Data Sufficiency

What is the tens digit of positive integer x?

1) x divided by 100 has a remainder of 30.

2) x divided by 110 has a remainder of 30.


I realize the answer is A, because the only tens digit for x divided by 100 is 3 for the answer to have a remainder of 30.

I am confused because the statement 2 seems to contradict statement 1.

w0283767 wrote:What is the tens digit of positive integer x?

1) x divided by 100 has a remainder of 30.

2) x divided by 110 has a remainder of 30.


I realize the answer is A, because the only tens digit for x divided by 100 is 3 for the answer to have a remainder of 30.

I am confused because the statement 2 seems to contradict statement 1.

"Contradict" means that two statements cannot simultaneously be true. That will NEVER happen in data sufficiency. The two statements will always have at least one answer in common.

In this case, 3330 satisfies both statements.

3330/100 = 33 rem 30
3330/110 = 30 rem 30

Of course, statement (1) is sufficient by itself, so on the actual GMAT you should never worry about combining them - you can rest assured that the statements won't be contradictory. If you ever come across a DS question that does have contradictory statements, you're working with questionable materials.

thanks

But since statement 2 is also sufficient, wouldn't it be D instead of A?

avitorio -

no, because you can get different values in statement 2 for the tens digit of x.