GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Nov 2019, 13:04 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If 0 < x < 1, is it possible to write x as a terminating dec

Author Message
TAGS:

### Hide Tags

Manager  Status: Final Lap
Joined: 25 Oct 2012
Posts: 227
Concentration: General Management, Entrepreneurship
GPA: 3.54
WE: Project Management (Retail Banking)
If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

17
46 00:00

Difficulty:   75% (hard)

Question Stats: 49% (01:45) correct 51% (01:30) wrong based on 627 sessions

### HideShow timer Statistics

If 0 < x < 1, is it possible to write x as a terminating decimal?

(1) 24x is an integer.

(2) 28x is an integer.

_________________
KUDOS is the good manner to help the entire community.

Math Expert V
Joined: 02 Sep 2009
Posts: 59039
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

27
24
If 0 < x < 1, is it possible to write x as a terminating decimal?

(1) 24x is an integer --> $$24x=m$$, where m an integer --> $$x=\frac{m}{24}=\frac{m}{2^3*3}$$, If m is a multiple of 3, then the answer is YES, else the answer is NO. Not sufficient.

(2) 28x is an integer --> $$28x=n$$, where n an integer --> $$x=\frac{n}{28}=\frac{n}{2^2*7}$$, If n is a multiple of 7, then the answer is YES, else the answer is NO. Not sufficient.

(1)+(2) $$x=\frac{m}{2^3*3}=\frac{n}{2^2*7}$$ --> $$\frac{m}{n}=\frac{2*3}{7}$$ --> m IS a multiple of 3 (as well as n IS multiple of 7). Sufficient.

Theory:
Reduced fraction $$\frac{a}{b}$$ (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only $$b$$ (denominator) is of the form $$2^n5^m$$, where $$m$$ and $$n$$ are non-negative integers. For example: $$\frac{7}{250}$$ is a terminating decimal $$0.028$$, as $$250$$ (denominator) equals to $$2*5^2$$. Fraction $$\frac{3}{30}$$ is also a terminating decimal, as $$\frac{3}{30}=\frac{1}{10}$$ and denominator $$10=2*5$$.

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example $$\frac{x}{2^n5^m}$$, (where x, n and m are integers) will always be the terminating decimal.

We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction $$\frac{6}{15}$$ has 3 as prime in denominator and we need to know if it can be reduced.

Questions testing this concept:
does-the-decimal-equivalent-of-p-q-where-p-and-q-are-89566.html
any-decimal-that-has-only-a-finite-number-of-nonzero-digits-101964.html
if-a-b-c-d-and-e-are-integers-and-p-2-a3-b-and-q-2-c3-d5-e-is-p-q-a-terminating-decimal-125789.html
700-question-94641.html
is-r-s2-is-a-terminating-decimal-91360.html
pl-explain-89566.html
which-of-the-following-fractions-88937.html

Hope it helps.
_________________
Senior Manager  B
Joined: 24 Aug 2009
Posts: 442
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: If 0 < x < 1, is it possible to write x as a terminating  [#permalink]

### Show Tags

24
5
If 0 < x < 1, is it possible to write x as a terminating decimal?
(1) 24x is an integer.
(2) 28x is an integer.

Reduced fraction $$\frac{a}{b}$$ (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only $$b$$ (denominator) is of the form $$2^n5^m$$, where $$m$$ and $$n$$ are non-negative integers

Statement 1- If 24x is an integer than x can take the following values
1/2, 1/3, 1/4, 1/6, 1/8, 1/12, 1/24
Some values of x can be reduced to a terminating decimal (1/2, 1/4, 1/8), while few can not be (1/3,1/6,1/12, 1/24)
Insufficient

Statement 2- If 28x is an integer than x can take the following values
1/2, 1/4, 1/7, 1/14, 1/28
Some values of x can be reduced to a terminating decimal (1/2, 1/4), while few can not be (1/7, 1/14, 1/28)
Insufficient

Statement 1& 2- If both 24x & 28x are integers than x can take the following values
1/2, 1/4
Both of these values of x can be reduced to a terminating decimal
Sufficient

Ans C.

