Divisibility

[jkandas]

Question from MGMAT flash cards:

If the ones digit of an integer is 0, then which (nonzero) one"digit integers is the integer definitely NOT divisible by?

Answer: None
It could be divisible by any of the one-digit integers! (Except
for 0; dividing by 0 is always off limits.)

To verify, take any nonzero one-digit integer, multiply it by ten, and the
product will end in zero and be divisible by the original one-digit integer.

I do not follow the explanation.

Lets say we choose 60...its not divisible by 7 and 9...how do we generalize this? I understand the explanation that if 6 is multiplied by 10, then 60 will definitely be divisible by 6...but what about 7 and 9...I thought the question asked for other factors that the integer won't be divisible by...

Am I reading the question wrong?

[ronaldramlan]

Your question is definitely the one that only the author of MGMAT flashcards can answer to.

[mschwrtz]

Yep, misreading the question. Rephrase he question in this way, "What one-digit number is a factor of no number ending in 0?"

You're right, of course, that 60 is not divisible by 7, but 70 is, and it ends with a zero.