Data Sufficiency

Hello,

Can you explain the answer to below question?
With below approach I thought 9 is the digit on the 100th place..


0.35 0.4 0.395 0.40
0.36 0.4 0.396 0.40
0.37 0.4 0.397 0.40
0.38 0.4 0.398 0.40
[u][b]0.39 0.4 0.399 0.40[/u]
0.4 0.4 0.4 0.40
0.41 0.4 0.401 0.40
0.42 0.4 0.402 0.40
0.43 0.4 0.403 0.40
0.44 0.4 0.404 0.40

Hi David,

But As I have listed down- two numbers- 0.39 and 0.399 give the rounding up as 0.4 and 0.40.

Then don't you think the answer is '9' that is on the 100th digit position? Hence, 'C'.

baalok88 wrote:Hi David,

But As I have listed down- two numbers- 0.39 and 0.399 give the rounding up as 0.4 and 0.40.

Then don't you think the answer is '9' that is on the 100th digit position? Hence, 'C'.

Two issues here. First, .39 is the same as .390. .390, when rounded to the nearest hundredth, would just be .39. So this number would violate statement 2. Second, even if .39 were an eligible number, the answer wouldn't be C, because .401 (or .402 or .403 or .404) is an eligible value, and the hundredth value here is 0. In data sufficiency questions, we can think of sufficiency as consistency. We have sufficiency in a value question if there is one and only one possible value. Because there are multiple possible values for the hundredth digit - 9 or 0 - the statements together are not sufficient.

We round UP when we reach the HALFWAY point between two values.
Any value BELOW the halfway point is rounded DOWN.

Let x = the number such that 0 < x < 1.

Statement 1: When rounded to the nearest tenth, the result is 0.4.
0.35 ≤ x < 0.45.
Please note that 0.45 is the UPPER LIMIT.
Any value below 0.45 -- even 0.4499 -- is rounded DOWN to 0.4.

Statement 2: When rounded to the nearest hundredth, the result is 0.40.
0.395 ≤ x < 0.405.
Please note that 0.405 is the UPPER LIMIT.
Any value below 0.405 -- even 0.40499 -- is rounded DOWN to 0.40.

Statements combined:
The range in blue is contained within the range in red.
Thus, the range in blue satisfies both statements.
If x = 0.395, then the hundredth digit of x is 9.
If x = 0.40499, then the hundreds digit of x is 0.
Since the hundredths digit of x can be different values, INSUFFICIENT.

The correct answer is E.