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[dunkin77]

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.

[moneyman]

The answer is A..

(1) says that the tenths digit in 1/n is n..This is possible only when n is 3.

(2) says that the hundreths digit in 1/n is n..This is possible for two values n=3 and n=6.

Therefore (1) is sufficient and so the answer is A.

[moneyman]

The answer is A..

(1) says that the tenths digit in 1/n is n..This is possible only when n is 3.

(2) says that the hundreths digit in 1/n is n..This is possible for two values n=3 and n=6.

Therefore (1) is sufficient and so the answer is A.

[jrbrown2]

With statement 1 alone, wouldn't n=3 and n=6 be possible?

1/3 = 0.3333333333....
1/6 = 0.1666666666....

Although the first decimal digit in 1/6 is 1 the rest of the decimal digits are all 6's and thus, the 10th decimal digit would also be 6.

With statement 2 alone, it seems to me that nothing new has been said, so n=3 and n=6 are also possible.

I choose E.

If I'm wrong please explain why.

[drhomler]

I agree with E its imperative to test every number in those scenarios

[netneoaaa]

With statement 1 alone, wouldn't n=3 and n=6 be possible?

1/3 = 0.3333333333....
1/6 = 0.1666666666....

Although the first decimal digit in 1/6 is 1 the rest of the decimal digits are all 6's and thus, the 10th decimal digit would also be 6.

With statement 2 alone, it seems to me that nothing new has been said, so n=3 and n=6 are also possible.

I choose E.

If I'm wrong please explain why.

After decimal point, the first digit would be the tenth place and then hundredth place .1 is 1/10 and .02 is 2/100 so it is only 3 which satisfies the conditions. Hence I think the first reasoning is correct. Please tell me why I am wrong !!

[drhomler]

The way it is written it is saying the tenth digit literally the digit that is 1,2,3,4......10 from the decimal. Not "the tenth"

[gabriel]

With statement 1 alone, wouldn't n=3 and n=6 be possible?

1/3 = 0.3333333333....
1/6 = 0.1666666666....

Although the first decimal digit in 1/6 is 1 the rest of the decimal digits are all 6's and thus, the 10th decimal digit would also be 6.

With statement 2 alone, it seems to me that nothing new has been said, so n=3 and n=6 are also possible.

I choose E.

If I'm wrong please explain why.

hmm .. me going for A ..

btw .. care to explain the darkened part ... how would 6 be the 10th decimal digit

[discreet]

Dear All,

It's important to understand the concept of digits for decimal...

eg: decimals place values are represented by using terms such as tenth digit,hundredth digit etc.

eg: 123.456
1 is hundreds,2 is tens and 3 is units digit
4 is 10th,5 is 100th and 6 is thousandth digit...

In my opinion,analogously,The question here refers to the tenth digit,hundredth digit and not counting places literally after the decimal point!

n=3, 1/3= 0.33333...
Here the tenth digit means the digit next to the decimal point on the right hand side.
0 is the units digit,3 is the tenth(and not counting the tenth digit after decimal!)

So,the answer has to be A.The number,n is 3.

Second statement is not sufficient as its possible to have 2 values for n when the hundredth digit is equal to n (3,6).

any other views ?

[drhomler]

Discreet-
the way I learned this in school, which was a while ago, when referring to the digit two decimal places from the right we would call it the "tenths" digit. So in your expamle you have hundreds, tens, ones, tenths, hundreths, thousandths and therefore when the question is asking for the tenth digit it is asking for the digit literally 10 digits form the right of the decimal place.

I think this is a very subtle issue with english(I could be wrong) hopefully nothing on the test will be this ambiguous.

[discreet]

Yes,I agree,
Hundredth should be hundredths..I am assuming this for this question....I missed the "s"
Sometimes, we use tenth, hundredth etc. while rounding numbers.
Question is surely ambigous!

[discreet]

Discreet-
the way I learned this in school, which was a while ago, when referring to the digit two decimal places from the right we would call it the "tenths" digit. So in your expamle you have hundreds, tens, ones, tenths, hundreths, thousandths and therefore when the question is asking for the tenth digit it is asking for the digit literally 10 digits form the right of the decimal place.

I think this is a very subtle issue with english(I could be wrong) hopefully nothing on the test will be this ambiguous.

I wd like to correct u here...tenths place is not 2 places to the right of decimal...its always next to the decimal...May be I am not able to understand what you are saying.

Also,If you search the web,you can easily find many sites referring to the tenths place as tenth etc...while rounding off...but that has a different meaning...the conventional method is tenths,hundredths etc.

Regarding this question....if you say counting digits in the literal sense...How will you count the tenth digit,hundredth???

The question says

(1) n is the tenth digit in the decimal representation of 1/n.

eg: for 0.3333....will you start counting from 0 which is the units place (in all situations here) or will you start counting after the decimal(towards right)?In this case,the digit won't vary but the meaning varies - isn't it??
So,to conclude and to remove ambiguity,the author must be referring to the tenths,hundredths place? do you agree?This is the reason for my earlier explanation....

[devesh]

i agree with discreet

tenths digit will be just next to decimal.

so answer should be A

[jrbrown2]

After reading everyone's responses, I can't come to a definite conclusion now. This question is too ambiguous. Is the question referring to the digit ten places to the right of the decimal point or is it referring to the digit in the tenths column?

If it were referring to the digit ten places to the right of the decimal point then the answer would be E.
If it were referring to the digit in the tenths column then the answer would be A.

IMO I think that the question is referring to the digit ten places to the right of the decimal point. It says "tenth digit in the decimal representation". If it were referring to the digit in the tenths column (or tenths place) then it should refer it in that way.

[discreet]

jrbrown2 -don't worry...the question is indeed confusing...
Why I assumed it as tenths , hundredths is that the author may have chosen some other numbers instead of tenth , hundredth if he were to imply the literal meaning....why not 15th,50th etc and why tenth,hundredth...also,counting methods vary based on from where you wd start counting....from units place or from the decimal point...thats my explanation...

anyway,its better you ignore all such ambiguities and stick to basics...lets forget the exceptions