Determine whether or not one or more pairs of twin primes exist between the pair of numbers given. if so, identify the twin primes. 1) 30 and 40 a) no b) 37,39 c) 31, 33 d) 35, 37 2) 4 and 15 a) 5,7 and 9, 11 b) no c) 5,7 d) 5, 7 and 11, 13 3) 16 and 24 a) 17, 19 and 21, 23 c) 21,23 b) no d) 17, 19 4) 35 and 50 a) 41, 42 and 47,49 c) no b) 43, 47 d) 41, 43

1) 30 and 40 : A) No

2) 4 and 15 : D) 5, 7 and 11, 13

3) 16 and 24 : D) 17, 19

4) 35 and 50 : D) 41, 43

Step-by-step explanation:

We have to define twin primes first

Twin primes are prime numbers that have a difference of 2.

So,

1) 30 and 40

The prime numbers between 30 and 40 are:

31 and 37

None of them has a difference of two so there are no twin primes between 30 and 40.

The answer is A) No

2) 4 and 15

The prime numbers between 4 and 15 are:

5,7,11,13

Twin primes are:

5 and 7

11 and 13

The answer is D) 5, 7 and 11, 13

3) 16 and 24

The prime numbers between 16 and 24 are:

17,19,23

Twin primes are 17 and 19

The answer is: D) 17, 19

4) 35 and 50

The prime numbers between 35 and 50 are:

37,41,43,47

Twin primes are 41 and 43.

The answer is: D) 41, 43 ..

Let's explain this by using an example. Let's take the square root of 4.
sqrt(4)
You'd think the answer is 2, and you are correct, but the answer is also -2.
Remember that a square root means that the two numbers must be the same, and multiply back up to 4. In this case, the number is 2.
2•2=4
BUT
-2•-2 ALSO =4
therefore there are two square roots...
2 is a square root
AND
-2 is a square root.
This goes with all positive numbers!

I hope this helps! Best wishes :)