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

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Difficulty:   95% (hard)

Question Stats: 45% (01:47) correct 55% (01:57) wrong based on 335 sessions

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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 V
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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]

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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
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VP  Joined: 24 Sep 2005
Posts: 1313
Re: If n is a positive integer that is less than 10, what is the  [#permalink]

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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
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Concentration: Finance, Strategy
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Re: If n is a positive integer that is less than 10, what is the  [#permalink]

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A

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

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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.
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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]

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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
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Re: If n is a positive integer that is less than 10, what is the  [#permalink]

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For both statements I got n=3 and 6. I think the answer should be E.
Math Expert V
Joined: 02 Sep 2009
Posts: 59588
Re: If n is a positive integer that is less than 10, what is the  [#permalink]

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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.
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Re: If n is a positive integer that is less than 10, what is the  [#permalink]

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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

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Re: If n is a positive integer that is less than 10, what is the  [#permalink]

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