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If n is a positive integer, then n ( n +1 ) (n+2 ) is which of the following?
- a)even only when n is even ?
- b)even only when n is odd ?
- c)divisible by 3 only when n is odd ?
- d)divisible by 12 whenever n is even ?
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If n is a positive integer, then n ( n +1 ) (n+2 ) is which of the fol...
Assume: n is even, then either n or n+2 is a multiple of 4. Hence, n(n+1)(n+2) is divisible by 4.
Therefore: whenever n is even, the term above is divisble by 4.
This question is part of UPSC exam. View all GMAT courses
Most Upvoted Answer
If n is a positive integer, then n ( n +1 ) (n+2 ) is which of the fol...
I think d is correct not c. the product of three consecutive numbers is divisible to 3, if n=2k => the product is also divisible to 4 => divisible to 12
Community Answer
If n is a positive integer, then n ( n +1 ) (n+2 ) is which of the fol...
To determine which of the given options is correct, let's analyze the expression n(n-1)(n+2) for different values of n.
1. n is even:
- When n is even, the expression can be written as n/2 * (n-1) * 2 * (n+1).
- In this case, the expression is divisible by 2 because it contains the factor 2. Therefore, option 'a' is incorrect.
- The expression is not divisible by 3 because it does not contain the factor 3. Therefore, option 'c' is incorrect.
- However, the expression is divisible by 12 because it contains the factors 2 and 3. Therefore, option 'd' is correct.
2. n is odd:
- When n is odd, the expression can be written as n * (n-1) * (n+1).
- In this case, the expression is not divisible by 2 because it does not contain the factor 2. Therefore, option 'a' is incorrect.
- The expression is divisible by 3 because it contains the factors 3 and (n-1). Therefore, option 'c' is correct.
- The expression is not divisible by 12 because it does not contain the factors 2 and 3. Therefore, option 'd' is incorrect.
Therefore, the correct answer is option 'c' - the expression n(n-1)(n+2) is divisible by 3 only when n is odd.
1. n is even:
- When n is even, the expression can be written as n/2 * (n-1) * 2 * (n+1).
- In this case, the expression is divisible by 2 because it contains the factor 2. Therefore, option 'a' is incorrect.
- The expression is not divisible by 3 because it does not contain the factor 3. Therefore, option 'c' is incorrect.
- However, the expression is divisible by 12 because it contains the factors 2 and 3. Therefore, option 'd' is correct.
2. n is odd:
- When n is odd, the expression can be written as n * (n-1) * (n+1).
- In this case, the expression is not divisible by 2 because it does not contain the factor 2. Therefore, option 'a' is incorrect.
- The expression is divisible by 3 because it contains the factors 3 and (n-1). Therefore, option 'c' is correct.
- The expression is not divisible by 12 because it does not contain the factors 2 and 3. Therefore, option 'd' is incorrect.
Therefore, the correct answer is option 'c' - the expression n(n-1)(n+2) is divisible by 3 only when n is odd.
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If n is a positive integer, then n ( n +1 ) (n+2 ) is which of the following?a)even only when n is even ?b)even only when n is odd ?c)divisible by 3 only when n is odd ?d)divisible by 12 whenever n is even ?Correct answer is option 'C'. Can you explain this answer?
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