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Math Expert V
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What is the tenths digit in the decimal representation of a  [#permalink]

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Difficulty:   5% (low)

Question Stats: 83% (01:05) correct 17% (01:03) wrong based on 1157 sessions

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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

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

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1
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.

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

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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
Answer E
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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

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]

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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

E is the answer
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When to actually consider a negitive (or unspecified bounds)  [#permalink]

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1
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]

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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.
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GRE 1: Q169 V154 Re: What is the tenths digit in the decimal representation of a  [#permalink]

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

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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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0.25 < x < 0.33
not sufficient
IMO E
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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.

The answer is E.
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GRE 1: Q169 V154 What is the tenths digit in the decimal representation of a  [#permalink]

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ScottTargetTestPrep wrote:
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). IT can be 0,1,2,3,4,5,6,7,8,9 considering the negatives 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)AGAIN IT can be 0,1,2,3,4,5,6,7,8,9 considering the negatives. 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.

The answer is E.

Hi Scott
Just to add to your solution =>
STATEMENT 1 AND 2 => Here the tenths digit can be 0,1,2,3,4,5,6,7,8,9
But combining 1 &2 => it can be a 2 or a 3

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

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If a question does not mention whether a number is positive or negative, do we have to always consider the positive numbers ? In which cases do we have to take the negative numbers ?

In this question...
Even if we consider the negative numbers, statement 1 won't be sufficient because the tenths digit can be 3, 2, 1, 0 and the digit on tenths place in negative numbers. So no unique solution.

The answer would still be E because when we combine both the statements the digits would overlap and we would not get a unique answer to the problem.

I hope my understanding is correct on the negative values.
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GRE 1: Q169 V154 Re: What is the tenths digit in the decimal representation of a  [#permalink]

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Krishna2016 wrote:
If a question does not mention whether a number is positive or negative, do we have to always consider the positive numbers ? In which cases do we have to take the negative numbers ?

In this question...
Even if we consider the negative numbers, statement 1 won't be sufficient because the tenths digit can be 3, 2, 1, 0 and the digit on tenths place in negative numbers. So no unique solution.

The answer would still be E because when we combine both the statements the digits would overlap and we would not get a unique answer to the problem.

I hope my understanding is correct on the negative values.

You are correct here mate Regards
Stone Cold
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Re: What is the tenths digit in the decimal representation of a  [#permalink]

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Hi,
Can anybody tell me what does the heading "topic statistics" under "Practice History" represent in the workbook.
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Re: What is the tenths digit in the decimal representation of a  [#permalink]

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9994ag wrote:
Hi,
Can anybody tell me what does the heading "topic statistics" under "Practice History" represent in the workbook?
Ashish

Hi 9994ag

First of all could you please clarify what work book you are referring to?

Second, I am not sure if this is the right forum to post your question, you have posted this question under one of the DS question, I don't see any correlation between the post and the question. Request you to create a separate thread for this question.
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Re: What is the tenths digit in the decimal representation of a  [#permalink]

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Hi ydmuley,
Sorry for my mistake. I am new to the club so did not know how to post this problem pertaining to workbook in the gmat club.
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Re: What is the tenths digit in the decimal representation of a  [#permalink]

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Top Contributor
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

Answer: E

Cheers,
Brent
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