this question illustrates is time wasted.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32627
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: If S is a set of integers and 5 is in S, is every multiple [#permalink] New post   23 May 2022, 08:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32627
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: If S is a set of integers and 5 is in S, is every multiple [#permalink] New post   12 Sep 2022, 17:07
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: If S is a set of integers and 5 is in S, is every multiple [#permalink]
12 Sep 2022, 17:07
Moderator:
Bunuel
Math Expert
92875 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