Question

Use the clues to find two prime numbers less than 20.
Prime number 1: Subtracting 4 from this prime number gives
a multiple of 5.
Prime number 2: This prime number is one more than a multiple
of 4, but not 1 less than a multiple of 3.
Prime number 1 is
19
Prime number 2 is
42

Answer 1

in question it is given that the answer is less than 20.

1) 19-4=15

it is also multiple of 5

2)19+1=20

it is also multiple of 4

19-1 =18

it is multiple of 3 also not less than multiple of 3

so finally the number is 19

Answer 2

Given:

Two prime numbers below 20 follow the given conditions.

1. The first prime number is 4 more than the multiple of 5.

2. The second prime number is one more than multiple of 4, but not 1 less than multiple of 3.  

To Find:

The two prime numbers.

Solution:

1. It is given that the two prime numbers are less than 20.

2. A prime number is defined as the number which has only two factors that are 1 and the number itself.

3. The first prime number is 4 more than the multiple of 5, The multiples of 5 below 20 are 5,10,15,20. The prime number 19 is 4 more than 15 which is a multiple of 5. Hence, the first prime number is 19, (19 has two factors 1 and 19).

 

4. The second prime number is one more than multiple of 4, Multiples of 4 below 20 are 4,8,12,16,20. The prime number is also not 1 less than multiple of 3, Multiples of 3 below 20 are 3,6,9,12,15,18. 13 is a prime number below 20 which is 1 more than multiples of 4 but not 1 less than the multiple of 3. Hence, the second prime number is 13 (1 and 13 are factors of 13, hence 13 is a prime number).

 

Therefore, the two prime numbers are 19 and 13.