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# What is the tenths digit in the decimal representation of a

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What is the tenths digit in the decimal representation of a [#permalink]  24 Sep 2012, 04:12
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What is the tenths digit in the decimal representation of a certain number?

(1) The number is less than 1/3
(2) The number is greater than 1/4

Practice Questions
Question: 46
Page: 279
Difficulty: 600
[Reveal] Spoiler: OA

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Re: What is the tenths digit in the decimal representation of a [#permalink]  24 Sep 2012, 04:12
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SOLUTION

What is the tenths digit in the decimal representation of a certain number?

(1) The number is less than 1/3.

(2) The number is greater than 1/4.

Each statement alone is clearly insufficient. When taken together we have $$0.25<x<0.333...$$. Hence the tenths digit can be 2 (for example if x= 0.251) or 3 (for example if x=0.3). Not sufficient.

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Re: What is the tenths digit in the decimal representation of a [#permalink]  24 Sep 2012, 04:28
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The number is less than 1/3
(2) The number is greater than 1/4
1) Tenth digit can be 0,1,2,3 - Insufficient
2) Tenth digit can be 2,3,4,5..-Insufficient
1+2) .25<x<.333 - x can be 2,3-Insufficient
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Re: What is the tenths digit in the decimal representation of a [#permalink]  24 Sep 2012, 08:28
Bunuel wrote:

What is the tenths digit in the decimal representation of a certain number?

(1) The number is less than 1/3
(2) The number is greater than 1/4

lets assume N = 0.xyz...

(1)
N < 1/3
N < 0.333333

Now, N can be 0.234 or 0.3111 or 0.121212
Basically, tenths digit can be 0 or 1 or 2 or 3
So, we cant say what would be the tenths digit
hence not sufficient.

(2)
N > 1/4
N > 0.25
Now, here digit can be 2,3,4,5,6,7,8,9
Hence this is also not sufficient

combining (1) and (2), the tenths digit can be either 2 or 3.
So, we can't answer the exact digit.

Hence E
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Re: What is the tenths digit in the decimal representation of a [#permalink]  28 Sep 2012, 04:06
Expert's post
SOLUTION

What is the tenths digit in the decimal representation of a certain number?

(1) The number is less than 1/3.

(2) The number is greater than 1/4.

Each statement alone is clearly insufficient. When taken together we have $$0.25<x<0.333...$$. Hence the tenths digit can be 2 (for example if x= 0.251) or 3 (for example if x=0.3). Not sufficient.

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Re: What is the tenths digit in the decimal representation of a [#permalink]  28 Sep 2012, 06:13
Expert's post
Quote:
What is the tenths digit in the decimal representation of a certain number?

(1) The number is less than 1/3
(2) The number is greater than 1/4

1) 1/3 is 0.33 (periodic) but could be also 1/4 = 0.25 so we have a 3 and a 2 . insuff

2) the same: the number could be 1/4 or 1/5 or 1/10 . insuff

1) + 2) x is between 1/3 and 1/4 but a lot of infinite value we could find

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When to actually consider a negitive (or unspecified bounds) [#permalink]  21 Mar 2013, 21:32
As I am going through the OG12 and other sources, I notice the use of when to consider a negitive (or similar) inconsistent during answer explainations from the question makers.

For example, today I came across this DS question:

OG12 question 43 page 276
What is the tenths digit in the decimal representation of a certain number?

1) the number is less than 1/3
2) the number is greater than 1/4

The OA states:

1) Since the number is less than 1/3, the tenths digit can be 0,1,2, or 3; NOT sufficient
2) Since the numebr is greater than 1/4, the tenths digit can be 2,3,4, ..., 9; NOT sufficient

My contention is that the OA doesn't take into consideration negitive numbers for S1, nor numbers greater than 1 for S2. Because of this, the tens digit could be any number 0-9 for either S1 or S2. Of course, in this question it doesn't affect the outcome of the correct answer being E; but I have seen questions inconsistently consider negitives or not

Any insight as to when to ignore negitives (or other bounds like non-integer/fractions) despite the question not stating it in any manner?

Thanks
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Re: What is the tenths digit in the decimal representation of a [#permalink]  02 May 2015, 03:45
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Re: What is the tenths digit in the decimal representation of a [#permalink]  03 May 2015, 08:38
We are looking for the tenths digit 0.(?)... and thus we ignore the following digits (...)

(1) X <1/3.

The number is smaller than 0.33.... This allows for the number to be 3,2,1,0 (and if we allow for X to be negative it could be any number. e.g. -0.9, -0.7 etc.) Not sufficient.

(2) X > 1/4

The number is thus larger than 0.25 allowing for the digit to be of any value. As such it's not sufficient.

(1)+(2) 1/4<X<1/3.

Or 0.25<X<0.33. This means we can have either 2 or 3 as the digit in the tenths place. Not sufficient together, E.
Re: What is the tenths digit in the decimal representation of a   [#permalink] 03 May 2015, 08:38
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