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

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

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.

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

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

(2) n^2 = 1

Simple one..

we have to find units digit of x..

(1) x = (25^2)/(10^n) => we get 625/(10^n) hence for different values of n we get different units digits
like for n=1 we get units digit as 2 , for n=0, units=5 soo cant arrive on an answer hence INSUFFICIENT

(2) n^2=1 now there are two possible values of n ie. -1 & 1 but they hold no relevance to original statement hence INSUFFICIENT

(1)+(2) for n=1 => x = (25^2)/(10^1) => 62.5 units digit is 2
for n=-1 => x= x = (25^2)/(10^-1)=> 6250 units digit is 0
INSUFFICIENT

ANSWER E

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.