MCQ
Number system, simplification, HCF and LCM MCQ - Practice Questions with Answers
Solve 10 Number system, simplification, HCF and LCM questions for RAS/RPSC preparation.
Practice questions
Q1Assertion (A): For 2/3 and 4/9, the HCF is 2/9. Reason (R): For fractions, HCF = HCF of numerators ÷ LCM of denominators. Choose the correct answer.
There is a separate rule for fractions: HCF of fractions equals HCF of numerators divided by LCM of denominators. For 2/3 and 4/9, the numerators are 2 and 4, whose HCF is 2. The denominators are 3 and 9, whose LCM is 9. Therefore the HCF is 2/9. The reason is not just true; it is the exact rule that explains why the assertion is true.
Q2Assertion (A): For two positive integers a and b, HCF(a, b) x LCM(a, b) = a x b. Reason (R): this relation should be used directly only after confirming that there are exactly two positive integers.
There is the relation HCF(a, b) x LCM(a, b) = a x b for two positive integers a and b. They also warn that the relation is powerful but narrow, and should be used directly only when there are exactly two positive integers. That limit matters because the same direct product relation is not stated for three or more numbers. Thus the formula is correct, and the reason explains the condition under which the assertion can be safely used.
Q3Which of the following is the least whole number according to the number-system map?
Number families differ by what values they allow. Natural numbers begin at 1 and are used for counting. Whole numbers are formed by adding 0 to the natural numbers. Integers then add negative numbers as well. Therefore the least whole number is 0. The value 1 is only the least natural number, while -1 belongs to integers but is not a whole number.
Q4Statement 1: In 24 - 6 ÷ 3 × 2 + 5, division and multiplication must be solved from left to right. Statement 2: The value of 24 - 6 ÷ 3 × 2 + 5 is 25. Which of the following is correct?
Simplification tests order, not only arithmetic. In BODMAS, division and multiplication have equal priority and are solved from left to right. For 24 - 6 ÷ 3 × 2 + 5, first calculate 6 ÷ 3 = 2, then 2 × 2 = 4. The expression becomes 24 - 4 + 5. Addition and subtraction are then handled from left to right, giving 20 + 5 = 25. Therefore both statements are accurate.
Q5Identify the correct statement about the divisibility of 7,326.
There are separate tests for different divisors. For 11, subtract the sums of digits in alternate positions; if the difference is 0 or a multiple of 11, the number is divisible by 11. In 7,326, the alternate sums are 7 + 2 = 9 and 3 + 6 = 9. Their difference is 0, so 7,326 is divisible by 11. The digit sum 18 supports divisibility by 3 and 9, not the 11-test.
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More questions
6Match List I with List II. List I: 1. HCF by prime factorisation 2. LCM by prime factorisation 3. HCF of fractions 4. LCM of fractions List II: a. HCF of numerators / LCM of denominators b. Every prime factor with the greatest power c. LCM of numerators / HCF of denominators d. Common prime factors with the smallest powers
7Statement 1: For divisibility by 9, the sum of the digits must be divisible by 9. Statement 2: For divisibility by 11, the difference between the sums of alternate digits must be 0 or a multiple of 11. Which of the following is correct?
8Using the BODMAS rule given find the value of 24 - 6 ÷ 3 x 2 + 5.
9Which of the following is a rational number?
10List I: 1. 12, 15 and 20 seconds 2. First time together again 3. Least number leaving remainder 2 when divided by 3, 4 and 5 List II: P. LCM + 2 Q. 60 seconds R. LCM Which matching is correct?