GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 26 Jan 2020, 16:32

### 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

# If n is a positive integer that is less than 10, what is the

Author Message
TAGS:

### Hide Tags

Manager
Joined: 10 Oct 2005
Posts: 103
Location: Hollywood
If n is a positive integer that is less than 10, what is the  [#permalink]

### Show Tags

10 Dec 2005, 16:19
1
1
18
00:00

Difficulty:

95% (hard)

Question Stats:

45% (01:47) correct 55% (01:57) wrong based on 346 sessions

### HideShow timer Statistics

If n is a positive integer that is less than 10, what is the value of n?

(1) n is the tenth digit in the decimal representation of 1/n.
(2) n is the hundredth digit in the decimal representation of 1/n.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15985
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If n is a positive integer that is less than 10, what is the  [#permalink]

### Show Tags

19 Jan 2015, 12:55
6
2
Hi All,

On Test Day, certain content knowledge is a must (math formulas, grammar rules, etc. ) while other knowledge can be really helpful (fraction-to-decimal conversations, perfect squares, "style" rules, knowing what the common wrong answers "look like", etc.)

The prompt tells us that N is a POSITIVE INTEGER less than 10. So N is 1 to 9, inclusive. We're asked for the value of N.

Fact 1: N is the tenth's digit of the decimal representation of 1/N

Since N can only be 9 different integers, I'm going to write them all down (in 1/N format) for reference:

1/1 = 1.00
1/2 = 0.50
1/3 = 0.333.....
1/4 = 0.25
1/5 = 0.20
1/6 = 0.166.....
1/7 = 0.142.....
1/8 = 0.125
1/9 = 0.111.....

So, what value of N matches the TENTH'S digit of it's matching fraction?

ONLY 1/3. N IS 3.
Fact 1 is SUFFICIENT

Fact 2: N is the hundredth's digit of the decimal representation of 1/N

Using the same information from above, we can now look for a matching HUNDREDTH's digit...

1/3 AND 1/6 fit this description. N can be 3 or 6.
Fact 2 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
##### General Discussion
VP
Joined: 24 Sep 2005
Posts: 1281
Re: If n is a positive integer that is less than 10, what is the  [#permalink]

### Show Tags

10 Dec 2005, 20:28
1
1
1. ----> 1/N= 0.Nabcd.... = N.abcd/10 ---> N*N.abcd... =10
----> N<= 3 coz if N>=4 --> N^2>10 . Since the statement says "tenth digit of 1/N" --> we eliminate N=1 ...check N=1,2 , we get N=3 is correct --->suff
2. N=3 --> 1/N= 0.33333... , this N=3 is ok
N=6 ----> 1/N= (1/3)/2= (0.3333....)/2= 0.1666666...... --> N=6 is also ok
---->insuff
Intern
Joined: 25 Mar 2014
Posts: 6
If n is a positive integer that is less than 10, what is the  [#permalink]

### Show Tags

24 Mar 2016, 15:02
1
EMPOWERgmatRichC wrote:
So, what value of N matches the TENTH'S digit of it's matching fraction?

The prompt says tenth and hundredth, not tenth's and hundredth's. Therefore I believe this is a faulty question, as we don't know whether to start counting the digits from the one's place or the tenth's place. Regardless, both 3 and 6 satisfy (1) and (2), therefore I believe the answer should be E.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15985
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If n is a positive integer that is less than 10, what is the  [#permalink]

### Show Tags

24 Mar 2016, 18:59
1
Hi mcolbert,

You bring up an interesting point; however, since the original post is over 10 years old and the GMAT is consistent in the types of language it uses and the concepts that are tested, it's likely that the original poster simply mis-typed the prompt. Considering the correct answer that is given, it's far more likely to be a couple of typos than a faulty question. If the Facts had stated...

"n is the tenth digit to the right of the decimal..."
"n is the hundredth digit to the right of the decimal...."

...then I'd agree with your interpretation.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Intern
Joined: 26 Mar 2013
Posts: 12
Location: India
Concentration: Finance, Strategy
Schools: Booth PT '18 (S)
Re: If n is a positive integer that is less than 10, what is the  [#permalink]

### Show Tags

19 Jan 2015, 01:26
A

Stat 1: only 3 works (chk it...)
=> suff
Stat 2: 3 and 6 both work
=> not suff
Intern
Joined: 11 Jul 2017
Posts: 9
Re: If n is a positive integer that is less than 10, what is the  [#permalink]

### Show Tags

02 Jun 2018, 05:47
For both statements I got n=3 and 6. I think the answer should be E.
Math Expert
Joined: 02 Sep 2009
Posts: 60646
Re: If n is a positive integer that is less than 10, what is the  [#permalink]

### Show Tags

02 Jun 2018, 05:53
PrabhaMithila wrote:
For both statements I got n=3 and 6. I think the answer should be E.

The tenths digit of 1/6 = 0.16666.... is 1, so n cannot be 6.
_________________
Intern
Joined: 29 Apr 2018
Posts: 13
Re: If n is a positive integer that is less than 10, what is the  [#permalink]

### Show Tags

21 Jun 2018, 10:27
EMPOWERgmatRichC wrote:
Hi All,

On Test Day, certain content knowledge is a must (math formulas, grammar rules, etc. ) while other knowledge can be really helpful (fraction-to-decimal conversations, perfect squares, "style" rules, knowing what the common wrong answers "look like", etc.)

The prompt tells us that N is a POSITIVE INTEGER less than 10. So N is 1 to 9, inclusive. We're asked for the value of N.

Fact 1: N is the tenth's digit of the decimal representation of 1/N

Since N can only be 9 different integers, I'm going to write them all down (in 1/N format) for reference:

1/1 = 1.00
1/2 = 0.50
1/3 = 0.333.....
1/4 = 0.25
1/5 = 0.20
1/6 = 0.166.....
1/7 = 0.142.....
1/8 = 0.125
1/9 = 0.111.....

So, what value of N matches the TENTH'S digit of it's matching fraction?

ONLY 1/3. N IS 3.
Fact 1 is SUFFICIENT

Fact 2: N is the hundredth's digit of the decimal representation of 1/N

Using the same information from above, we can now look for a matching HUNDREDTH's digit...

1/3 AND 1/6 fit this description. N can be 3 or 6.
Fact 2 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich

What do you mean by style rule

Posted from my mobile device
Non-Human User
Joined: 09 Sep 2013
Posts: 14013
Re: If n is a positive integer that is less than 10, what is the  [#permalink]

### Show Tags

30 Nov 2019, 12:31
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 n is a positive integer that is less than 10, what is the   [#permalink] 30 Nov 2019, 12:31
Display posts from previous: Sort by