Q. If a number is a factor of 100, which of the following cannot be a factor?
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Solution
75 is not a factor of 100.
Correct Answer:
D
— 75
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Q. If a number is a factor of 24 and a multiple of 3, which of the following could be that number?
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Solution
6 is a factor of 24 and also a multiple of 3.
Correct Answer:
A
— 6
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Q. If a number is a factor of 24 and a multiple of 3, which of the following is the smallest such number?
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Solution
The smallest number that is both a factor of 24 and a multiple of 3 is 3.
Correct Answer:
A
— 3
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Q. If a number is a factor of 36 and a multiple of 4, which of the following numbers could it be?
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Solution
12 is a factor of 36 and also a multiple of 4, as 12 = 4 * 3.
Correct Answer:
B
— 12
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Q. If a number is a factor of 36, which of the following numbers is NOT a factor?
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Solution
All options are factors of 36 except for 9, which is a factor but not a multiple of 4.
Correct Answer:
D
— 9
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Q. If a number is a multiple of 15, which of the following cannot be true?
A.
It is a multiple of 3.
B.
It is a multiple of 5.
C.
It is an even number.
D.
It is a multiple of 30.
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Solution
A multiple of 15 is not guaranteed to be even, as 15 itself is odd.
Correct Answer:
C
— It is an even number.
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Q. If a number is a multiple of 15, which of the following must also be true?
A.
It is a multiple of 3.
B.
It is a multiple of 5.
C.
It is a multiple of 10.
D.
Both 1 and 2.
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Solution
Since 15 = 3 × 5, any multiple of 15 must also be a multiple of both 3 and 5.
Correct Answer:
D
— Both 1 and 2.
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Q. If a number is a multiple of 7 and 9, which of the following numbers could it be? (2023)
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Solution
63 is a multiple of both 7 and 9 (7*9=63), while the others are not.
Correct Answer:
A
— 63
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Q. If a number is a multiple of 8 and 12, which of the following is the smallest such number? (2023)
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Solution
The least common multiple of 8 and 12 is 24, making it the smallest number that is a multiple of both.
Correct Answer:
A
— 24
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Q. If a number is a multiple of 8, which of the following must also be true?
A.
It is a multiple of 4.
B.
It is a multiple of 2.
C.
It is an even number.
D.
All of the above.
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Solution
All statements are true as multiples of 8 are also multiples of 4, 2, and are even.
Correct Answer:
D
— All of the above.
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Q. If a number is a multiple of 9, which of the following must also be true?
A.
It is a multiple of 3.
B.
It is a multiple of 27.
C.
It is a prime number.
D.
It is an even number.
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Solution
All multiples of 9 are also multiples of 3.
Correct Answer:
A
— It is a multiple of 3.
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Q. If a number is a multiple of both 3 and 4, which of the following is guaranteed to be true?
A.
It is a multiple of 7.
B.
It is a multiple of 12.
C.
It is a multiple of 10.
D.
It is a multiple of 9.
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Solution
The least common multiple of 3 and 4 is 12, so any multiple of both must also be a multiple of 12.
Correct Answer:
B
— It is a multiple of 12.
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Q. If a number is a multiple of both 4 and 6, which of the following must also be true?
A.
It is a multiple of 12.
B.
It is a multiple of 24.
C.
It is a multiple of 10.
D.
It is a multiple of 8.
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Solution
The least common multiple of 4 and 6 is 12, so any number that is a multiple of both must also be a multiple of 12.
Correct Answer:
A
— It is a multiple of 12.
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Q. If a number is a multiple of both 4 and 6, which of the following must it also be a multiple of?
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Solution
The least common multiple of 4 and 6 is 12, so any multiple of both must also be a multiple of 12.
Correct Answer:
A
— 12
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Q. If a number is a multiple of both 5 and 7, which of the following is a possible value for this number?
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Solution
35 is a multiple of both 5 and 7 (5*7=35).
Correct Answer:
A
— 35
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Q. If a number is a multiple of both 5 and 7, which of the following is true?
A.
It is a multiple of 35.
B.
It is a multiple of 12.
C.
It is a multiple of 10.
D.
It is a multiple of 14.
Show solution
Solution
The least common multiple of 5 and 7 is 35, so any number that is a multiple of both must also be a multiple of 35.
Correct Answer:
A
— It is a multiple of 35.
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Q. If a number is a multiple of both 7 and 9, which of the following numbers is a possible candidate?
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Solution
63 is a multiple of both 7 (7x9) and 9 (9x7).
Correct Answer:
A
— 63
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Q. If a number is a multiple of both 8 and 14, which of the following numbers is guaranteed to be a factor of that number? (2023)
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Solution
Since any multiple of 8 and 14 must also be a multiple of their GCD, which includes 2 as a factor.
