Given below are two statements:
Statement (I): 2469385422 is divisible by 18.
Statement (II): 3475824638 is divisible by 11.
In light of the above statements, choose the most appropriate answer from the options given below.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Both Statements are true.
We will check each statement using divisibility rules.
Statement (I): 2469385422 divisible by 18
- A number is divisible by 18 if it is divisible by 2 and 9.
Step 1: Divisible by 2 → last digit = 2 → divisible
Step 2: Divisible by 9 → sum of digits divisible by 9
Digits: 2 + 4 + 6 + 9 + 3 + 8 + 5 + 4 + 2 + 2 = 45
45 ÷ 9 = 5 → divisible
Statement (I) is true
Statement (II): 3475824638 divisible by 11
- Rule: Difference between sum of odd-position digits and even-position digits divisible by 11
Positions: 1 2 3 4 5 6 7 8 9 10
Digits: 3 4 7 5 8 2 4 6 3 8
- Sum of digits at odd positions (1,3,5,7,9) = 3+7+8+4+3 = 25
- Sum of digits at even positions (2,4,6,8,10) = 4+5+2+6+8 = 25
Difference = 25 - 25 = 0 → divisible by 11
Statement (II) is true