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If x is an integer from 1 to 10. x=?

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If x is an integer from 1 to 10. x=? [#permalink] New post 16 Feb 2013, 16:55
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Question Stats:

47% (02:17) correct 53% (01:01) wrong based on 70 sessions
x is an integer from 1 to 10. x=?

(1) The tenth digit of 1/x is x
(2) The hundredth digit of 1/x is x

[Reveal] Spoiler:
Hi guys I'm running through a 700-800 level download I got from the gmat club downloads section and I am wondering about this question. I searched the forum and didn't see anything posted about this specific question so I hope I am not reposting.

#46 from Gmat Special Questions called "125 Awesome Quant questions.pdf"

* I immediately think, "Ok this is an easy 700 level question, it must be a repeating decimal and the only #'s that don't repeat have 2's and 5's as primes! It must be either 3,6,7,9 right?" Then I think about the length of 1/7 and it's an odd length like 6 numbers so I doubt that's it, it's probably like 3,6,or 9 since you can guarantee .3333 or .16666 or .1111. *

neither option narrows the answer any farther to me so I guessed E

Looked in the answer key and they have [spoiler=ANSWER]A


Can anyone explain where I went wrong?[/spoiler]
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Jul 2014, 08:59, edited 2 times in total.
Edited the question.
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Re: If x is an integer from 1 to 10. x=? [#permalink] New post 16 Feb 2013, 22:44
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Just to clarify the question, it is as follows:

If X is an integer from 1 to X, then X = ?

(1) The tenth's digit of 1/X is X

(2) The hundredth's digit of 1/X is X


To answer this question, we must refresh our memories on what the tenth's and hundredth's digits are. For an integer of the form A.BC (e.g. 2.34, 4.67 etc), the tenth's digit is B and the hundredth's digit is C.

Consider statement (1) first. For which integers (1 to 10) is the tenth's digit the same as the integer itself? This is true only for the integer 3 (1/3 = 0.333333...). Therefore X can only be 3. Sufficient.

Consider statement (2) next. For which integers (1 to 10) is the hundredth's digit the same as the integer itself? This is true for 3 (1/3 = 0.333333...) as well as for 6(1/6=0.16666....). We can't say which of the two it will be. Insufficient.

The answer is therefore A.
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Re: If x is an integer from 1 to 10. x=? [#permalink] New post 17 Feb 2013, 08:38
GyanOne Thanks!!

When I was reading the question I was miffed on if they meant the tenth's unit digit or the TENTH unit digit which to me would be something totally different. After reading your response the answer is so clear it's probably makes the question too easy! lol I'm not even sure why I thought of 1/9 I guess I was so focused on the fact that it is repeating like 1/3 I forgot that the number that is repeating is not the same as X.

Thanks again.
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Re: If x is an integer from 1 to 10. x=? [#permalink] New post 17 Jul 2014, 08:24
Hello from the GMAT Club BumpBot!

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Re: If x is an integer from 1 to 10. x=?   [#permalink] 17 Jul 2014, 08:24
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