Subject: General Aptitude · Chapter: Number System · Exam: 2007 · Marks: · Difficulty:
The remainder obtained when any prime number greater than 6 is divided by 6 must be
(a)either 1 or 2
(b)either 1 or 3
(c)either 1 or 5
(d)either 3 or 5
Answer
Answer (as printed): C
Explanation
Let the required prime number be $p$. Let $p$ when divided by 6 give $n$ as quotient and $r$ as remainder. Then $p=6 n+r$, where $0 \leq r<6$ Now, $r=0, r=2, r=3$ and $r=4$ do not give $p$ as prime. $\therefore \quad r \neq 0, r \neq 2, r \neq 3$ and $r \neq 4$. Hence, $r=1$ or $r=5$.
Explanation as extracted from the printed page; notation may be imperfect.