Hope the explanation will help many.
_________________
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
##### General Discussion
Senior Manager  Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 447
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49 GPA: 3.3
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

Can someone explain me what is the meaning of terminating decimal.
_________________
Like my post Send me a Kudos It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html
Director  Joined: 14 Dec 2012
Posts: 688
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34 GPA: 3.6
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

1
trafficspinners wrote:
Can someone explain me what is the meaning of terminating decimal.

A decimal number that has digits that do not go on forever.

Examples:

0.25 (it has two decimal digits)
0.123456789 (it has nine decimal digits)

In contrast a Recurring Decimal has digits that go on forever

Example of a Recurring Decimal: 1/3 = 0.333... (the 3 repeats forever)
_________________
When you want to succeed as bad as you want to breathe ...then you will be successfull....

GIVE VALUE TO OFFICIAL QUESTIONS...

learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment
Manager  Joined: 14 Nov 2008
Posts: 57
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

2
Rock750 wrote:
If 0 < x < 1, is it possible to write x as a terminating decimal?

(1) 24x is an integer.

(2) 28x is an integer.

I have a bit of difficulty in understanding the intended meaning of "is it possible" part of the question.

The answer can be yes and ofcourse no, but just that there is a possibility that the answer could be yes confuses me a bit. Had the question been framed like this " is x a terminating decimal?", then it would have been clearer. The use of the term "possible" makes it just a bit ambiguous.

Math Expert V
Joined: 02 Sep 2009
Posts: 59039
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

agourav wrote:
Rock750 wrote:
If 0 < x < 1, is it possible to write x as a terminating decimal?

(1) 24x is an integer.

(2) 28x is an integer.

I have a bit of difficulty in understanding the intended meaning of "is it possible" part of the question.

The answer can be yes and ofcourse no, but just that there is a possibility that the answer could be yes confuses me a bit. Had the question been framed like this " is x a terminating decimal?", then it would have been clearer. The use of the term "possible" makes it just a bit ambiguous.

The question basically asks: if x is written as a decimal will it be a terminating decimal?

Hope it's clear.
_________________
Intern  Joined: 17 Sep 2012
Posts: 11
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

since the question asks "is it possible", wouldn't the answer be D since .5 is a terminating decimal and 24*.5=12, and 28*.5=24?
Math Expert V
Joined: 02 Sep 2009
Posts: 59039
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

thebloke wrote:
since the question asks "is it possible", wouldn't the answer be D since .5 is a terminating decimal and 24*.5=12, and 28*.5=24?

You misinterpret the question. The question asks: if x is written as a decimal will it be a terminating decimal? Thus the correct answer is C, not D.
_________________
Manager  Joined: 04 Oct 2013
Posts: 158
GMAT 1: 590 Q40 V30 GMAT 2: 730 Q49 V40 WE: Project Management (Entertainment and Sports)
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

we know that x is a proper positive fraction. we need to check whether x has powers of 5 or 2 in the denominator or not.

1. 24(x)=INT ---> $$x=Int/24$$ if our integer is 3 then x is can be written as a terminating decimal otherwise x will be a non-terminating decimal

2. 28(x)=INT ----> same story here if our int is 7 then x can be written as a terminating decimal, otherwise x will be a non-terminating decimal

1+2 $$Int/3(2^3)=Int/7(2^2)$$ -----> 7(4)Int=8(3)Int the expression has to be equal on both sides thus on the right hand side we need a 7 and on the right hand side we need a 3 and a two. We now know that our integer a terminating decimal because we can get rid of both 7 and 3 in the denominator.

C.

Hope it helps.
_________________
learn the rules of the game, then play better than anyone else.
Director  Joined: 07 Aug 2011
Posts: 500
GMAT 1: 630 Q49 V27 Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

fameatop wrote:
If 0 < x < 1, is it possible to write x as a terminating decimal?
(1) 24x is an integer.
(2) 28x is an integer.

Reduced fraction $$\frac{a}{b}$$ (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only $$b$$ (denominator) is of the form $$2^n5^m$$, where $$m$$ and $$n$$ are non-negative integers

Statement 1- If 24x is an integer than x can take the following values
1/2, 1/3, 1/4, 1/6, 1/8, 1/12, 1/24
Some values of x can be reduced to a terminating decimal (1/2, 1/4, 1/8), while few can not be (1/3,1/6,1/12, 1/24)
Insufficient

Statement 2- If 28x is an integer than x can take the following values
1/2, 1/4, 1/7, 1/14, 1/28
Some values of x can be reduced to a terminating decimal (1/2, 1/4), while few can not be (1/7, 1/14, 1/28)
Insufficient

Statement 1& 2- If both 24x & 28x are integers than x can take the following values
1/2, 1/4
Both of these values of x can be reduced to a terminating decimal
Sufficient

Ans C.

