Number Systems

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Q. Which of the following numbers is NOT divisible by 7?
  • A. 21
  • B. 28
  • C. 35
  • D. 40
Q. Which of the following numbers is NOT divisible by 8?
  • A. 64
  • B. 72
  • C. 80
  • D. 90
Q. Which of the following numbers is NOT divisible by 9?
  • A. 81
  • B. 72
  • C. 63
  • D. 50
Q. Which of the following numbers is the largest in base-6?
  • A. 54
  • B. 45
  • C. 63
  • D. 36
Q. Which of the following numbers is the largest in base-8?
  • A. 57
  • B. 70
  • C. 61
  • D. 72
Q. Which of the following numeral systems is most commonly used in digital electronics?
  • A. Decimal
  • B. Binary
  • C. Octal
  • D. Hexadecimal
Q. Which of the following numeral systems is not positional?
  • A. Decimal
  • B. Binary
  • C. Roman
  • D. Hexadecimal
Q. Which of the following pairs of numbers are congruent modulo 6?
  • A. 8 and 14
  • B. 10 and 16
  • C. 12 and 18
  • D. All of the above
Q. Which of the following pairs of numbers has a GCD of 1?
  • A. 8 and 12
  • B. 15 and 28
  • C. 9 and 27
  • D. 10 and 20
Q. Which of the following pairs of numbers has a greatest common divisor (GCD) of 1?
  • A. 8 and 12
  • B. 15 and 28
  • C. 9 and 27
  • D. 10 and 20
Q. Which of the following pairs of numbers has a least common multiple (LCM) of 36?
  • A. 6 and 12
  • B. 4 and 9
  • C. 3 and 18
  • D. 2 and 18
Q. Which of the following pairs of numbers has an HCF of 1? (2023)
  • A. 8 and 12
  • B. 15 and 28
  • C. 9 and 27
  • D. 14 and 21
Q. Which of the following pairs of numbers has an HCF of 6? (2023)
  • A. 12 and 18
  • B. 15 and 25
  • C. 10 and 20
  • D. 8 and 16
Q. Which of the following pairs of numbers has the greatest common factor (GCF) of 1?
  • A. 8 and 12
  • B. 15 and 28
  • C. 9 and 27
  • D. 14 and 21
Q. Which of the following statements about base systems is incorrect? (2023)
  • A. Base 2 is used in digital electronics.
  • B. Base 10 is the most widely used numeral system.
  • C. Base 16 can represent more values than base 10.
  • D. Base 8 is more efficient than base 2.
Q. Which of the following statements about factors and multiples is correct? (2023)
  • A. Every multiple of a number is also a factor of that number.
  • B. Factors of a number are always greater than the number itself.
  • C. A number can have an infinite number of multiples.
  • D. The smallest multiple of any number is always the number itself.
Q. Which of the following statements about factors and multiples is incorrect? (2023)
  • A. Every multiple of a number is greater than or equal to that number.
  • B. A number can have an infinite number of factors.
  • C. The product of two numbers is always a multiple of both.
  • D. A factor of a number is always greater than the number.
Q. Which of the following statements about factors is incorrect?
  • A. Every number has at least two factors.
  • B. Factors can be negative.
  • C. The number itself is always a factor.
  • D. Factors of a prime number are only 1 and the number itself.
Q. Which of the following statements about multiples is true?
  • A. The multiples of a number are infinite.
  • B. The multiples of a number are always positive.
  • C. The first multiple of any number is the number itself.
  • D. All of the above.
Q. Which of the following statements about number systems is true?
  • A. Base-10 is the only positional system
  • B. Base-2 can represent all integers
  • C. Base-16 is less efficient than base-10
  • D. Base-5 cannot represent fractions
Q. Which of the following statements about numeral systems is correct?
  • A. All numeral systems are based on the same principles.
  • B. Different numeral systems can represent the same value.
  • C. The decimal system is the only system used in mathematics.
  • D. Base systems are irrelevant in modern computing.
Q. Which of the following statements about numeral systems is incorrect?
  • A. Base-10 is the most commonly used system.
  • B. Base-16 is used in color codes in web design.
  • C. Base-2 is used in human languages.
  • D. Base-8 is less common than base-2.
Q. Which of the following statements about the decimal system is incorrect? (2023)
  • A. It is a base 10 system.
  • B. It uses digits from 0 to 9.
  • C. It is the only system used in mathematics.
  • D. It is widely used in everyday life.
Q. Which of the following statements about the number 30 is true?
  • A. It is a prime number
  • B. It has exactly 4 factors
  • C. It is a multiple of 5
  • D. It is not a composite number
Q. Which of the following statements can be inferred from the passage about the future of digital sum? (2023)
  • A. It will become obsolete with the rise of quantum computing.
  • B. It will continue to evolve and integrate with new technologies.
  • C. It is likely to be replaced by simpler methods.
  • D. It will remain unchanged for the foreseeable future.
Q. Which of the following statements can be inferred from the passage about the importance of digital sum? (2023)
  • A. Digital sum is obsolete in today's technology.
  • B. Understanding digital sum is crucial for data analysis.
  • C. Digital sum has no practical applications.
  • D. Only mathematicians need to understand digital sum.
Q. Which of the following statements is logically consistent with the definition of a multiple?
  • A. A multiple of a number is always greater than the number itself.
  • B. A multiple of a number can be negative.
  • C. A multiple of a number is always an integer.
  • D. All of the above.
Q. Which of the following statements is logically consistent with the definition of a factor?
  • A. A factor of a number is always greater than the number.
  • B. A factor of a number divides the number without leaving a remainder.
  • C. A factor can only be a prime number.
  • D. A factor is always a multiple of the number.
Q. Which of the following statements is logically consistent with the definition of multiples?
  • A. Every multiple of 7 is also a multiple of 14.
  • B. A number cannot be a multiple of itself.
  • C. The sum of two multiples of 3 is always a multiple of 3.
  • D. A multiple of 5 is never a multiple of 10.
Q. Which of the following statements is logically consistent with the properties of factors?
  • A. Every factor of a number is also a multiple of that number.
  • B. A number can have an infinite number of factors.
  • C. The smallest factor of any number is always 1.
  • D. All prime numbers have exactly two factors.
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