Question

Daphne wants to decode the three codes using the given statements.
Code 1: A prime number that is just greater than $40$.
Code 2: A composite number that lies between $22$ and $25$.
Code 3: A prime number that lies between $36$ and $40$.

• A. Code $1=41$, Code $2=24$, and Code $3=39$
• B. Code $1=43$, Code $2=23$, and Code $3=43$
• C. Code $1=41$, Code $2=24$, and Code $3=37$
• D. Code $1=41$, Code $2=25$, and Code $3=38$

Answer 1

The correct option is C Code $1=41$, Code $2=24$, and Code $3=37$

To solve code $1$, write the numbers greater than $41$.

• $41,42,43,44,45,\dots$
• We see that $41$ is the number that is just greater than $40.41$ is also a prime number.
• To solve code $2$, write the numbers that lie between $22$ and $25$.
• $23$ and $24$
• $24$ is the composite number that lies between $22$ and $25$.
• To solve code $3$, write numbers between $36$ and $40$.
• $37,38,39$, and $40$
• $37$ is the only prime number between $36$ and $40$.

Hence the three codes are $41,24,$ and $37$.