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Question 40
Z is the product of first 31 natural numbers. If X = Z + 1, then the numbers of primes among X + 1, X + 2, ..., X + 29, X + 30 is
Solution
It is given that Z = 31!
X = 31! + 1
X+1 = 31!+2 this is divisible by 2
X+2 = 31!+3 this is divisible by 3
X+3 = 31!+4 this is divisible by 4
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.
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X+29 = 31!+30 this is divisible by 30
X+30 = 31!+31 this is divisible by 31
Hence, none of X + 1, X + 2, ..., X + 29, X + 30 is a prime number.
Hence, option D is the correct answer.
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