What is the least value of the positive integer \(n?\)

[Gmat_mission]

What is the least value of the positive integer \(n?\)

I. The unit digit of \(n\) is equal to the unit digit of the sum of \(n\) and \((n + 1).\)
II. n is the square of a single-digit odd prime number.

Answer: D

Source: e-GMAT

[deloitte247]

Statement 1: The unit digit of n is equal to the unit digit of the sum of n and (n+1)
n + (n+1) = 2n + 1 which is an odd number.
So, testing all odd unit integer 1, 3, 5, 7, and 9.
If n=1, then 2n+1 = 3 units are not equal.
$$So,\ n\ne1$$
If n=3, then 2n+1 = 7 units are not equal.
$$So,\ n\ne3$$
If n=5, then 2n+1 = 11 units are not equal.
$$So,\ n\ne5$$
If n=7, then 2n+1 = 15 units are not equal.
$$So,\ n\ne7$$
If n=9, then 2n+1 = 19 units are not equal.
$$So,\ n=9$$

Statement 2: n is the square of a single-digit odd prime number.
Odd prime unit integers are 3, 5, and 7. So,
$$n=3^2\ or\ n=5^2\ or\ n=7^2$$
$$n=9\ or\ n=25\ or\ n=49$$
But among these values the least of them is 9. So, n=9. Hence, statement 2 is SUFFICIENT.

Since each statement alone is SUFFICIENT, the correct answer is option D