Q. Which of the following statements is true regarding divisibility by 5?
A.
A number must end in 0 or 5
B.
A number must be even
C.
A number must be a multiple of 10
D.
A number must be a prime number
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Solution
A number is divisible by 5 if it ends in either 0 or 5.
Correct Answer:
A
— A number must end in 0 or 5
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Q. Which of the following statements is true regarding divisibility by 9?
A.
The number must end in 0
B.
The sum of the digits must be divisible by 9
C.
The number must be even
D.
The last digit must be 9
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Solution
A number is divisible by 9 if the sum of its digits is divisible by 9.
Correct Answer:
B
— The sum of the digits must be divisible by 9
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Q. Which of the following statements is true regarding factors and multiples?
A.
All factors are multiples.
B.
All multiples are factors.
C.
Factors are always less than multiples.
D.
Multiples are always less than factors.
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Solution
Factors of a number are the integers that can divide that number without leaving a remainder, while multiples are the result of multiplying that number by an integer. Hence, factors are always less than or equal to multiples.
Correct Answer:
C
— Factors are always less than multiples.
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Q. Which of the following statements is true regarding HCF and LCM? (2023)
A.
HCF is always greater than LCM
B.
HCF and LCM can be equal
C.
HCF is the product of prime factors
D.
LCM is always less than HCF
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Solution
HCF and LCM can be equal when both numbers are the same.
Correct Answer:
B
— HCF and LCM can be equal
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Q. Which of the following statements is true regarding modular arithmetic?
A.
It is only applicable to integers.
B.
It can be used for real numbers.
C.
It is not useful in computer science.
D.
It is only used in cryptography.
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Solution
Modular arithmetic is primarily applicable to integers, making the first statement true.
Correct Answer:
A
— It is only applicable to integers.
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Q. Which of the following statements is true regarding prime numbers? (2023)
A.
Every prime number is a multiple of 1.
B.
Prime numbers have exactly two distinct positive divisors.
C.
All even numbers are prime.
D.
The number 1 is a prime number.
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Solution
Prime numbers are defined as having exactly two distinct positive divisors: 1 and the number itself.
Correct Answer:
B
— Prime numbers have exactly two distinct positive divisors.
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Q. Which of the following statements is true regarding the base-8 number system?
A.
It uses digits 0-7
B.
It uses digits 0-8
C.
It is a binary system
D.
It is a hexadecimal system
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Solution
The base-8 number system, also known as octal, uses digits from 0 to 7. Therefore, the correct statement is that it uses digits 0-7.
Correct Answer:
A
— It uses digits 0-7
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Q. Which of the following statements is true regarding the expression (a + b) mod n?
A.
It is always equal to (a mod n) + (b mod n)
B.
It is always equal to (a mod n) - (b mod n)
C.
It is always equal to (a mod n) * (b mod n)
D.
It is always equal to (a mod n) / (b mod n)
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Solution
The property of modular arithmetic states that (a + b) mod n = [(a mod n) + (b mod n)] mod n.
Correct Answer:
A
— It is always equal to (a mod n) + (b mod n)
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Q. Which of the following statements is true regarding the factors of 36?
A.
36 has 8 factors
B.
36 is a prime number
C.
All factors of 36 are even
D.
36 is a perfect square
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Solution
36 is indeed a perfect square as it can be expressed as 6 x 6.
Correct Answer:
D
— 36 is a perfect square
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Q. Which of the following statements is true regarding the HCF and LCM of two numbers? (2023)
A.
HCF is always greater than LCM
B.
HCF is the product of the numbers
C.
LCM is always less than the product of the numbers
D.
HCF * LCM = Product of the numbers
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Solution
The correct statement is that HCF * LCM = Product of the numbers.
Correct Answer:
D
— HCF * LCM = Product of the numbers
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Q. Which of the following statements is true regarding the number '0' in any number system?
A.
It is always positive
B.
It is always negative
C.
It is neither positive nor negative
D.
It is undefined
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Solution
Zero is neither positive nor negative in any number system.
Correct Answer:
C
— It is neither positive nor negative
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Q. Which of the following statements is true regarding the number '100' in base 3?
A.
It is equal to 9
B.
It is equal to 10
C.
It is equal to 12
D.
It is equal to 27
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Solution
'100' in base 3 is calculated as 1*3^2 + 0*3^1 + 0*3^0 = 9.
Correct Answer:
A
— It is equal to 9
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Q. Which of the following statements is true regarding the number 'A' in hexadecimal?
A.
A is equal to 10
B.
A is equal to 11
C.
A is equal to 12
D.
A is equal to 13
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Solution
In hexadecimal, 'A' represents the decimal value 10.
Correct Answer:
A
— A is equal to 10
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Q. Which of the following statements is true regarding the number 36?
A.
It has exactly 9 factors.
B.
It is a prime number.
C.
It is a perfect square.
D.
It is a multiple of 10.
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Solution
36 is a perfect square as it can be expressed as 6 * 6.
Correct Answer:
C
— It is a perfect square.
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Q. Which of the following statements is true regarding the numbers 8, 12, and 16?
A.
8 is a multiple of 12
B.
12 is a factor of 16
C.
16 is a multiple of 8
D.
12 is a multiple of 8
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Solution
16 is a multiple of 8, as 16 = 8 * 2.
Correct Answer:
C
— 16 is a multiple of 8
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Q. Which of the following words best captures the essence of 'digital sum' as used in the passage? (2023)
A.
Calculation.
B.
Innovation.
C.
Complexity.
D.
Obsolescence.
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Solution
The word 'calculation' best captures the essence of 'digital sum', as it fundamentally involves the process of adding digits.
Correct Answer:
A
— Calculation.
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Q. Which of the following words best captures the essence of digital sum as described in the passage? (2023)
A.
Obsolete.
B.
Innovative.
C.
Complicated.
D.
Irrelevant.
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Solution
The passage describes digital sum as innovative, reflecting its role in advancing technology.
Correct Answer:
B
— Innovative.
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Q. Which vocabulary word in the passage best describes the nature of digital sum?
A.
Obsolete.
B.
Innovative.
C.
Complicated.
D.
Redundant.
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Solution
The passage characterizes digital sum as innovative, highlighting its modern applications.
Correct Answer:
B
— Innovative.
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