Categories

# Composite number Problem | B.Stat Objective | TOMATO 75

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Logic True-False Reasoning. You may use sequential hints.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Sequence and composite number.

## Composite number Problem (B.Stat Objective)

Consider the sequence $$a_1$$=101, $$a_2$$=10101,$$a_3$$=1010101 and so on. Then $$a_k$$ is a composite number ( that is not a prime number)

• if and only if $$k \geq 2$$ and $$11|(10^{k+1}+1)$$
• if and only if $$k \geq 2$$ and k-2 is divisible by 3
• if and only if $$k \geq 2$$ and $$11|(10^{k+1}-1)$$
• if and only if $$k \geq 2$$

### Key Concepts

Logic

Sequence

Composite number

But try the problem first…

Answer: if and only if $$k \geq 2$$ and k-2 is divisible by 3

Source

B.Stat Objective Question 75

Challenges and Thrills of Pre-College Mathematics by University Press

## Try with Hints

First hint

for $$a_k$$ $$k \geq 2$$ may be prime also then not considering this here

Second Hint

for $$a_{8}$$ $$10^{9}-1$$ and $$10^{9}+1$$ not divisible by 11

Final Step

8-2 is divisible by 3 and $$a_{8}$$ is composite number then $$a_{k}$$ is composite if and only if $$k \geq 2$$ and k-2 is divisible by 3.

## One reply on “Composite number Problem | B.Stat Objective | TOMATO 75”

Kush Mazumdarsays:

If and only if k>=2 and k-2 is divisible by 3

This site uses Akismet to reduce spam. Learn how your comment data is processed.