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

Question

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.

EMPOWERgmatRichC · Accepted Answer

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:  A

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

laxieqv · Answer

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

baadshah · Answer

A

Stat 1: only 3 works (chk it...)
=> suff
Stat 2: 3 and 6 both work
=> not suff

mcolbert · Answer

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.

EMPOWERgmatRichC · Answer

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

PrabhaMithila · Answer

For both statements I got n=3 and 6. I think the answer should be E.

Bunuel · Answer

The tenths digit of 1/6 = 0. 1 6666.... is 1, so n cannot be 6.

Jammy88 · Answer

I enjoyed this question and I’m glad I got it right

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

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