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What is the remainder when the positive integer n is divided by 3?
1) The remainder when n is divided by 2 is 1.?
2) The remainder when n + 1 is divided by 3 is 2.
- a)Exactly one of the statements can answer the question
- b)Both statements are required to answer the question
- c)Each statement can answer the question individually
- d)More information is required as the information provided is insufficient to answer the question
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
What is the remainder when the positive integer n is divided by 3?1) T...
(1) The remainder when n is divided by 2 is 1.
n is odd, some odd nos are evenly divisble by 3, some are not INSUFF
(2) The remainder when n + 1 is divided by 3 is 2.
n+1 = 3a +2
n =3a +1
so remainder is 1
SUFF
Most Upvoted Answer
What is the remainder when the positive integer n is divided by 3?1) T...
Statement 1: The remainder when n is divided by 2 is 1.
Statement 2: The remainder when n - 1 is divided by 3 is 2.
To find: The remainder when n is divided by 3.
Explanation:
To determine the remainder when n is divided by 3, we need to analyze both statements.
Statement 1: The remainder when n is divided by 2 is 1.
- This means that n is an odd number since any odd number divided by 2 will have a remainder of 1.
- However, this information alone does not provide any insight into the remainder when n is divided by 3.
Statement 2: The remainder when n - 1 is divided by 3 is 2.
- This means that (n - 1) is two more than a multiple of 3.
- In other words, (n - 1) = 3k + 2, where k is an integer.
- Simplifying the equation, we get n = 3k + 3 = 3(k + 1).
- This shows that n is a multiple of 3, or in other words, n is divisible by 3.
- Since n is divisible by 3, the remainder when n is divided by 3 is 0.
Combining the Statements:
From statement 1, we know that n is an odd number.
From statement 2, we know that n is divisible by 3, leading to a remainder of 0 when divided by 3.
Since the statements provide conflicting information about the divisibility of n by 3, we can conclude that neither statement alone is sufficient to determine the remainder when n is divided by 3.
Therefore, the correct answer is option A - exactly one of the statements can answer the question.
Statement 2: The remainder when n - 1 is divided by 3 is 2.
To find: The remainder when n is divided by 3.
Explanation:
To determine the remainder when n is divided by 3, we need to analyze both statements.
Statement 1: The remainder when n is divided by 2 is 1.
- This means that n is an odd number since any odd number divided by 2 will have a remainder of 1.
- However, this information alone does not provide any insight into the remainder when n is divided by 3.
Statement 2: The remainder when n - 1 is divided by 3 is 2.
- This means that (n - 1) is two more than a multiple of 3.
- In other words, (n - 1) = 3k + 2, where k is an integer.
- Simplifying the equation, we get n = 3k + 3 = 3(k + 1).
- This shows that n is a multiple of 3, or in other words, n is divisible by 3.
- Since n is divisible by 3, the remainder when n is divided by 3 is 0.
Combining the Statements:
From statement 1, we know that n is an odd number.
From statement 2, we know that n is divisible by 3, leading to a remainder of 0 when divided by 3.
Since the statements provide conflicting information about the divisibility of n by 3, we can conclude that neither statement alone is sufficient to determine the remainder when n is divided by 3.
Therefore, the correct answer is option A - exactly one of the statements can answer the question.
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What is the remainder when the positive integer n is divided by 3?1) The remainder when n is divided by 2 is 1.?2) The remainder when n+ 1 is divided by 3 is 2.a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. Can you explain this answer?
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