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

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

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New post 10 Dec 2005, 16:19
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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.
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Re: If n is a positive integer that is less than 10, what is the  [#permalink]

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New post 19 Jan 2015, 12:55
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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.)

Here, knowing your basic fraction-to-decimal conversations would help you to answer this question really easily.

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

Final Answer:

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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New post 10 Dec 2005, 20:28
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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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Re: If n is a positive integer that is less than 10, what is the  [#permalink]

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New post 19 Jan 2015, 01:26
A

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

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New post 24 Mar 2016, 15:02
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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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Re: If n is a positive integer that is less than 10, what is the  [#permalink]

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New post 24 Mar 2016, 18:59
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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.

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

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New post 02 Jun 2018, 05:53
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Re: If n is a positive integer that is less than 10, what is the  [#permalink]

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New post 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.)

Here, knowing your basic fraction-to-decimal conversations would help you to answer this question really easily.

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

Final Answer:

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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Re: If n is a positive integer that is less than 10, what is the   [#permalink] 30 Nov 2019, 12:31
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