Number System Worksheet-4 featuring multiple choice questions on mathematical concepts like odd/even numbers, divisibility by 3 and 6, and order of operations.

Let me work through each question carefully.

Question 1: The sum of two odd numbers is ___ an even number.
- Odd + Odd = Even (e.g., 3+5=8, 7+9=16)
- This is ALWAYS true.
- Answer: (A) Always

Question 2: ___ is the key to find that the number is multiple of 3 or not.
- Divisibility rule for 3: Sum of digits must be divisible by 3.
- The smallest odd natural number is 1, second smallest odd natural number is 3.
- So option (B): "The sum of all the digits of a number should be divisible by second smallest odd natural number" = divisible by 3. ✓
- Answer: (B)

Question 3: The number is divisible by 6. So; it is divisible by ___ and ___ also.
- 6 = 2 × 3
- If divisible by 6, then divisible by both 2 and 3.
- Answer: (A) 2, 3

Question 4: If 24 is divisible by 4 so, we can say that ___ is also divisible by 4.
- Divisibility rule for 4: Last two digits must be divisible by 4.
- Let me check each option's last two digits:
- (A) 245123 → last two digits: 23 → 23÷4 = 5.75
- (B) 251234 → last two digits: 34 → 34÷4 = 8.5 ✗
- (C) 512324 → last two digits: 24 → 24÷4 = 6 ✓
- (D) 451322 → last two digits: 22 → 22÷4 = 5.5 ✗
- Answer: (C) 512324

Question 5: In the order of operation, the predecessor of multiplication is ___ operation.
- Order of operations: Division/Multiplication (same level), then Addition/Subtraction (same level).
- Wait, let me think about this differently. In PEMDAS/BODMAS:
- B/P (Brackets/Parentheses)
- O/E (Orders/Exponents)
- D/M (Division/Multiplication) - left to right
- A/S (Addition/Subtraction) - left to right
- The "predecessor" means what comes before multiplication in the order.
- Actually, division and multiplication are at the same level. But if we consider the traditional order where division comes before multiplication in some conventions...
- Hmm, but actually in standard order, division and multiplication are equal priority, done left to right.
- Wait, let me reconsider. In BODMAS: Brackets, Orders, Division, Multiplication, Addition, Subtraction. So Division comes before Multiplication.
- Answer: (A) Division

Question 6: Among four operators, ___ is used at the last in order of operation.
- BODMAS: Brackets, Orders, Division, Multiplication, Addition, Subtraction
- Subtraction is last.
- Answer: (B) −

Question 7: 5986236 is divisible by ___ because ___ is divisible by 4.
- Divisibility by 4: Check last two digits.
- Last two digits of 5986236: 36
- 36 ÷ 4 = 9 ✓
- So 5986236 is divisible by 4 because 36 is divisible by 4.
- Answer: (C) 4, 36

Question 8: The digit at units place is 5 and the sum of all the digits is a factor of 3, we can say that the number is divisible by ___.
- Units digit is 5 → divisible by 5
- Sum of digits is a factor of 3 → divisible by 3
- So the number is divisible by both 5 AND 3.
- Answer: (B) '5 and 3' both

Let me verify my answers once more:
1. (A) Always - correct
2. (B) - correct (second smallest odd natural number = 3)
3. (A) 2, 3 - correct
4. (C) 512324 - correct (last two digits 24, divisible by 4)
5. (A) Division - correct (in BODMAS, D comes before M)
6. (B) − - correct (subtraction is last in BODMAS)
7. (C) 4, 36 - correct
8. (B) '5 and 3' both