Question

An example of twin primes is _____.
(a) 5, 11
(b) 3, 5
(c) 11, 17
(d) 3, 7

Answer 1

Hint: In this question, we are supposed to choose an example of twin primes from the options and to do this, we will first define the what is the condition for two numbers to twin primes and then we will check all the options, as to whether they satisfy the conditions for two numbers to be twin primes.

Complete step-by-step answer:
For a pair numbers to be twin primes, it has to satisfy the following two conditions:
1. Both the numbers should be primes: This is fairly straightforward condition and we can deduce them by the title twin ‘primes’
2. The difference between the two numbers must be 2: This is a very important condition and this is what differentiates a pair of prime numbers with twin primes.
Now, we will verify the options one by one to see whether they comply with these conditions or not.
Option (a): 5, 11.
As we know, both 5 and 11 are prime numbers, so the first condition is satisfied.
11 – 5 = 6 $ \ne $ 2. Thus, the second condition is not satisfied.
Hence, option (a) does not satisfy.
Option (b): 3, 5.
As we know, both 3 and 5 are prime numbers, so the first condition is satisfied.
5 – 3 = 2. Thus, the second condition also satisfies.
Hence, option (b) satisfy.
Option (c): 11, 17.
As we know, both 11 and 17 are prime numbers, so the first condition is satisfied.
17 – 11 = 6 $ \ne $ 2. Thus, the second condition is not satisfied.
Hence, option (c) does not satisfy.
Option (d): 3, 7.
As we know, both 3 and 7 are prime numbers, so the first condition is satisfied.
7 – 3 = 4 $ \ne $ 2. Thus, the second condition is not satisfied.
Hence, option (d) does not satisfy.
Hence, option (b) is the correct option.

Note: Option verification is the only method to solve this question as there can be many examples of twin primes like 17 and 19, 41 and 43, etc.