GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Oct 2019, 18:29 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 S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Manager  Joined: 25 Dec 2011
Posts: 51
GMAT Date: 05-31-2012
If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

6
26 00:00

Difficulty:   45% (medium)

Question Stats: 63% (01:39) correct 37% (01:26) wrong based on 923 sessions

HideShow timer Statistics

If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.

I think with statement 2 - if P is 3 then all the terms in the sequence are divisible by P
So my answer is B

Originally posted by morya003 on 19 Feb 2012, 09:49.
Last edited by Bunuel on 21 Jun 2014, 04:05, edited 1 time in total.
Edited the question
Math Expert V
Joined: 02 Sep 2009
Posts: 58402
If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

7
1
morya003 wrote:
If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.

I think with statement 2 - if P is 3 then all the terms in the sequence are divisible by P
So my answer is B

No, B is not correct. It's straight E: if p=3 then every term in S is divisible by p but if p=11 then some terms in S are divisible by p (for example 99 and 9999) and some are not (for example 9 and 999). Not sufficient.

hope it's clear.
_________________
General Discussion
Manager  B
Status: May The Force Be With Me (D-DAY 15 May 2012)
Joined: 06 Jan 2012
Posts: 198
Location: India
Concentration: General Management, Entrepreneurship
Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

1
+1 E

Question tends to make you just go for 3 & you choose C but as Bunuel pointed out if you use 11 the assumption fails
_________________
Giving +1 kudos is a better way of saying 'Thank You'.
Director  Joined: 29 Nov 2012
Posts: 697
Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

what would be the equations for each statement?
Math Expert V
Joined: 02 Sep 2009
Posts: 58402
Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

fozzzy wrote:
what would be the equations for each statement?

What equations are you talking about?
_________________
Director  Joined: 29 Nov 2012
Posts: 697
Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

If you were to test examples to satisfy the equations what would they be examples for each statement.
Math Expert V
Joined: 02 Sep 2009
Posts: 58402
Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

fozzzy wrote:
If you were to test examples to satisfy the equations what would they be examples for each statement.

Since the answer is E, then the examples given in my post to show that the two statements taken together are not sufficient to answer the question, would also serve to discard each statement.
_________________
Intern  Joined: 22 Jun 2013
Posts: 35
Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

Bunuel wrote:
morya003 wrote:
If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.

No, B is not correct. It's straight E: if p=3 then every term in S is divisible by p but if p=11 then some terms in S are divisible by p (for example 99 and 9999) and some are not (for example 9 and 999). Not sufficient.

hope it's clear.

Hello Bunuel

I have a doubt here.
Since we know after combining the 2 statements that the Prime number will NOT be 3 but any other Prime number that divides at least 1 number in the sequence.
So now we know for SURE that EVERY TERM IS NOT Divisible by a particular Prime number( Which the Questions asks). 11 will also not divide all terms but few only.

SO should the Answer not be "C" ?

Thankyou
Math Expert V
Joined: 02 Sep 2009
Posts: 58402
Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

niyantg wrote:
Bunuel wrote:
morya003 wrote:
If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.

No, B is not correct. It's straight E: if p=3 then every term in S is divisible by p but if p=11 then some terms in S are divisible by p (for example 99 and 9999) and some are not (for example 9 and 999). Not sufficient.

hope it's clear.

Hello Bunuel

I have a doubt here.
Since we know after combining the 2 statements that the Prime number will NOT be 3 but any other Prime number that divides at least 1 number in the sequence.
So now we know for SURE that EVERY TERM IS NOT Divisible by a particular Prime number( Which the Questions asks). 11 will also not divide all terms but few only.

SO should the Answer not be "C" ?

Thankyou

______________

Why cannot p be 3?
_________________
Senior Manager  Joined: 06 Aug 2011
Posts: 318
Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

1
niyantg wrote:
Bunuel wrote:
morya003 wrote:
If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.

No, B is not correct. It's straight E: if p=3 then every term in S is divisible by p but if p=11 then some terms in S are divisible by p (for example 99 and 9999) and some are not (for example 9 and 999). Not sufficient.

hope it's clear.

Hello Bunuel

I have a doubt here.
Since we know after combining the 2 statements that the Prime number will NOT be 3 but any other Prime number that divides at least 1 number in the sequence.
So now we know for SURE that EVERY TERM IS NOT Divisible by a particular Prime number( Which the Questions asks). 11 will also not divide all terms but few only.

SO should the Answer not be "C" ?

Thankyou

Actually question is asking , is every term in S divisible by the prime number p?

