Let a, b, α and β be prime numbers. n is the number of ordered pairs of a and b where 2< a < b < 50 and b-a=2. Also, α and β are the least and the greatest prime numbers less than 50. What is the value of n(α+β)?

Correct option is C

Given
a, b, α, and β are prime numbers
Condition for twin primes: b - a = 2 (where 2 < a < b < 50)
α = least prime number less than 50
β = greatest prime number less than 50
Solution
Twin primes pairs (a, b) between 2 and 50 are: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43).
Total number of valid pairs (n) = 6
Least prime number less than 50 (α) = 2
Greatest prime number less than 50 (β) = 47
Now substitute values into n(α + β):
Value = 6 × (2 + 47)
= 6 × 49 = 294
Final Answer
So the correct answer is (c)