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17, 19, p, 29, 31, q, 41 is a list of prime numbers in ascending order. What is the value of q - p?
- a)60
- b)37
- c)23
- d)14
Correct answer is option 'D'. Can you explain this answer?
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17, 19, p, 29, 31, q, 41 is a list of prime numbers in ascending order...
Solution:To solve this problem, we need to find the values of p and q and then find their difference.Finding p:We know that 17 and 19 are prime numbers. The next prime number after 19 is 23. Therefore, p must be a prime number between 19 and 23. We can check each number in this range to see which one is prime:- 20 is not prime (it is divisible by 2 and 5)- 21 is not prime (it is divisible by 3 and 7)- 22 is not prime (it is divisible by 2 and 11)- Therefore, p must be 23.Finding q:We know that q is a prime number that comes after 31. We can check each number after 31 to see which one is prime:- 32 is not prime (it is divisible by 2)- 33 is not prime (it is divisible by 3)- 34 is not prime (it is divisible by 2 and 17)- 35 is not prime (it is divisible by 5 and 7)- 36 is not prime (it is divisible by 2, 3, and 6)- 37 is prime, so q must be 37.Finding q - p:Now that we know the values of p and q, we can find their difference:q - p = 37 - 23 = 14.Therefore, the answer is (d) 14.
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17, 19, p, 29, 31, q, 41 is a list of prime numbers in ascending order. What is the value of q - p?a)60 b)37c)23 d)14Correct answer is option 'D'. Can you explain this answer?
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