Subject: General Aptitude · Chapter: Number System · Exam: 2006 · Marks: · Difficulty:
Four prime numbers are arranged in ascending order. The product of first three is 385 and that of last three is 1001 . The largest prime number is
(a)9
(b)11
(c)13
(d)17
Answer
Answer (as printed): C
Explanation
Let the given prime numbers be $p, q, r$ and $s$. Then $$\begin{gathered} p \times q \times r=385 \text { and } q \times r \times s=1001 \\ \Rightarrow \frac{p \times q \times r}{q \times r \times s}=\frac{\frac{55^{5}}{385}}{\frac{1001}{443_{13}}}=\frac{5}{13} \Rightarrow \frac{p}{s}=\frac{5}{13} \Rightarrow p=5 \text { and } s=13 . \end{gathered}$$ Hence the largest of these prime numbers is 13.
Explanation as extracted from the printed page; notation may be imperfect.