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

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

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New post 30 Jun 2012, 07:00
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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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Re: If n is an integer, what is the units digit of x?  [#permalink]

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New post 30 Jun 2012, 07:07
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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.

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

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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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New post 24 Jun 2013, 08:31
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Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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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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New post 23 Oct 2018, 08:09
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.
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Re: If n is an integer, what is the units digit of x? &nbs [#permalink] 23 Oct 2018, 08:09
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