1)
x divided by 100 has a remainder of 30 can be written like that:
x=100*k+30 (with k a constant superior or equal to 0 given x >0)
So x can be 30, 130, 230, 330, 430, ........, 930, 1030 it depends on k
In all these integers, the tens digit is "3"

2)
x divided by 110 has a remainder of 30 can be written like it:
x=110*m + 30 ( with m...)
So x can be 30, 140, 250 ...
In that case we cannot state anything about the value of the tens digit of x.

The answer is A. However, I don't understand how 1) can be sufficient. If you divide 130 by 100, you get 1 r 30. In this case the tens digit is 0.

In this case, the tens digit of 130 is "3" but I think that I do not understand what you ask.

hengirl03 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



The answer is A. However, I don't understand how 1) can be sufficient. If you divide 130 by 100, you get 1 r 30. In this case the tens digit is 0.

1 ---- the number x can be written as 100 * d + 30.. no matter what the d value is, the ten's digit will always be 3 --- 1 is sufficient

2 ---- 110 * d + 30... take d = 1 then x = 140 .. take d = 2 then x value is 250.. Ten's digit changed.. so 2 is not sufficent

hence A