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30 Dec 2019, 07:14
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
70% (01:21) correct
30%
(01:16)
wrong
based on 224
sessions
History
Date
Time
Result
Not Attempted Yet
If n is a positive integer, which of the following statements are correct?
1. All the prime numbers can be represented in the form 6n – 1 or 6n + 1
2. All numbers of the form 4n + 1 and 4n + 3 are prime numbers
3. 2 and 3 are the only 2 consecutive numbers that are prime.
A. 1st statement only
B. 2nd statement only
C. 3rd statement only
D. 1st and 2nd statements
E. 1st and 3rd statements
1. All the prime numbers can be represented in the form 6n – 1 or 6n + 1
2. All numbers of the form 4n + 1 and 4n + 3 are prime numbers
3. 2 and 3 are the only 2 consecutive numbers that are prime.
A. 1st statement only
B. 2nd statement only
C. 3rd statement only
D. 1st and 2nd statements
E. 1st and 3rd statements
30 Dec 2019, 11:13
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Solution
Given
In this question, we are given that
- • The number n is a positive integer
To find
We need to determine
- • Among the given statements which ones are true
Approach and Working out
Statement 1: All the prime numbers can be represented in the form 6n – 1 or 6n + 1
- This is a property applicable to any prime number, provided it is greater than 3. There are two exceptions to this rule – for prime numbers 2 and 3, this rule is not applicable.
Hence, statement 1 is not necessarily true.
Statement 2: All numbers of the form 4n + 1 and 4n + 3 are prime numbers
- If we consider n = 5, then 4n + 1 = 4 x 5 + 1 = 21, which is not a prime number.
Hence, statement 2 is not necessarily true.
Statement 3: 2 and 3 are the only 2 consecutive numbers that are prime
- Among all the prime numbers, 2 and 3 are the only consecutive numbers that are prime. We cannot have any other consecutive numbers’ pair as prime, because in a consecutive numbers’ pair one number will be even, and apart from 2 no other even number can be prime.
Hence, statement 3 is necessarily true.
Thus, option C is the correct answer.
Correct Answer: Option C
30 Dec 2019, 11:28
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Solution :
Statement 1: All the prime numbers can be represented in the form 6n – 1 or 6n + 1
Prime Numbers : 2,3,5,7,11 .....
2,3 can't be expressed in the above form.
INCORRECT
Statement 2: All numbers of the form 4n + 1 and 4n + 3 are prime numbers
Take 4n+1 for instance
Put n=2 you get 4(2)+1 =9
9 isn't a prime number
INCORRECT
Statement 3: 2 and 3 are the only 2 consecutive numbers that are prime
CORRECT
Yes, ONLY STATEMENT 3 is correct
Option C
Statement 1: All the prime numbers can be represented in the form 6n – 1 or 6n + 1
Prime Numbers : 2,3,5,7,11 .....
2,3 can't be expressed in the above form.
INCORRECT
Statement 2: All numbers of the form 4n + 1 and 4n + 3 are prime numbers
Take 4n+1 for instance
Put n=2 you get 4(2)+1 =9
9 isn't a prime number
INCORRECT
Statement 3: 2 and 3 are the only 2 consecutive numbers that are prime
CORRECT
Yes, ONLY STATEMENT 3 is correct
Option C
