Which one of the following statements is/are true?
A. 48713280 is divisible by 11
B. 59761543 is not divisible by 3
C. 342221319 is divisible by 99
D. 10050432 is not divisible by 8
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A, B and C only
Each statement is checked with its divisibility rule.
A. 48713280 is divisible by 11 Correct. A number is divisible by 11 when the difference between the sums of its alternate digits is 0 or a multiple of 11.
Digits in the 1st, 3rd, 5th and 7th places from the right: \(0+2+1+8=11\)
Digits in the 2nd, 4th, 6th and 8th places: \(8+3+7+4=22\)
Difference \(22-11=11\), a multiple of 11
B. 59761543 is not divisible by 3 Correct. The digit sum is \(5+9+7+6+1+5+4+3=40\), which is not a multiple of 3, so the number is not divisible by 3.
C. 342221319 is divisible by 99 Correct. \(99=9\times11\), and 9 and 11 have no common factor, so the number must be divisible by both 9 and 11.
Digit sum \(3+4+2+2+2+1+3+1+9=27\), a multiple of 9
Alternate sums: \(9+3+2+2+3=19\) and \(1+1+2+4=8\); difference \(19-8=11\), a multiple of 11
D. 10050432 is not divisible by 8 Incorrect. A number is divisible by 8 when its last three digits are. Here \(432=8\times54\), so the number is divisible by 8.
Tip: For 99, add the number in pairs of digits from the right: \(19+13+22+42+3=99\). If this sum is divisible by 99, so is the number.