100th Digit- DS question

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100th Digit- DS question

by baalok88 » Wed Nov 02, 2016 9:17 am
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
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by DavidG@VeritasPrep » Wed Nov 02, 2016 10:06 am
baalok88 wrote: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
0.39 0.4 0.399 0.40
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


If we're testing the statements together, then we can only use numbers that when rounded to the tenths digit, give us .4 and when rounded to the hundredth digit give us .40.

Case 1: .399 (When rounded to the nearest tenths or hundredths, we get .40. so it works.) Here the hundredths digit is 9
Case 2: .401 When rounded to the nearest tenths or hundredths, we get .40. so it works.) Here the hundredths digit is 0

Because we can different results (9 or 0), the statements together are not sufficient to answer the question. The answer is E
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by baalok88 » Wed Nov 02, 2016 7:48 pm
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'.

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by DavidG@VeritasPrep » Thu Nov 03, 2016 5:48 am
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.
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by GMATGuruNY » Thu Nov 03, 2016 6:17 am
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.
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