CAT Exam > CAT Questions > Ex.1 If a, a 2, a 4 are consecutive prime...
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Ex.1 If a, a 2, a 4 are consecutive prime numbers. Then how many solutions ‘a’ can have? (1) one (2) two (3) three (4) more than three Sol. No even value of ‘a’ satisfies this. So ‘a’ should be odd. But out of three consecutive odd numbers, atleast one number is a multiple of 3. So, only possibility is a = 3 and the numbers are 3, 5, 7. Answer: (1) This is given is your binder but I think the ques is incomplete. Either u should mention that all prime numbers a divisible by three?
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Ex.1 If a, a 2, a 4 are consecutive prime numbers. Then how many s...
Question Analysis:
The question asks about the possible values of 'a' if 'a', 'a+2', and 'a+4' are consecutive prime numbers. We need to determine the number of solutions for 'a'.
Given Information:
- 'a', 'a+2', and 'a+4' are consecutive prime numbers.
Solution:
To find the possible values of 'a', we need to consider the properties of prime numbers.
Property 1: All prime numbers except 2 are odd.
Property 2: Among any three consecutive odd numbers, at least one number is a multiple of 3.
Analysis of Properties:
From Property 1, we can conclude that 'a' must be an odd number. If 'a' were even, it would not be a prime number.
From Property 2, we know that among any three consecutive odd numbers, at least one number is a multiple of 3. Therefore, if 'a' is the first number in the sequence, then 'a+2' or 'a+4' must be divisible by 3. However, since 'a+2' and 'a+4' are prime numbers, they cannot be divisible by 3. Therefore, 'a' cannot be the first number in the sequence.
Hence, the only possibility is that 'a' is equal to 3. In this case, the three consecutive prime numbers are 3, 5, and 7.
Conclusion:
Based on the given information and the properties of prime numbers, the only solution for 'a' is 3. Therefore, the number of solutions for 'a' is one.
Answer: (1) one
The question asks about the possible values of 'a' if 'a', 'a+2', and 'a+4' are consecutive prime numbers. We need to determine the number of solutions for 'a'.
Given Information:
- 'a', 'a+2', and 'a+4' are consecutive prime numbers.
Solution:
To find the possible values of 'a', we need to consider the properties of prime numbers.
Property 1: All prime numbers except 2 are odd.
Property 2: Among any three consecutive odd numbers, at least one number is a multiple of 3.
Analysis of Properties:
From Property 1, we can conclude that 'a' must be an odd number. If 'a' were even, it would not be a prime number.
From Property 2, we know that among any three consecutive odd numbers, at least one number is a multiple of 3. Therefore, if 'a' is the first number in the sequence, then 'a+2' or 'a+4' must be divisible by 3. However, since 'a+2' and 'a+4' are prime numbers, they cannot be divisible by 3. Therefore, 'a' cannot be the first number in the sequence.
Hence, the only possibility is that 'a' is equal to 3. In this case, the three consecutive prime numbers are 3, 5, and 7.
Conclusion:
Based on the given information and the properties of prime numbers, the only solution for 'a' is 3. Therefore, the number of solutions for 'a' is one.
Answer: (1) one
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Ex.1 If a, a 2, a 4 are consecutive prime numbers. Then how many solutions ‘a’ can have? (1) one (2) two (3) three (4) more than three Sol. No even value of ‘a’ satisfies this. So ‘a’ should be odd. But out of three consecutive odd numbers, atleast one number is a multiple of 3. So, only possibility is a = 3 and the numbers are 3, 5, 7. Answer: (1) This is given is your binder but I think the ques is incomplete. Either u should mention that all prime numbers a divisible by three?
