Q. Which of the following numbers is NOT divisible by 7?
Solution
40 is not divisible by 7, while 21, 28, and 35 are all multiples of 7.
Correct Answer:
D
— 40
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Q. Which of the following numbers is NOT divisible by 8?
Solution
A number is divisible by 8 if the number formed by its last three digits is divisible by 8. 90 is not divisible by 8.
Correct Answer:
D
— 90
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Q. Which of the following numbers is NOT divisible by 9?
Solution
A number is divisible by 9 if the sum of its digits is divisible by 9. The sum of the digits of 50 (5 + 0 = 5) is not divisible by 9.
Correct Answer:
D
— 50
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Q. Which of the following numbers is the largest in base-6?
Solution
In decimal, '54' = 32, '45' = 29, '63' = 39, '36' = 22. '63' is the largest.
Correct Answer:
C
— 63
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Q. Which of the following numbers is the largest in base-8?
Solution
'72' in base-8 is 58 in decimal, which is larger than the others.
Correct Answer:
D
— 72
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Q. Which of the following numeral systems is most commonly used in digital electronics?
-
A.
Decimal
-
B.
Binary
-
C.
Octal
-
D.
Hexadecimal
Solution
The binary system is the most commonly used in digital electronics due to its two-state nature.
Correct Answer:
B
— Binary
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Q. Which of the following numeral systems is not positional?
-
A.
Decimal
-
B.
Binary
-
C.
Roman
-
D.
Hexadecimal
Solution
The Roman numeral system is not positional, as it does not use place value to determine the value of digits.
Correct Answer:
C
— Roman
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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
Solution
All pairs have the same remainder when divided by 6: 8 mod 6 = 2, 14 mod 6 = 2; 10 mod 6 = 4, 16 mod 6 = 4; 12 mod 6 = 0, 18 mod 6 = 0.
Correct Answer:
D
— All of the above
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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
Solution
15 and 28 have no common factors other than 1, making their GCD equal to 1.
Correct Answer:
B
— 15 and 28
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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
Solution
15 and 28 are coprime, meaning their GCD is 1.
Correct Answer:
B
— 15 and 28
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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
Solution
The LCM of 4 and 9 is 36.
Correct Answer:
B
— 4 and 9
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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
Solution
The HCF of 15 and 28 is 1, making them coprime.
Correct Answer:
B
— 15 and 28
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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
Solution
The HCF of 12 and 18 is 6, as both numbers are divisible by 6, while the other pairs have higher HCFs.
Correct Answer:
A
— 12 and 18
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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
Solution
The GCF of 15 and 28 is 1, making them coprime, while the other pairs share common factors.
Correct Answer:
B
— 15 and 28
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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.
Solution
Base 8 (octal) is not more efficient than base 2 (binary); it simply represents values in a different way.
Correct Answer:
D
— Base 8 is more efficient than base 2.
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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.
Solution
A number can have an infinite number of multiples, as you can keep adding the number to itself indefinitely.
Correct Answer:
C
— A number can have an infinite number of multiples.
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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.
Solution
A factor of a number is always less than or equal to that number, making the last statement incorrect.
Correct Answer:
D
— A factor of a number is always greater than the number.
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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.
Solution
Every number has at least two factors: 1 and the number itself, but some numbers can have more than two factors.
Correct Answer:
A
— Every number has at least two factors.
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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.
Solution
All statements are true regarding multiples.
Correct Answer:
D
— All of the above.
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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
Solution
Base-2 can represent all integers, as it is a complete positional system.
Correct Answer:
B
— Base-2 can represent all integers
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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.
Solution
Different numeral systems can represent the same value, such as the decimal 10 and binary 1010.
Correct Answer:
B
— Different numeral systems can represent the same value.
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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.
Solution
Base-2 (binary) is not used in human languages; it is primarily used in computing.
Correct Answer:
C
— Base-2 is used in human languages.
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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.
Solution
The statement that the decimal system is the only system used in mathematics is incorrect; other systems like binary and hexadecimal are also used.
Correct Answer:
C
— It is the only system used in mathematics.
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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
Solution
30 is a multiple of 5, as it can be expressed as 5 multiplied by 6.
Correct Answer:
C
— It is a multiple of 5
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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.
Solution
The passage suggests that digital sum will evolve and integrate with emerging technologies, indicating a promising future.
Correct Answer:
B
— It will continue to evolve and integrate with new technologies.
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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.
Solution
The passage suggests that a solid understanding of digital sum is essential for effective data analysis in various fields.
Correct Answer:
B
— Understanding digital sum is crucial for data analysis.
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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.
Solution
All statements are true; multiples can be negative, can be equal to the number, and are always integers.
Correct Answer:
D
— All of the above.
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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.
Solution
By definition, a factor divides the number evenly, leaving no remainder.
Correct Answer:
B
— A factor of a number divides the number without leaving a remainder.
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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.
Solution
The sum of two multiples of 3 is always a multiple of 3, as multiples of a number are closed under addition.
Correct Answer:
C
— The sum of two multiples of 3 is always a multiple of 3.
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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.
Solution
The smallest factor of any number is always 1, as 1 divides every integer.
Correct Answer:
C
— The smallest factor of any number is always 1.
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