S1: p is greater than 2..Means wat? it means p cud b 3 ,5,7,11. If we say 3 then ans will be yes, Bt if we say 5 then we say no. Thats why Insufficient.

S2: at least one term is divisible by p. so ans wud b 3 or 11. 3 wud be divisible by every term of S, Bt 11 cud not be divisible by first term 9, and 999 etc.

Take both statement togather. still we cant give the ans, because p cud b 3 or 11.
_________________
Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !
Senior Manager  Status: Stay focused...
Joined: 20 Apr 2014
Posts: 433
Location: United States (MI)
Concentration: Finance, Strategy
Schools: Ross School of Business - Class of 2017
GMAT 1: 760 Q50 V41 GPA: 3.2
WE: Project Management (Other)
Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

1
morya003 wrote:
If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.

I think with statement 2 - if P is 3 then all the terms in the sequence are divisible by P
So my answer is B

Hi All,
Can any of the moderators amend this post to create a gap between the question and the query posted by morya003?
_________________
Raves, rants and war stories of First Year MBA Students

Received an offer? Congrats! You might want to 'Negotiate the Offer'.

I'm happy to help if you wanna know about Ross & UMich, but please do not come to me with your GMAT issues or questions. And please add a bit of humor to your questions or you'll bore me to death.
Math Expert V
Joined: 02 Sep 2009
Posts: 58402
Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

neo656 wrote:
morya003 wrote:
If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.

I think with statement 2 - if P is 3 then all the terms in the sequence are divisible by P
So my answer is B

Hi All,
Can any of the moderators amend this post to create a gap between the question and the query posted by morya003?

______________
Done. Thank you.
_________________
Manager  B
Joined: 13 Feb 2011
Posts: 79
Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

The only prime that divides all terms in the sequence: 9, 99, 999,.. is 3. So the question is essentially asking: is p=3?
(1) p can be any prime number greater than 2, hence not sufficient.
(2) p can be 3 or 11, hence not sufficient.
Both taken together, again insufficient to identify p as 3.

boomtangboy summarizes aptly that the question tends to prey on the mistake that the test taker will consider 3 as the only possible value from statement (2).
Current Student D
Joined: 12 Aug 2015
Posts: 2568
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

Here we can choose 11 and 3 as test cases and we will get E answer fairly easily
_________________
Director  B
Joined: 04 Jun 2016
Posts: 556
GMAT 1: 750 Q49 V43 Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

1
morya003 wrote:
If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.

From question stem we know S={9,99,999,9999,99999,999999...................99999999999999....}
We can easily eye ball that this is divisible by either 3 or 11 or a combination of their multiples.

(1) p is greater than 2.
Insufficient :- p can be 3 or 5 or 7 or 11 or 13
In some cases p divides ; in some cases it don't

(2) At least one term in sequence S is divisible by p.
Insufficient again
starting from the second term (99) all terms are divisible by either 3 and 11
But the first team 9 is divisible only by 3 and not by 11

So we cannot for sure whether the prime p that the question stem is referring to is 3 or 11.

BOTH STATEMENT INSUFFICIENT
_________________
Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.
Director  D
Joined: 13 Mar 2017
Posts: 728
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

morya003 wrote:
If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.

I think with statement 2 - if P is 3 then all the terms in the sequence are divisible by P
So my answer is B

Question is tricky and seems very tough in the first instance. Though I understood that every term is not divisible by p, but I marked C option due to my understanding that every term is not divisible by p (I did a mistake here... Every term is divisible by 3 and not by 11 as correctly suggested by @bunuel). So, the reading and understanding the language of the question in such problems is very important.

So, finally the solution goes like this.

Given : infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1
DS: is S1, S2, S3, ......, SK divisible by the prime number p.

Statement 1 : P>2. So, p can be 3,5,7,11,.....
We can clearly see that every term is divisible by 3 but not by 5,7,11.....
NOT SUFFICIENT

Statement 2 : At least one term in sequence S is divisible by p. So, we can see that 9 is divisble by 3 and 99 is divisible by 11.
Here again every term is divisible by 3
But every term is not divisible by 11.
NOT SUFFICIENT

Combined : p>2 and At least one term in sequence S is divisible by p. So, p can be 3 or 11 or...
Its clear that every term is divisible by 3, but every term is not divisible by 11.
NOT SUFFICIENT

_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Non-Human User Joined: 09 Sep 2013
Posts: 13246
Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1  [#permalink]

Show Tags

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.
_________________ Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1   [#permalink] 05 Oct 2018, 15:27
Display posts from previous: Sort by

If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  