Question Description
Ex.1 If a, a 2, a 4 are consecutive prime numbers. Then how many solutions ‘a’ can have? (1) one (2) two (3) three (4) more than three Sol. No even value of ‘a’ satisfies this. So ‘a’ should be odd. But out of three consecutive odd numbers, atleast one number is a multiple of 3. So, only possibility is a = 3 and the numbers are 3, 5, 7. Answer: (1) This is given is your binder but I think the ques is incomplete. Either u should mention that all prime numbers a divisible by three? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Ex.1 If a, a 2, a 4 are consecutive prime numbers. Then how many solutions ‘a’ can have? (1) one (2) two (3) three (4) more than three Sol. No even value of ‘a’ satisfies this. So ‘a’ should be odd. But out of three consecutive odd numbers, atleast one number is a multiple of 3. So, only possibility is a = 3 and the numbers are 3, 5, 7. Answer: (1) This is given is your binder but I think the ques is incomplete. Either u should mention that all prime numbers a divisible by three? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ex.1 If a, a 2, a 4 are consecutive prime numbers. Then how many solutions ‘a’ can have? (1) one (2) two (3) three (4) more than three Sol. No even value of ‘a’ satisfies this. So ‘a’ should be odd. But out of three consecutive odd numbers, atleast one number is a multiple of 3. So, only possibility is a = 3 and the numbers are 3, 5, 7. Answer: (1) This is given is your binder but I think the ques is incomplete. Either u should mention that all prime numbers a divisible by three?.
Ex.1 If a, a 2, a 4 are consecutive prime numbers. Then how many solutions ‘a’ can have? (1) one (2) two (3) three (4) more than three Sol. No even value of ‘a’ satisfies this. So ‘a’ should be odd. But out of three consecutive odd numbers, atleast one number is a multiple of 3. So, only possibility is a = 3 and the numbers are 3, 5, 7. Answer: (1) This is given is your binder but I think the ques is incomplete. Either u should mention that all prime numbers a divisible by three? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Ex.1 If a, a 2, a 4 are consecutive prime numbers. Then how many solutions ‘a’ can have? (1) one (2) two (3) three (4) more than three Sol. No even value of ‘a’ satisfies this. So ‘a’ should be odd. But out of three consecutive odd numbers, atleast one number is a multiple of 3. So, only possibility is a = 3 and the numbers are 3, 5, 7. Answer: (1) This is given is your binder but I think the ques is incomplete. Either u should mention that all prime numbers a divisible by three? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ex.1 If a, a 2, a 4 are consecutive prime numbers. Then how many solutions ‘a’ can have? (1) one (2) two (3) three (4) more than three Sol. No even value of ‘a’ satisfies this. So ‘a’ should be odd. But out of three consecutive odd numbers, atleast one number is a multiple of 3. So, only possibility is a = 3 and the numbers are 3, 5, 7. Answer: (1) This is given is your binder but I think the ques is incomplete. Either u should mention that all prime numbers a divisible by three?.
Solutions for Ex.1 If a, a 2, a 4 are consecutive prime numbers. Then how many solutions ‘a’ can have? (1) one (2) two (3) three (4) more than three Sol. No even value of ‘a’ satisfies this. So ‘a’ should be odd. But out of three consecutive odd numbers, atleast one number is a multiple of 3. So, only possibility is a = 3 and the numbers are 3, 5, 7. Answer: (1) This is given is your binder but I think the ques is incomplete. Either u should mention that all prime numbers a divisible by three? in English & in Hindi are available as part of our courses for CAT.
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Ex.1 If a, a 2, a 4 are consecutive prime numbers. Then how many solutions ‘a’ can have? (1) one (2) two (3) three (4) more than three Sol. No even value of ‘a’ satisfies this. So ‘a’ should be odd. But out of three consecutive odd numbers, atleast one number is a multiple of 3. So, only possibility is a = 3 and the numbers are 3, 5, 7. Answer: (1) This is given is your binder but I think the ques is incomplete. Either u should mention that all prime numbers a divisible by three?, a detailed solution for Ex.1 If a, a 2, a 4 are consecutive prime numbers. Then how many solutions ‘a’ can have? (1) one (2) two (3) three (4) more than three Sol. No even value of ‘a’ satisfies this. So ‘a’ should be odd. But out of three consecutive odd numbers, atleast one number is a multiple of 3. So, only possibility is a = 3 and the numbers are 3, 5, 7. Answer: (1) This is given is your binder but I think the ques is incomplete. Either u should mention that all prime numbers a divisible by three? has been provided alongside types of Ex.1 If a, a 2, a 4 are consecutive prime numbers. Then how many solutions ‘a’ can have? (1) one (2) two (3) three (4) more than three Sol. No even value of ‘a’ satisfies this. So ‘a’ should be odd. But out of three consecutive odd numbers, atleast one number is a multiple of 3. So, only possibility is a = 3 and the numbers are 3, 5, 7. Answer: (1) This is given is your binder but I think the ques is incomplete. Either u should mention that all prime numbers a divisible by three? theory, EduRev gives you an
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