Solve the following problems.

Question

Solve the following problems.

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

1)the two prime numbers will be 23 and 10, since rest of the combinations are not prime, the difference between these two numbers will be 23-13=10

2)The least even number between 100 and 200 is 102, and the greatest even number is 198.The sum of these two numbers is: 102 + 198 = 300.

3)To find a pair of factors of 72 whose sum is 22, we can use trial and error or systematic testing.

The factors of 72 are:

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Now, let's check which pairs have a sum of 22:

1. 1 + 72 = 73
2. 2 + 36 = 38
3. 3 + 24 = 27
4. 4 + 18 = 22 (Here, we have a pair with a sum of 22)
5. 6 + 12 = 18
6. 8 + 9 = 17

So, the pair of factors of 72 whose sum is 22 is 4 and 18.

4)the pair of factors of 48 whose quotient is 12 is 24 and 2 (i can explain it if you want)

5)

1. Multiples of 25 less than 100:
2. The multiples of 25 less than 100 are 25, 50, and 75.
3. Reversing the digits:
4. Reversing the digits of 25 gives us 52.
5. Reversing the digits of 50 gives us 5 (which is less than 19, so it's not a multiple of 19).
6. Reversing the digits of 75 gives us 57.
7. Checking for multiples of 19:
8. 52 is not a multiple of 19.
9. 57 is a multiple of 19.

so the answer is 57

6)The prime factorizations are:

1. 6=2×36=2×3
2. 77 is a prime number itself
3. 8=2×2×28=2×2×2

The LCM of 2, 3, 7, and 8 is 2×2×2×3×7=1682×2×2×3×7=168.

Therefore, the least value of N is 168.

you can reach me if you didnt undestand any of them