Q. What is the product of '12' and '3' in base-4?
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Solution
'12' (base 4) is 6 in decimal, and '3' is 3. Their product is 18, which is '40' in base 4.
Correct Answer:
B
— 40
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Q. What is the product of the base-5 numbers 23 and 14 in base-10?
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Solution
Convert 23 (base-5) to decimal: 2*5^1 + 3*5^0 = 10 + 3 = 13. Convert 14 (base-5) to decimal: 1*5^1 + 4*5^0 = 5 + 4 = 9. The product is 13 * 9 = 117.
Correct Answer:
B
— 70
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Q. What is the product of the numbers 12 (base 10) and 3 (base 4) when both are converted to decimal?
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Solution
Convert 3 (base 4) to decimal: 3*4^0 = 3. The product is 12 * 3 = 36.
Correct Answer:
A
— 36
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Q. What is the relationship between digital sum and data integrity as mentioned in the passage? (2023)
A.
Digital sum enhances data integrity.
B.
Digital sum has no impact on data integrity.
C.
Digital sum complicates data integrity.
D.
Digital sum is irrelevant to data integrity.
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Solution
The passage states that digital sum plays a crucial role in enhancing data integrity, ensuring accurate data processing.
Correct Answer:
A
— Digital sum enhances data integrity.
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Q. What is the relationship between digital sum and data processing as described in the passage? (2023)
A.
Digital sum is a minor aspect of data processing.
B.
Digital sum enhances the efficiency of data processing.
C.
Digital sum complicates data processing.
D.
Digital sum is irrelevant to data processing.
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Solution
The passage indicates that digital sum enhances the efficiency of data processing, making it a significant aspect.
Correct Answer:
B
— Digital sum enhances the efficiency of data processing.
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Q. What is the relationship between digital sum and error detection as mentioned in the passage? (2023)
A.
Digital sum is irrelevant to error detection.
B.
Digital sum can enhance error detection methods.
C.
Error detection methods are based solely on digital sum.
D.
Digital sum complicates error detection processes.
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Solution
The passage indicates that digital sum plays a significant role in improving error detection techniques.
Correct Answer:
B
— Digital sum can enhance error detection methods.
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Q. What is the relationship between digital sum and traditional calculation methods as described in the passage?
A.
Digital sum is a direct replacement for traditional methods.
B.
Digital sum complements traditional methods.
C.
Digital sum is less efficient than traditional methods.
D.
Digital sum is unrelated to traditional methods.
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Solution
The passage indicates that digital sum complements traditional methods by providing additional efficiency.
Correct Answer:
B
— Digital sum complements traditional methods.
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Q. What is the remainder when 1000 is divided by 6?
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Solution
1000 divided by 6 gives a quotient of 166 and a remainder of 4.
Correct Answer:
A
— 4
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Q. What is the remainder when 1000 is divided by 9? (2023)
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Solution
1000 divided by 9 gives a remainder of 1 (1000 = 9*111 + 1).
Correct Answer:
B
— 2
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Q. What is the remainder when 123456 is divided by 10? (2023)
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Solution
The remainder when a number is divided by 10 is the last digit of the number, which is 6.
Correct Answer:
D
— 6
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Q. What is the remainder when 123456 is divided by 11? (2023)
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Solution
123456 mod 11 = 0, as 123456 is divisible by 11.
Correct Answer:
A
— 0
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Q. What is the remainder when 144 is divided by 11?
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Solution
144 divided by 11 gives a remainder of 1.
Correct Answer:
A
— 0
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Q. What is the remainder when 145 is divided by 12?
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Solution
145 divided by 12 gives a remainder of 1.
Correct Answer:
B
— 2
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Q. What is the remainder when 250 is divided by 7?
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Solution
250 divided by 7 gives a quotient of 35 and a remainder of 5.
Correct Answer:
A
— 1
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Q. What is the remainder when 256 is divided by 11?
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Solution
256 divided by 11 gives a quotient of 23 and a remainder of 3.
Correct Answer:
A
— 2
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Q. What is the remainder when 256 is divided by 7?