Hope the explanation will help many.

indeed i am benefited by this solution . Kudos to you !!
Intern  Joined: 06 Apr 2015
Posts: 7
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

1
thebloke wrote:
since the question asks "is it possible", wouldn't the answer be D since .5 is a terminating decimal and 24*.5=12, and 28*.5=24?

i agree with this. The way it is phrased, it should be D. I understand how the answer C is achieved, but I don't think this question is worded well....

The fact that a terminating decimal is possible should be enough. The only way, in my mind that C is correct is if the question asks "is X a terminating decimal?".
Current Student Joined: 18 Oct 2014
Posts: 797
Location: United States
GMAT 1: 660 Q49 V31 GPA: 3.98
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

Rock750 wrote:
If 0 < x < 1, is it possible to write x as a terminating decimal?

(1) 24x is an integer.

(2) 28x is an integer.

Given information :- 0 < x < 1 (x is a fraction between 0 and 1)

Question asked:- x as a terminating decimal?

x can only be written as terminating decimal when the denominator can be written in the form of 2^n or 5^n

(1) 24x is an integer

x can be any factor of 24
1, 2, 4, 3, 6, 8, 12, 24

So x may or may not be a terminating decimal.

(2) 28x is an integer

x can be any factor of 28
1, 2, 4, 7, 14, 28

So x may or may not be a terminating decimal

Combining both statements, only 4 is common between these two. Hence, combining the statements we get one digit that could be the denominator- 4.

_________________
I welcome critical analysis of my post!! That will help me reach 700+
Manager  B
Joined: 20 Apr 2014
Posts: 87
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

Bunuel
I am sorry
I can not get the combining statements.
We do not need to prove that n is a multiple of 7 ?
another question regarding the denominator, is it enough to be 2s or 5s to terminate X as decimal or 2s * 5s is a must.
Math Expert V
Joined: 02 Sep 2009
Posts: 59039
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

hatemnag wrote:
Bunuel
I am sorry
I can not get the combining statements.
We do not need to prove that n is a multiple of 7 ?
another question regarding the denominator, is it enough to be 2s or 5s to terminate X as decimal or 2s * 5s is a must.

From (1) we have that $$x=\frac{m}{24}=\frac{m}{2^3*3}$$. If m is a multiple of 3, then 3 in the denominator will be reduced and x will be a terminating decimal.

Similarly, from (2) we have that $$x=\frac{n}{28}=\frac{n}{2^2*7}$$. If n is a multiple of 7, then 7 in the denominator will be reduced and x will be a terminating decimal.

The answer to your other question is yes, if a fraction has only 2's or 5's in the denominator it'll terminate.

Check Terminating and Recurring Decimals Problems in our Special Questions Directory.

Hope it helps.
_________________
Senior Manager  G
Status: love the club...
Joined: 24 Mar 2015
Posts: 265
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

Bunuel wrote:
If 0 < x < 1, is it possible to write x as a terminating decimal?

(1) 24x is an integer --> $$24x=m$$, where m an integer --> $$x=\frac{m}{24}=\frac{m}{2^3*3}$$, If m is a multiple of 3, then the answer is YES, else the answer is NO. Not sufficient.

(2) 28x is an integer --> $$28x=n$$, where n an integer --> $$x=\frac{n}{28}=\frac{n}{2^2*7}$$, If n is a multiple of 7, then the answer is YES, else the answer is NO. Not sufficient.

(1)+(2) $$x=\frac{m}{2^3*3}=\frac{n}{2^2*7}$$ --> $$\frac{m}{n}=\frac{2*3}{7}$$ --> m IS a multiple of 3 (as well as n IS multiple of 7). Sufficient.

