Solve the following problems.

Question

1. Janna has a collection of four cards numbered 1 to 4. He pairs them up so that each pair will form a two digit prime number. What is the difference between two prime numbers formed?

2. Find the sum of the least and greatest even numbers between 100 and 200?

3. Find a pair factors of 72 whose sum is 22.

4. Find a pair factors of 48 whose quotient us 12.

5. Reverse the digit of a multiple of 25 which is less than 100 to get a multiple of 19.

6. Given a 3 digit number N which is a multiple of 6,7 and 8, what is the least value of N?

Answer 1

Q1. Janna has a collection of four cards numbered 1 to 4. He pairs them up so that each pair will form a two digit prime number. What is the difference between two prime numbers formed?

Answer: To solve this problem, we need to find pairs of numbers from 1 to 4 such that when they are combined in two different ways, they form two-digit prime numbers. Let's start by listing all the two-digit prime numbers:

1. 11
2. 13
3. 17
4. 19
5. 23
6. 29
7. 31
8. 37
9. 41
10. 43
11. 47
12. 53
13. 59
14. 61
15. 67
16. 71
17. 73
18. 79
19. 83
20. 89
21. 97

Now, let's see if we can form any of these prime numbers using pairs of the numbers 1 to 4:

1. The only prime number that can be formed using 1 and 2 is 12, which is not a prime.
2. The only prime number that can be formed using 1 and 3 is 13, which is a prime.
3. The only prime number that can be formed using 1 and 4 is 41, which is a prime.
4. The only prime number that can be formed using 2 and 3 is 23, which is a prime.
5. The only prime number that can be formed using 2 and 4 is 24, which is not a prime.
6. The only prime number that can be formed using 3 and 4 is 34, which is not a prime.

So, we have two pairs of numbers (1, 3) and (2, 3) that can be combined to form the prime numbers 13 and 23. Now, let's find the difference between these two prime numbers:

Difference = 23 - 13 = 10

The difference between the two prime numbers formed is 10.