Does the value of x remain unchanged when rounded to the tenths place?

Taking this into account,
(1) The value of x remains unchanged when rounded to the hundredths place.
It implies that the hundredths digit is the rightmost nonzero digit of x. So we cannot say anything about value of x when rounded to the tenths place as we don't know the digit in hundredths place.
(2) The value of x remains unchanged when rounded to the units place.
It implies that the units digit is the rightmost nonzero digit of x. So on rounding off x to tenths digit will remain same as we know that there is no digit in tenths place. Sufficient.
Answer B

But my doubt is will the rounding off (tenths place) be applied on x as per its actual value or the tenth's place rounding off will be applied after x has been rounded off as per given statements.

Hello Bunuel,

Can you please explain the concept of rounding?
What does rounding to the hundredth place means? Does it mean we are rounding the hundredth place number or we are rounding the thousandth place number? Also how is this question different, if we sat rounding to the nearest hundredth place?

­Rounding to the hundredth's place implies that whatever the number is we write it only uptil the nearest hundredth.

For example 3.2456 would become 3.25 or 1.778 would become 1.78.

The question asks us to check whether the value remains unchanged when we round to the 10ths place. The only time this is possible is if the number has no further values after the 10ths. Eg: 3.20 or 4.10. This is because if there was any value in the hundreths place or beyond, rounding would change the number no matter how miniscule this change might be.

Statement 1: The value does not change after rounding to the hundreths place.

This tells us that the number has no values after its hundreths place eg: 3.540 or 3.620 or 3.600

In all these cases we get the same value after rounding to 100ths ie 3.54 or 3.62 or 3.6.

However when we round to the 10th's we notice that the values become:  3.5 or 3.6 or 3.6

Here two values have changed and one remains the same.

Hence this statement is not enough. Eliminate A&D

Statement 2: The value does not change after rounding to the units place.

This statement tells us that the number has no decimal values and is a whole number since if it did have decimal values the number would change post rounding. Eg: 3.4 becomes 3 or 4.255 becomes 4

When we round a value with no decimal values to the 10ths place it would remain unchanged. Eg: 3 becomes 3.0 or 6 becomes 6.0

Hence this statement is sufficient

ANSWER: B