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

Question

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

(2) n^2 = 1

Bunuel · Accepted Answer

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.

Bunuel · Answer

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kpali · Answer

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

Bismarck · Answer

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.

GMATmronevsall · Answer

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

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

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