If n is positive integer, what is the units digit of n?

Here is the OE

Solution:
Step 1: Analyse Question Stem
• We know n is a positive integer.
• We need to find the units digit of n.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: \(n^2\) -25n + 150 < 0
\(n^2\) -25n + 150 < 0
⟹ \(n^2\) -10n – 15n + 150 < 0
⟹ (n – 10) (n – 15) < 0
⟹ 10 < n < 15
Thus, n can be 11, 12, 13, or 14.
Since we are not getting a unique value of n, statement 1 is not sufficient to answer the question. We can eliminate answer options A and D.
Statement 2: n2 and n5 have the same units digit
If \(n^2\) and \(n^5\) have the same units digit, then the units digit of n can be
• Units digit of n = 0
• Units digit of n = 1
• Units digit of n = 5
• Units digit of n = 6
Since, we are not getting a unique units digit, statement 2 is also not sufficient to answer the question. And we can eliminate answer option B.

Step 3: Analyse Statements by Combining
From statement 1: n can be 11, 12, 13, or 14
From statement 2: the units digit of n can be 0, 1, 5, or 6
Combining, we can say that n has to be 11.
Thus, the correct answer is Option C.