I just made a careless mistake on the easiest question. Even though i read the question thouroughly and properly, while looking at answer choices, I completely forgot the 'even number' part and selected C

No problem GRE is all about learning from our mistakes and not repeating them, I can understand.

Thank you for your reply.. Now I have understood it .. the wording of this question was a bit tricky for me, I should have looked at the answer choices however.

Why do you say 16 = 4096? isn't 16 squared = 256? Or am i missing something

Step 1: Check constraints

n must be a positive even number.
The units digit of $n$ must equal the units digit of \(n^2\) .


Step 2: Test the units digit behavior for even numbers
The possible units digits for an even integer n are 0,2,4,6 , and 8 :

If units digit of $n$ is \(\mathbf{0}\) : \(0^2=0 \Longrightarrow\) units digit is \(\mathbf{0}\) (Matches)
If units digit of n is 2: \(2^2=4 \Longrightarrow \) units digit is 4 (No)
If units digit of n is 4: \(4^2=16 \Longrightarrow\) units digit is \(\mathbf{6}\) (No)
If units digit of n is 6 : \(6^2=36 \Longrightarrow\) units digit is 6 (Matches)
If units digit of n is 8: \(8^2=64 \Longrightarrow\) units digit is 4 (No)


Thus, an even number $n$ whose units digit equals the units digit of \(n^2\) must end in 0 or
Step 3: Evaluate the options

(A) 12: Ends in \(2\left(2^2=4 \neq 2\right)\)
(C) 15: Not even
(D) 16: Even, ends in 6 ( \( 6^2=36\) , units digit is 6 )
(E) 17: Not even


Correct Answer: (D) 16