Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
Let $X_{k}=\left(p_{1} p_{2} \ldots \ldots . p_{k}\right)+1$, where $p_{1}, p_{2}, \ldots \ldots \ldots, p_{k}$ are the first $k$ primes. Consider the following:
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
$X_{2}=(2 \times 3)+1=7$, which is prime and $X_{2}+1=8$, which is even. $X_{3}=(2 \times 3 \times 5)+1=31$, which is prime and $X_{3}+1=32$, which is even. $X_{4}=(2 \times 3 \times 5 \times 7)+1=211$, which is prime and $X_{4}+1=212$, which is even and so on. Thus $X_{k}$ is prime and $\left(X_{k}+1\right)$ is even. Hence, 1 and 3 are true statements.
Explanation as extracted from the printed page; notation may be imperfect.