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.
A number is divisible by 18 when it is divisible by both 2 and 9, because \(18=2\times9\) and 2 and 9 have no common factor. A number is divisible by 11 when the difference between the sums of its alternate digits is 0 or a multiple of 11.
Statement (I): 2469385422 is divisible by 18. Correct.
The last digit is 2, so the number is even: divisible by 2
Sum of the digits \(=2+4+6+9+3+8+5+4+2+2=45\), a multiple of 9: divisible by 9
Statement (II): 3475824638 is divisible by 11. Correct.
Digits in the odd places from the right: \(8+6+2+5+4=25\)
Digits in the even places from the right: \(3+4+8+7+3=25\)
Difference \(=25-25=0\), so the number is divisible by 11