Question

Three natural numbers are said to be tri-prime, if they are pair-wise co-prime. Then one triplet which is not tri-prime is

• A. $(2,3,7)$
• B. $(2,9,11)$
• C. $(3,5,7)$
• D. $(3,4,9)$

Answer 1

Answer: (D)

$(3,4,9)$

We know that prime number is a number which is only divisible by itself.

(a) In the triplet $(2,3,7),$ all the three numbers $2,3$ and $7$ are prime numbers, so they are pairwise co-prime. Therefore, these numbers are tri-prime.

(b) In the triplet $(2,9,11),$ all the three numbers $2,9$ and $11$ are prime numbers, so they are pairwise co-prime. Therefore, these numbers are tri-prime.

(c) In the triplet $(3,5,7),$ all the three numbers $3,5$ and $7$ are prime numbers, so they are pairwise co-prime. Therefore, these numbers are tri-prime.

(d) In the triplet $(3,4,9),$ the numbers $3$ and $9$ are not pairwise prime because $9$ is divisible by $3$. Therefore, these numbers are not tri-prime.

Hence, the triplet $(3,4,9)$ is not tri-prime.