Correct Answer:
D
— 2
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Q. If a number is both a factor and a multiple of 6, which of the following could it be?
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Solution
The number 6 is a factor of itself and also a multiple of 6, making it the only valid option.
Correct Answer:
A
— 6
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Q. If a number is both a factor of 24 and a multiple of 3, which of the following could it be?
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Solution
12 is a factor of 24 and also a multiple of 3, as 12 = 3 * 4.
Correct Answer:
D
— 12
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Q. If a number is both a factor of 36 and a multiple of 4, which of the following could be that number?
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Solution
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Among these, 12 is a multiple of 4.
Correct Answer:
B
— 12
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Q. If a number is both a factor of 36 and a multiple of 6, which of the following is the largest such number?
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Solution
The factors of 36 that are also multiples of 6 are 6, 12, and 18. Among these, 18 is the largest.
Correct Answer:
C
— 18
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Q. If a number is both a multiple of 4 and a factor of 48, which of the following numbers could it be?
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Solution
The multiples of 4 that are also factors of 48 are 4, 8, 12, and 16. Among the options, 8 is valid.
Correct Answer:
A
— 8
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Q. If a number is congruent to 0 modulo 6, which of the following could be a possible value?
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Solution
A number congruent to 0 mod 6 must be a multiple of 6. 12 is a multiple of 6.
Correct Answer:
B
— 12
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Q. If a number is divided by 11 and gives a remainder of 7, what is the remainder when this number is divided by 3? (2023)
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Solution
The number can be expressed as 11k + 7. When divided by 3, the remainder is 1 (7 % 3 = 1).
Correct Answer:
B
— 1
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Q. If a number is divided by 12 and gives a remainder of 7, what is the possible range of this number? (2023)
A.
7 to 19
B.
19 to 31
C.
31 to 43
D.
43 to 55
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Solution
The number can be expressed as 12k + 7, where k is a non-negative integer. For k=0, the number is 7; for k=1, it is 19.
Correct Answer:
A
— 7 to 19
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Q. If a number is divided by 12 and gives a remainder of 7, what will be the remainder when this number is divided by 3?
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Solution
Since 7 divided by 3 gives a remainder of 1, the answer is 1.
Correct Answer:
B
— 1
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Q. If a number is divided by 12 and gives a remainder of 7, what will be the remainder when the same number is divided by 3? (2023)
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Solution
The number can be expressed as 12k + 7. When divided by 3, the remainder is 1 (7 % 3 = 1).
Correct Answer:
B
— 1
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Q. If a number is divided by 12 and gives a remainder of 7, which of the following numbers could it be?
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Solution
23 gives a remainder of 7 when divided by 12 (12*1 + 7 = 19).
Correct Answer:
B
— 23
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Q. If a number is divided by 12 and leaves a remainder of 7, what is the remainder when the same number is divided by 3? (2023)
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Solution
Since 7 mod 3 = 1, the remainder when the number is divided by 3 is 1.
Correct Answer:
B
— 1
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Showing 91 to 120 of 618 (21 Pages)
Number Systems MCQ & Objective Questions
Understanding number systems is crucial for students preparing for various exams in India. Mastering this topic not only enhances your mathematical skills but also boosts your confidence in tackling objective questions. Practicing MCQs related to number systems helps in identifying important questions and solidifying your exam preparation strategy.
What You Will Practise Here
Types of number systems: Natural, Whole, Integers, Rational, and Irrational numbers
Conversion between different number systems: Decimal, Binary, Octal, and Hexadecimal
Arithmetic operations in various number systems
Properties of numbers: Even, Odd, Prime, and Composite numbers
Understanding place value and significance in different bases
Common number system problems and their solutions
Real-world applications of number systems in technology and computing
Exam Relevance
Number systems are a fundamental part of the curriculum for CBSE, State Boards, NEET, and JEE. Questions related to this topic frequently appear in both objective and subjective formats. Students can expect to encounter problems that require conversions between bases, operations on numbers in different systems, and theoretical questions about properties of numbers. Familiarity with common question patterns will significantly enhance your performance in these exams.
Common Mistakes Students Make
Confusing the conversion process between different number systems
Overlooking the significance of place value in non-decimal systems
Misapplying arithmetic operations when dealing with binary or hexadecimal numbers
Ignoring the properties of numbers, leading to incorrect answers in problem-solving
FAQs
Question: What are the different types of number systems I should know for exams?Answer: You should be familiar with natural numbers, whole numbers, integers, rational numbers, and irrational numbers, as these are commonly tested.
Question: How can I effectively practice number systems for my exams?Answer: Regularly solving Number Systems MCQ questions and objective questions with answers will help reinforce your understanding and improve your speed.
Start solving practice MCQs today to test your understanding of number systems and boost your exam readiness. Remember, consistent practice is the key to success!
