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What is the remainder when the two-digit, positive integer x is divided by 3 ?
1) The sum of the digits of x is 5.?
2) The remainder when x is divided by 9 is 5.
- 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 'C'. Can you explain this answer?
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What is the remainder when the two-digit, positive integer x is divide...
To find the remainder when a two-digit positive integer x is divided by 3, we need to determine the value of x modulo 3.
Statement 1: The sum of the digits of x is 5.
This statement does not provide enough information to determine the remainder when x is divided by 3. For example, if x is 14, the remainder when divided by 3 is 2, but if x is 23, the remainder is 1. Therefore, statement 1 alone is insufficient.
Statement 2: The remainder when x is divided by 9 is 5.
This statement also does not provide enough information to determine the remainder when x is divided by 3. For example, if x is 23, the remainder when divided by 3 is 2, but if x is 32, the remainder is 1. Therefore, statement 2 alone is insufficient.
Combining both statements:
By considering both statements together, we can determine the value of x modulo 3. Since the remainder when x is divided by 9 is 5, we know that x is of the form 9k + 5, where k is an integer. Additionally, since the sum of the digits of x is 5, the possible values for x are 14, 23, 32, etc.
Analyzing the possible values of x modulo 3:
For x = 14, the remainder when divided by 3 is 2.
For x = 23, the remainder when divided by 3 is 2.
For x = 32, the remainder when divided by 3 is 2.
From the analysis above, we can see that regardless of the specific value of x, the remainder when x is divided by 3 is always 2. Therefore, by combining both statements, we can answer the question and statement 1 and 2 together are sufficient to answer the question.
Therefore, the correct answer is (C) Each statement can answer the question individually.
Statement 1: The sum of the digits of x is 5.
This statement does not provide enough information to determine the remainder when x is divided by 3. For example, if x is 14, the remainder when divided by 3 is 2, but if x is 23, the remainder is 1. Therefore, statement 1 alone is insufficient.
Statement 2: The remainder when x is divided by 9 is 5.
This statement also does not provide enough information to determine the remainder when x is divided by 3. For example, if x is 23, the remainder when divided by 3 is 2, but if x is 32, the remainder is 1. Therefore, statement 2 alone is insufficient.
Combining both statements:
By considering both statements together, we can determine the value of x modulo 3. Since the remainder when x is divided by 9 is 5, we know that x is of the form 9k + 5, where k is an integer. Additionally, since the sum of the digits of x is 5, the possible values for x are 14, 23, 32, etc.
Analyzing the possible values of x modulo 3:
For x = 14, the remainder when divided by 3 is 2.
For x = 23, the remainder when divided by 3 is 2.
For x = 32, the remainder when divided by 3 is 2.
From the analysis above, we can see that regardless of the specific value of x, the remainder when x is divided by 3 is always 2. Therefore, by combining both statements, we can answer the question and statement 1 and 2 together are sufficient to answer the question.
Therefore, the correct answer is (C) Each statement can answer the question individually.
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What is the remainder when the two-digit, positive integer x is divided by 3 ?1) The sum of the digits of x is 5.?2) The remainder when x is divided by 9 is 5.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 'C'. Can you explain this answer?
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