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Question

Answers

(a). (2, 3), (0, 5), (13, 17)

(b). (2, 3), (3, 7), (13, 17)

(c). (2, 3), (3, 7), (2, 8)

(d). (2, 3), (2, 17), (13, 17)

Answer
Verified

Hint: Find all the prime numbers less than 20 and then try to pair them such that their sum is divisible by 5. Then, check the options and choose the correct answer.

__Complete step-by-step answer:__

Prime numbers are numbers that have factors as one and itself. It is not completely divisible by any other number except 1 and the number itself. The number 1 is neither prime nor composite.

The prime numbers less than 20 are 2, 3, 5, 7, 11, 13, and 17.

We need to form pairs such that the sum of the above prime numbers is divisible by 5.

For a number to be divisible by 5, the last digit of the number should be either 5 or 0. Hence, we form pairs such that the ending digit of their sum is 5 or 0.

The sum of the prime numbers 2 and 3 is 5 and 5 is divisible by 5.

The sum of the prime numbers 3 and 7 is 10 and 10 is divisible by 5.

The sum of the prime numbers 7 and 13 is 20 and 20 is divisible by 5.

The sum of the prime numbers 3 and 17 is 20 and 20 is divisible by 5.

The sum of the prime numbers 13 and 17 is 30 and 30 is divisible by 5.

The sum of the prime numbers 2 and 13 is 15 and 15 is divisible by 5.

Hence, the pairs are (2, 3), (3, 7), (7, 13), (3, 17), (13, 17), and (2, 13).

Comparing the given options, we observe that option (b) belongs to these pairs.

Hence, the correct answer is option (b).

Note: You can also directly identify the answer from the given options by eliminating other options with the given two criteria that the pair should be a prime number less than 20 and their sum should be divisible by 5.

Prime numbers are numbers that have factors as one and itself. It is not completely divisible by any other number except 1 and the number itself. The number 1 is neither prime nor composite.

The prime numbers less than 20 are 2, 3, 5, 7, 11, 13, and 17.

We need to form pairs such that the sum of the above prime numbers is divisible by 5.

For a number to be divisible by 5, the last digit of the number should be either 5 or 0. Hence, we form pairs such that the ending digit of their sum is 5 or 0.

The sum of the prime numbers 2 and 3 is 5 and 5 is divisible by 5.

The sum of the prime numbers 3 and 7 is 10 and 10 is divisible by 5.

The sum of the prime numbers 7 and 13 is 20 and 20 is divisible by 5.

The sum of the prime numbers 3 and 17 is 20 and 20 is divisible by 5.

The sum of the prime numbers 13 and 17 is 30 and 30 is divisible by 5.

The sum of the prime numbers 2 and 13 is 15 and 15 is divisible by 5.

Hence, the pairs are (2, 3), (3, 7), (7, 13), (3, 17), (13, 17), and (2, 13).

Comparing the given options, we observe that option (b) belongs to these pairs.

Hence, the correct answer is option (b).

Note: You can also directly identify the answer from the given options by eliminating other options with the given two criteria that the pair should be a prime number less than 20 and their sum should be divisible by 5.

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