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

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Re: What is the tenths digit in the decimal representation of a [#permalink]
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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?

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Re: What is the tenths digit in the decimal representation of a [#permalink]
Hey chetan2u i have a question regarding this official question.
The answer is clearly E but here is my doubt=>
the official guide says that that for statement 1 the unit digits can be 0 or 1 or 2 or 3
now what if the number is -2.55 or -198.67 My point being the negative numbers are possible too but why is not GMAT offical testmakers considering them ..
Similarly for statement two the tens digits can be 8 or 1 or 3 or anything as per me.

Just lemme know if i am missing something here ?

Regards
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Re: What is the tenths digit in the decimal representation of a [#permalink]
stonecold wrote:
Hey chetan2u i have a question regarding this official question.
The answer is clearly E but here is my doubt=>
the official guide says that that for statement 1 the unit digits can be 0 or 1 or 2 or 3
now what if the number is -2.55 or -198.67 My point being the negative numbers are possible too but why is not GMAT offical testmakers considering them ..
Similarly for statement two the tens digits can be 8 or 1 or 3 or anything as per me.

Just lemme know if i am missing something here ?

Regards
StoneCold

hi,

I would say that we consider the negative too..
the Q nowhere mentions that the number is positive..
the GMAT nowhere says a decimal cannot be negative..
so may be the explanation has missed out on these numbers as the answer does not get affected..
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Re: What is the tenths digit in the decimal representation of a [#permalink]
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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

We need to determine the value of the tenths place of a particular number.

Statement One Alone:

The number is less than 1/3.

Since the number is less than 1/3, it is less than 0.333…. Thus, we could have values such as 0.3 (with a tenths place of 3) or 0.2 (with a tenths place of 2). Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The number is greater than 1/4.

Since the number is greater than 1/4, it is greater than 0.25. Thus, we could have values such as 0.3 (with a tenths place of 3) or 0.4 (with a tenths place of 4). Statement two does not provide enough information to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two we know that the decimal value is between 0.25 and 0.333…. We could still have decimals values with different tenths places, such as 0.28 or 0.3.

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Re: What is the tenths digit in the decimal representation of a [#permalink]
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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

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

Statement 1: The number is less than 1/3
There are several values that satisfy statement 1. Here are two:
Case a: the number = 0.31, in which case the value of the tenths digit is 3.
Case b: the number = 0.298, in which case the value of the tenths digit is 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 1: The number is greater than 1/4
There are several values that satisfy statement 2. Here are two:
Case a: the number = 0.31, in which case the value of the tenths digit is 3.
Case b: the number = 0.298, in which case the value of the tenths digit is 2
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: the number = 0.31, in which case the value of the tenths digit is 3.
Case b: the number = 0.298, in which case the value of the tenths digit is 2
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
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Re: What is the tenths digit in the decimal representation of a [#permalink]
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

Practice Questions
Question: 46
Page: 279
Difficulty: 600

Hello
Bunuel IanStewart
Can we consider 'negative' (e.g., -0.332) number when we explain statement 1?
Thanks__
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Q51  V47
Re: What is the tenths digit in the decimal representation of a [#permalink]
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Hello
Bunuel IanStewart
Can we consider 'negative' (e.g., -0.332) number when we explain statement 1?
Thanks__

Technically, I suppose so, but I've never seen (and would bet I will never see) an official question about digits in which you'd ever need to think about negative numbers to get the right answer.
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Re: What is the tenths digit in the decimal representation of a [#permalink]
IanStewart wrote:
Hello
Bunuel IanStewart
Can we consider 'negative' (e.g., -0.332) number when we explain statement 1?
Thanks__

Technically, I suppose so, but I've never seen (and would bet I will never see) an official question about digits in which you'd ever need to think about negative numbers to get the right answer.

Thank you so much for your response. May I have your reasoning on this ground, please? In short, why do you think so?
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