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

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Question Stats: 64% (01:29) correct 36% (01:19) wrong based on 576 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
Math Expert V
Joined: 02 Sep 2009
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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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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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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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ferrarih wrote:
If n is an integer, what is the units digit of x?

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

(2) n^2 = 1

OA: E

$$(1)\quad x = \frac{25^2}{10^n}$$

taking value of $$n=0$$, we get $$x=\frac{25^2}{10^0}$$ ; $$x =625$$
Units digit is $$5$$.

taking value of $$n=1$$, we get $$x=\frac{25^2}{10^1}$$ ; $$x =62.5$$
Units digit is $$2$$.

As we are not getting a unique value of units digit of $$x$$, Statement $$1$$ alone is insufficient.

$$(2)\quad n^2 = 1$$
$$n^2-1=0$$; $$n$$ can be $$1$$ or $$-1$$.
Statement $$2$$ does not give any information about $$x$$ , Statement $$2$$ alone is insufficient.

Combining $$(1)$$ and $$(2)$$, we get
Putting $$n=1$$, We get $$x=\frac{25^2}{10^1}$$ ; $$x =62.5$$
Units digit is $$2$$.

Putting $$n=-1$$, We get $$x=\frac{25^2}{10^{-1}}$$ ; $$x =6250$$
Units digit is $$0$$.

As we are not getting a unique value of units digit of $$x$$, Combining Statement $$1$$ and Statement $$2$$ also is not sufficient. Re: If n is an integer, what is the units digit of x?   [#permalink] 23 Oct 2018, 09:09
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