j_shreyans wrote:If n is an integer between 100 and 900, what is the tens digit of n?

(1) If n is rounded to the nearest ten and the result is then rounded to the nearest hundred, the final value differs from the result of rounding n to the nearest hundred.

(2) The tens digit of n is half the units digit of n and is twice the hundreds digit of n.

Given that n is between 100 and 900 we know that n is a three digit number.

For Statement 1, we know that 5 is the cutoff for rounding up or rounding down. Anything 5 or above is rounded up. Anything below 5 is rounded down.

When rounding to the nearest 100, one looks only at the tens digit. If the tens digit is 5 or higher, one rounds up. If the tens digit is five or lower, one rounds down.

So the only way rounding n to the nearest ten and then rounding the result to the nearest hundred could result in a final value different from that resulting from merely rounding n to the nearest hundred is the tens digit being 4 and the ones digit being 5 or greater.

If the tens digit were below 4, there is no way that rounding would make it 5 or higher.

If the tens digit were 5 or higher, rounding it up could not result in a hundreds digit different from that which would result from first rounding up to the nearest 10.

Here are some examples.

135 -> Ones Rounded -> 140 -> Tens Rounded -> 100
135 -> Tens Rounded -> 100

145 -> Ones Rounded -> 150 -> Tens Rounded -> 200
145 -> Tens Rounded -> 100

195 -> Ones Rounded -> 200 -> Tens Rounded -> 200
195 -> Tens Rounded -> 200

So given Statement 1, 4 is the only possible value of the tens digit, and so Statement 1 is sufficient.

Statement 2 could be satisfied with 124 or 248. So Statement 2 on its own is insufficient.

Choose A.