Divisibility rule of 2: The number should be even or the last digit should be divisible by 2
Divisibility rule of 3: The sum of all the digits of the number should be divisible by 3


I. 234,124,422
Last digit -2. This is divisible by 2
Sum of digits = 24. This is divisible by 3
Hence the number is divisible by both 2 and 3

II. 88,865,544,264
Last digit -2. This is divisible by 2
Sum of digits = 60. This is divisible by 3
Hence the number is divisible by both 2 and 3

III. 5,555,554,673
Last digit - 3. This is not divisible by 2.

Hence only I and II are divisible by both 2 and 3
Correct Option: B

III. is not divisible by 2 since the last digit is odd so we eliminate option C and E, we are left with option A, B and D

Among option I and II lets check the divisibility of 3

I. is divisible by 3 since sum of the digits is 24 , which is divisible by 3
II. is divisible by 3 since sum of the digits is 60 , which is divisible by 3

Thus among the given options only (B) holds true.

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