Question 1

Which method applies to this question?

Accepted Answer

Use divisibility rules or modular arithmetic, reducing large values before calculation.

Question 2

What is the verified answer?

Accepted Answer

1, option C.

Question 3

What is a common error?

Accepted Answer

Changing operation order, losing a sign, or simplifying a factor where cancellation is invalid.

Question 4

How can the result be checked?

Accepted Answer

Substitute it back, estimate its magnitude, or recompute using an equivalent form.

Question 5

What is Number System in mathematics and what types of numbers are important for exams?

Accepted Answer

Number System covers Natural Numbers (1,2,3), Whole Numbers (0,1,2,3), Integers, Rational Numbers (p/q form), Irrational Numbers (like pi and root 2), and Real Numbers. For competitive exams like SSC CGL and IBPS, focus on: divisibility rules, LCM and HCF, factors, prime numbers, and unit digit calculations.

Question 6

What are the important divisibility rules in Number System?

Accepted Answer

Divisibility rules: Divisible by 2 - last digit even. By 3 - sum of digits divisible by 3. By 4 - last two digits divisible by 4. By 5 - last digit 0 or 5. By 6 - divisible by both 2 and 3. By 8 - last three digits divisible by 8. By 9 - sum of digits divisible by 9. By 11 - difference of alternating digit sums divisible by 11. Mastering these rules helps solve Number System questions faster in competitive exams.

Question 7

What is LCM and HCF and how are they calculated?

Accepted Answer

LCM (Least Common Multiple) is the smallest number divisible by all given numbers. HCF (Highest Common Factor) is the largest number that divides all given numbers. Methods: For HCF - prime factorization or Euclidean algorithm. For LCM - prime factorization. Key relationship: LCM x HCF = Product of two numbers (only for two numbers). LCM and HCF questions appear in all major competitive exams.

Question 8

How to find the unit digit of large powers?

Accepted Answer

Unit digits follow cyclicity patterns: For 2 - cycle is 2,4,8,6 (length 4). For 3 - cycle is 3,9,7,1 (length 4). For 4 - cycle is 4,6 (length 2). For 7 - cycle is 7,9,3,1 (length 4). For 8 - cycle is 8,4,2,6 (length 4). For 0,1,5,6 - unit digit is always 0,1,5,6 regardless of power. Divide the power by the cycle length and use the remainder to find the unit digit.

Question 9

What are prime numbers and composite numbers up to 100?

Accepted Answer

Prime numbers up to 100 (25 total): 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. All other numbers (except 1) are composite. 1 is neither prime nor composite. 2 is the only even prime. To check if a number N is prime, check divisibility only up to the square root of N.

What least number must be added to 1056 so that the sum is completely divisible by 23?

Explanation

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