In the decimal representation of x, where 0 < x < 1, is the : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 22 Jan 2017, 23:04

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In the decimal representation of x, where 0 < x < 1, is the

Author Message
TAGS:

### Hide Tags

Manager
Joined: 06 Apr 2010
Posts: 144
Followers: 3

Kudos [?]: 659 [2] , given: 15

In the decimal representation of x, where 0 < x < 1, is the [#permalink]

### Show Tags

17 Aug 2010, 05:37
2
KUDOS
24
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

45% (02:26) correct 55% (01:36) wrong based on 613 sessions

### HideShow timer Statistics

In the decimal representation of x, where 0 < x < 1, is the tenths digit of x nonzero?

(1) 16x is an integer.
(2) 8x is an integer.
[Reveal] Spoiler: OA
Manager
Joined: 20 Jul 2010
Posts: 78
Followers: 5

Kudos [?]: 71 [0], given: 32

### Show Tags

17 Aug 2010, 08:43
Are you sure the question stem given is correct?

(1) 0 < x < 1 is already saying x is non zero. Then why to use the phrase "if x non zero"

(2) I think what word is missing in the below ...

what is the tenth digit...

Cheers!
Ravi
Math Expert
Joined: 02 Sep 2009
Posts: 36601
Followers: 7098

Kudos [?]: 93487 [10] , given: 10563

### Show Tags

17 Aug 2010, 09:11
10
KUDOS
Expert's post
15
This post was
BOOKMARKED
udaymathapati wrote:
3. In the decimal representation of x, where 0 < x < 1, is the tenths digit of x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.

OA B

1234.567

1 - THOUSANDS
2 - HUNDREDS
3 - TENS
4 - UNITS
. - decimal point
5 - TENTHS
6 - HUNDREDTHS
7 - THOUSANDTHS

Given: $$x$$ is a fraction in the range $$0<x<1$$ --> $$x=0,abcd...$$ Question: is $$a=0$$?

(1) 16x is an integer --> $$x=\frac{integer}{16}$$, where $$0<integer<16$$ (as $$0<x<1$$). Now, the least value of $$x$$ is $$x=\frac{1}{16}=0.0625$$ and the tenth digit is zero BUT the highest value of $$x$$ is $$x=\frac{15}{16}=0.9375$$ and the tenth digit is nonzero (9). Not sufficient.

(2) 8x is an integer --> $$x=\frac{integer}{8}$$, where $$0<integer<8$$ (as $$0<x<1$$). Now, the least value of $$x$$ is $$x=\frac{1}{8}={0.125}$$ and the tenth digit is already nonzero thus all other values of $$x$$ will be more than 0.125 and therefore will have nonzero tenth digit. Sufficient.

_________________
Director
Joined: 24 Aug 2009
Posts: 507
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 17

Kudos [?]: 679 [6] , given: 276

Re: In the decimal representation of x, where 0 < x < 1, is the [#permalink]

### Show Tags

20 Sep 2012, 04:28
6
KUDOS
An alternate & probably easy solution for this problem

1) x can be 1/2,1/4,1/8,1/16 & all will give integer when multiplied by 16. X can be = .5, .25, .125 or .0625 –Tenth digit can be zero but its not sure - Not Sufficient
2) x can be 1/2,1/4,1/8, & all will give integer when multiplied by 16. X can be = .5, .25, .125 –Tenth digit is always non zero – Sufficient

Hope it will help
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Math Expert
Joined: 02 Sep 2009
Posts: 36601
Followers: 7098

Kudos [?]: 93487 [0], given: 10563

Re: In the decimal representation of x, where 0 < x < 1, is the [#permalink]

### Show Tags

24 Jun 2013, 02:17
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=36
All PS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=57

_________________
Manager
Joined: 18 Oct 2011
Posts: 90
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Followers: 2

Kudos [?]: 69 [2] , given: 0

Re: In the decimal representation of x, where 0 < x < 1, is the [#permalink]

### Show Tags

24 Jun 2013, 13:09
2
KUDOS
Statement 1: For tenth digit to to be zero the fraction multiplied by 16 must be less than 1/10. For 16x to be an integer, x could be 1/16 or 1/8. Not Sufficient

Statement 2: Same logic as above except for 8 to be an integer it can only be multiplied by 1/8 (which is more than 1/10)
Sufficient.
Director
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21
Followers: 43

Kudos [?]: 698 [1] , given: 723

Re: In the decimal representation of x, where 0 < x < 1, is the [#permalink]

### Show Tags

25 Jun 2013, 09:11
1
KUDOS
udaymathapati wrote:
In the decimal representation of x, where 0 < x < 1, is the tenths digit of x nonzero?

