What is the value of integer A ? (1) n = nA (2) 1^n ≠ n

Question

What is the value of integer A ?

(1) n = nA

(2) 1^n ≠ n

lipikatiwari · Answer

IMO  ANSWER should be 'E'

1. n=nA 
Now anything multiplied by 1 gives the same number. 
If n=2, then 2=2A, that means A=1.
But if n=0, then 0=0A. We can plug in any value of A and we will still get 0.
So the  value of A can be anything if n=0 . Since we don't exactly know the value of n, this statement is  not sufficient  to find a distinct value of A.

2)1^n ≠ n 
1 raised to any power always gives 1. So, 1^n should be 1.
It's given in the statement that 1^n is not equal to n. That means  n ≠ 1. 
But does that information help us in anyway? 
I mean,  A could be anything whether n is 1 or not. 
So,  clearly insufficient

Now using both statements: 
We know  n ≠ 1  and  n=nA 
So once again, if n=2, then 2=2A, that means A=1.
But if n=0, then 0=0A. We can plug in any value of A and we will still get 0.
 Together => Insufficient

Hence E

GMATinsight · Answer

Question: Integer A = ?

Statement 1 : n = nA

i.e. nA - n = 0

i.e. n(A-1) = 0

i.e. n = 0 or A = 1

i.e. if n = 0 then A can take any value hence

NOT SUFFICIENT

STatement 2 : 1^n ≠ n

i.e. n = 1 but the relation of n with A is unknown hence

COmbining the statements

SInce, n = 1, therefore A can take any value hence

NOT SUFFICIENT

Answer: Option E

lipikatiwari · Answer

I'm a little confused. According to you, since 1^n ≠ n, then n ≠ 0
How did you figure this out? 
If n=0, then 1^0 will be 1, which is not equal to 0 (the value of n in this case). Hence, for n=0, the condition 1^n ≠ n remains true. Only for n=1, the condition 1^n ≠ n will be false. So, clearly n ≠ 1
Then how can it be concluded that n ≠ 0? Am I missing out something? 🤔

Archit3110 · Answer

target find value of integer A
#1
n = nA
if n = 0 then a can be 0 or any integer value hence insufficient
#2
1^n ≠ n
means that only possible of n not possible is 1 ; but relation with A is not known insufficient
from 1&2 we get n = 0,2,3, so on 
so possible value of A can be any integer value when n is 0 or A can be 1 when n is any other value 
insufficient
option E

Archit3110 · Answer

GMATinsight 
sir shouldnt the highlighted part be n ≠1 ? because at n =0 satisfies the #2 of 1^n ≠ n...

What is the value of integer A ? (1) n = nA (2) 1^n ≠ n

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What is the value of integer A ? (1) n = nA (2) 1^n ≠ n

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