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# If n is an integer, what is the units digit of x?

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Joined: 30 Jun 2012
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If n is an integer, what is the units digit of x?  [#permalink]

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30 Jun 2012, 08:00
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Difficulty:

45% (medium)

Question Stats:

65% (01:30) correct 35% (01:26) wrong based on 439 sessions

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If n is an integer, what is the units digit of x?

(1) x = (25^2)/(10^n)

(2) n^2 = 1
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Joined: 02 Sep 2009
Posts: 49860
Re: If n is an integer, what is the units digit of x?  [#permalink]

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30 Jun 2012, 08:07
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If n is an integer, what is the units digit of x?

(1) x = (25^2)/(10^n). If $$n=0$$ then $$x=\frac{25^2}{10^0}=625$$ and the units digit of $$x$$ is 5 but if $$n=-1$$ then $$x=\frac{25^2}{10^{-1}}=6250$$ and the units digit of $$x$$ is 0. Not sufficient.

(2) n^2 = 1 --> $$n=1$$ or $$n=-1$$. Not sufficient as no info about $$x$$.

(1)+(2) If $$n=1$$ then $$x=\frac{25^2}{10^1}=62.5$$ and the units digit of $$x$$ is 2 but if $$n=-1$$ then $$x=\frac{25^2}{10^{-1}}=6250$$ and the units digit of $$x$$ is 0. Not sufficient.

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Re: If n is an integer, what is the units digit of x?  [#permalink]

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24 Jun 2013, 03:17
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: If n is an integer, what is the units digit of x?  [#permalink]

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24 Jun 2013, 09:31
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Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=36
All PS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=57

Question: Its a value question, we need to know the units place of x, so irrespective of the no if we can get the same units place always, this should be fine.

(1) x = (25^2)/(10^n)

n is an integer, can be positive/negative and even/odd anything.
With any little slight change in value of n the units place digit will change => Not sufficient

(2) n^2 =1

Well n's units place must be always 1, but what about the relation b/w n and x? we still dont know anything about x => Not sufficient

Both combined. (1) + (2)

take n= -1 and n=1
again without any calculation we can see that we will get x=6250 and 62.5 respectively => Not sufficient

Ans=>E
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Re: If n is an integer, what is the units digit of x?  [#permalink]

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22 Oct 2017, 09:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If n is an integer, what is the units digit of x? &nbs [#permalink] 22 Oct 2017, 09:23
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