(1) 16x is an integer.
(2) 8x is an integer.

From the given statement we can conclude that x is terminating decimal. Let x = .abc where we need to find whether a equal to 0 or not

From St 1 : 16x is an Integer ------->x can be 0.125 or 0.0625 as when multiplied by 16 both the values of x give us Integer values 2 and 1 respectively

From St 2: 8x is integer. Knowing that 8X is an integer we can safely conclude that "a" not equal to 0. The least possible value of x will be 0.125 and other possible values of x can be multiple of 0.125 only i.e 0.250, 0.375, 0.500 and hence "a" will never be zero.

Ans is B
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Current Student
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 992
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)
Followers: 164

Kudos [?]: 1467 [0], given: 227

Re: In the decimal representation of x, where 0 < x < 1, is the [#permalink]

### Show Tags

15 Sep 2014, 00:04
udaymathapati wrote:
In the decimal representation of x, where 0 < x < 1, is the tenths digit of x nonzero?

(1) 16x is an integer.
(2) 8x is an integer.

Basically this question is asking whether x lies in 0 < x < 0.099999 or not ?

1) 16x is an integer.

multiply 16 x 0.099 = 1.44 << it means we can have some value less then 0.099 at which product with 16 yields 1. further 16x0.5=8 is also integer.
Therefore, at some value 0.0xy and 0.5 I am getting integer value and thus, 1 is not sufficient.

2) 8x is an integer.
multiply 8 x 0.099 = 0.72; we can see that 0.72 is less than nearest integer 1 and thus we will have to multiply 8 with some number greater than 0.099 and that number will definitely not have 0 in tenths place. e.g x = 1/8 = 0.125
Therefore Statement 2 is sufficient.

Ans B.
_________________

Piyush K
-----------------------
Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison
Don't forget to press--> Kudos
My Articles: 1. WOULD: when to use? | 2. All GMATPrep RCs (New)
Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".

Intern
Joined: 08 Jan 2015
Posts: 34
Followers: 0

Kudos [?]: 55 [0], given: 31

In the decimal representation of [i]x[/i], where 0 < [i]x[/i] < 1, is [#permalink]

### Show Tags

03 Apr 2015, 09:15
In the decimal representation of x, where 0 < x < 1, is the tenths digit of x nonzero?

1) 16x is an integer

2) 8x is an integer
Math Expert
Joined: 02 Sep 2009
Posts: 36601
Followers: 7098

Kudos [?]: 93487 [1] , given: 10563

Re: In the decimal representation of x, where 0 < x < 1, is the [#permalink]

### Show Tags

03 Apr 2015, 09:17
1
KUDOS
Expert's post
Awli wrote:
In the decimal representation of x, where 0 < x < 1, is the tenths digit of x nonzero?

1) 16x is an integer

2) 8x is an integer

Merging similar topics.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13508
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: In the decimal representation of x, where 0 < x < 1, is the [#permalink]

### Show Tags

18 Apr 2016, 04:58
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Director
Joined: 11 Sep 2015
Posts: 903
Followers: 107

Kudos [?]: 869 [2] , given: 108

In the decimal representation of x, where 0 < x < 1, is the [#permalink]

### Show Tags

28 Sep 2016, 15:07
2
KUDOS
Top Contributor
1
This post was
BOOKMARKED
udaymathapati wrote:
In the decimal representation of x, where 0 < x < 1, is the tenths digit of x nonzero?

(1) 16x is an integer.
(2) 8x is an integer.

Target question:Is the tenths digit of x nonzero?

This is a good candidate for rephrasing the target question.

Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

First recognize that the tenths digit of x will equal ZERO, if x is LESS THAN 0.1
For example, if x = 0.04, the tenths digit is 0
So, the tenths digit of x will be NONZERO if x > 0.1
In other words, the tenths digit of x will be NONZERO if x > 1/10
Since we're already told that x < 1, we can REPHRASE the target question...
REPHRASED target question: Is 1/10 < x < 1?

Statement 1: 16x is an integer.
Since we're told that 0 < x (i.e., x is positive), we know that 16x is positive
So, let's say that 16x = k, where k is some positive integer
Solve for x to get: x = k/16 (where k is some positive integer)
There are several values of k that satisfy statement 1. Here are two:
Case a: k = 8, in which case x = 8/16 = 1/2, which means it IS the case that 1/10 < x < 1
Case b: k = 1, in which case x = 1/16, which means it is NOT the case that 1/10 < x < 1
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 8x is an integer.
Let's say that 8x = j, where j is some positive integer
Solve for x to get: x = j/8 (where j is some positive integer)
Since j is a positive integer, then j = 1 or 2 or 3 or ....
In all of these cases, j/8 will be GREATER than 1/10
In other words, x must be GREATER than 1/10
Since we're also told that x < 1, we can be certain that 1/10 < x < 1
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

[Reveal] Spoiler:
B

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Brent also tutors students for the GMAT

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7128
Location: Pune, India
Followers: 2139

Kudos [?]: 13699 [2] , given: 222

Re: In the decimal representation of x, where 0 < x < 1, is the [#permalink]

### Show Tags

28 Sep 2016, 22:14
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
udaymathapati wrote:
In the decimal representation of x, where 0 < x < 1, is the tenths digit of x nonzero?

(1) 16x is an integer.
(2) 8x is an integer.

The question is an application of the concept of terminating decimals. Recall that when the denominator of a fraction has only 2s and/or 5s as factors, it is a terminating decimal.

x could be 0.345 or 0.02 etc.
To create integers, you need to move the decimal to the right. This is done by making 10s.
16 and 8 in the statements should remind you of powers of 2. This should make you think of powers of 5 to make 10s.

(1) 16x is an integer.

Your have four 2s here. When you multiply them by four 5s (i.e. 625), you can make four 10s.

So if x = 0.625, then 16x will be an integer
But if x = 0.0625, then also 16x will be an integer
Not sufficient.

(2) 8x is an integer.

Here you have three 2s. When you multiply them by three 5s (i.e. 125), you can make three 10s.

So if x = 0.125, then 8x will be an integer.
What about when x = 0.0125? No, 8x will not be an integer. We can make three 10s but 125 itself has 3 digits. You cannot have an additional 0 digit immediately after the decimal point.
So we know that tenths digit of x cannot be 0.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Intern
Joined: 18 Sep 2016
Posts: 49
Followers: 0

Kudos [?]: 4 [0], given: 97

In the decimal representation of x, where 0 < x < 1, is the [#permalink]

### Show Tags

28 Sep 2016, 23:57
udaymathapati wrote:
In the decimal representation of x, where 0 < x < 1, is the tenths digit of x nonzero?

(1) 16x is an integer.
(2) 8x is an integer.

i think it is easier.

to check if (1) is sufficient just think about the shortest number which make 16 an integer.
it will be surely $$x=$$$$\frac{1}{16}$$=0.0...something
so (1) is not sufficient

with the same logic the shortest number which make 8 an integer is $$x=\frac{1}{8}$$=0.1...something
therfore statement (2) is sufficient.

_________________

Please press Kudos if you like my post

In the decimal representation of x, where 0 < x < 1, is the   [#permalink] 28 Sep 2016, 23:57
Similar topics Replies Last post
Similar
Topics:
3 If x<0, is y/x < 1 ? 8 06 Oct 2016, 07:04
4 If 2.5 < x < 4.5, is the tenths digit of the decimal representation of 2 06 Oct 2015, 04:51
3 In the decimal representation of x, where 0 < x < 1, is the 6 03 Mar 2014, 22:07
5 If x 0, is x^2 / |x| < 1? 12 14 Dec 2009, 00:03
18 If x≠0, is |x| < 1? 10 19 Oct 2009, 06:10
Display posts from previous: Sort by