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Solution
256 divided by 7 gives a quotient of 36 and a remainder of 4.
Correct Answer:
B
— 4
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Q. What is the remainder when 256 is divided by 9?
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Solution
256 divided by 9 gives a quotient of 28 and a remainder of 4.
Correct Answer:
B
— 2
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Q. What is the remainder when 987654 is divided by 9?
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Solution
The sum of the digits of 987654 is 39, which is divisible by 9, hence the remainder is 0.
Correct Answer:
A
— 0
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Q. What is the remainder when 987654321 is divided by 9? (2023)
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Solution
The remainder when a number is divided by 9 can be found by summing its digits. The sum of the digits of 987654321 is 45, which is divisible by 9, hence the remainder is 0.
Correct Answer:
A
— 0
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Q. What is the result of (10 + 15) mod 7?
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Solution
(10 + 15) = 25; 25 mod 7 = 4.
Correct Answer:
B
— 2
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Q. What is the result of (15 + 10) mod 12?
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Solution
(15 + 10) = 25; 25 mod 12 = 1.
Correct Answer:
A
— 5
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Q. What is the result of (3 * 4) mod 5?
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Solution
Calculating (3 * 4) = 12, and then 12 mod 5 = 2.
Correct Answer:
C
— 4
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Q. What is the result of 10 mod 3?
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Solution
10 divided by 3 gives a remainder of 1, so 10 mod 3 = 1.
Correct Answer:
B
— 2
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Q. What is the result of adding the binary numbers 1011 and 1101?
A.
11000
B.
10100
C.
10010
D.
11110
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Solution
Adding 1011 and 1101 in binary results in 11110.
Correct Answer:
D
— 11110
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Q. What is the rule for a number to be divisible by 8?
A.
It must end in 0
B.
The last three digits must form a number divisible by 8
C.
It must be even
D.
The sum of the digits must be even
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Solution
A number is divisible by 8 if the last three digits form a number that is divisible by 8.
Correct Answer:
B
— The last three digits must form a number divisible by 8
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Q. What is the rule for determining if a number is divisible by 11?
A.
The sum of the digits must be even
B.
The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be divisible by 11
C.
It must end in 1
D.
It must be a prime number
Show solution
Solution
A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is divisible by 11.
Correct Answer:
B
— The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be divisible by 11
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Q. What is the rule for determining if a number is divisible by 7?
A.
The last digit must be 0
B.
Double the last digit and subtract it from the rest of the number
C.
The sum of the digits must be divisible by 7
D.
The number must end in 7
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Solution
To check if a number is divisible by 7, you can double the last digit and subtract it from the rest of the number; if the result is divisible by 7, then the original number is as well.
Correct Answer:
B
— Double the last digit and subtract it from the rest of the number
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Q. What is the significance of digital sum in data analysis as mentioned in the passage? (2023)
A.
It reduces the complexity of data sets.
B.
It enhances the accuracy of data interpretation.
C.
It simplifies the process of data storage.
D.
It increases the speed of data processing.
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Solution
The passage highlights that digital sum plays a crucial role in enhancing the accuracy of data interpretation.
Correct Answer:
B
— It enhances the accuracy of data interpretation.
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Q. What is the significance of digital sum in data processing as mentioned in the passage? (2023)
A.
It simplifies the data entry process.
B.
It ensures the integrity of data during transmission.
C.
It reduces the need for manual calculations.
D.
It allows for faster data retrieval.
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Solution
The passage highlights that digital sum plays a crucial role in ensuring data integrity during transmission, making it significant in data processing.
Correct Answer:
B
— It ensures the integrity of data during transmission.
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Q. What is the significance of digital sum in error detection as mentioned in the passage? (2023)
A.
It simplifies the error detection process.
B.
It is the only method used for error detection.
C.
It increases the likelihood of errors.
D.
It is irrelevant to error detection.
Show solution
Solution
The passage highlights that digital sum simplifies the error detection process, making it significant.
Correct Answer:
A
— It simplifies the error detection process.
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