Theory:
Reduced fraction $$\frac{a}{b}$$ (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only $$b$$ (denominator) is of the form $$2^n5^m$$, where $$m$$ and $$n$$ are non-negative integers. For example: $$\frac{7}{250}$$ is a terminating decimal $$0.028$$, as $$250$$ (denominator) equals to $$2*5^2$$. Fraction $$\frac{3}{30}$$ is also a terminating decimal, as $$\frac{3}{30}=\frac{1}{10}$$ and denominator $$10=2*5$$.

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example $$\frac{x}{2^n5^m}$$, (where x, n and m are integers) will always be the terminating decimal.

We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction $$\frac{6}{15}$$ has 3 as prime in denominator and we need to know if it can be reduced.

Questions testing this concept:
http://gmatclub.com/forum/does-the-deci ... 89566.html
http://gmatclub.com/forum/any-decimal-t ... 01964.html
http://gmatclub.com/forum/if-a-b-c-d-an ... 25789.html
http://gmatclub.com/forum/700-question-94641.html
http://gmatclub.com/forum/is-r-s2-is-a- ... 91360.html
http://gmatclub.com/forum/pl-explain-89566.html
http://gmatclub.com/forum/which-of-the- ... 88937.html

Hope it helps.

hi man

since 0<x<1, say x is a proper fraction ....

taking 2 statements together,

x cannot be 1/3, as 3 can divide 24, but cannot divide 28...
in the same line of reasoning, x cannot be 1/7, as 7 can divide 28, but cannot divide 24...
So, for both of the two statements to hold true, x cannot be 3 and/or 7, thus we are left with only 2s in the denominator. Sufficient ....

please say to me whether the reasoning is okay.... Math Expert V
Joined: 02 Sep 2009
Posts: 59039
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

gmatcracker2017 wrote:
Bunuel wrote:
If 0 < x < 1, is it possible to write x as a terminating decimal?

(1) 24x is an integer --> $$24x=m$$, where m an integer --> $$x=\frac{m}{24}=\frac{m}{2^3*3}$$, If m is a multiple of 3, then the answer is YES, else the answer is NO. Not sufficient.

(2) 28x is an integer --> $$28x=n$$, where n an integer --> $$x=\frac{n}{28}=\frac{n}{2^2*7}$$, If n is a multiple of 7, then the answer is YES, else the answer is NO. Not sufficient.

(1)+(2) $$x=\frac{m}{2^3*3}=\frac{n}{2^2*7}$$ --> $$\frac{m}{n}=\frac{2*3}{7}$$ --> m IS a multiple of 3 (as well as n IS multiple of 7). Sufficient.

Theory:
Reduced fraction $$\frac{a}{b}$$ (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only $$b$$ (denominator) is of the form $$2^n5^m$$, where $$m$$ and $$n$$ are non-negative integers. For example: $$\frac{7}{250}$$ is a terminating decimal $$0.028$$, as $$250$$ (denominator) equals to $$2*5^2$$. Fraction $$\frac{3}{30}$$ is also a terminating decimal, as $$\frac{3}{30}=\frac{1}{10}$$ and denominator $$10=2*5$$.

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example $$\frac{x}{2^n5^m}$$, (where x, n and m are integers) will always be the terminating decimal.

We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction $$\frac{6}{15}$$ has 3 as prime in denominator and we need to know if it can be reduced.

Questions testing this concept:
http://gmatclub.com/forum/does-the-deci ... 89566.html
http://gmatclub.com/forum/any-decimal-t ... 01964.html
http://gmatclub.com/forum/if-a-b-c-d-an ... 25789.html
http://gmatclub.com/forum/700-question-94641.html
http://gmatclub.com/forum/is-r-s2-is-a- ... 91360.html
http://gmatclub.com/forum/pl-explain-89566.html
http://gmatclub.com/forum/which-of-the- ... 88937.html

Hope it helps.

hi man

since 0<x<1, say x is a proper fraction ....

taking 2 statements together,

x cannot be 1/3, as 3 can divide 24, but cannot divide 28...
in the same line of reasoning, x cannot be 1/7, as 7 can divide 28, but cannot divide 24...
So, for both of the two statements to hold true, x cannot be 3 and/or 7, thus we are left with only 2s in the denominator. Sufficient ....

please say to me whether the reasoning is okay.... Yes, x, when reduced to its simplest form must have 2 or 2^2 in the denominator.
_________________
Senior Manager  G
Status: love the club...
Joined: 24 Mar 2015
Posts: 265
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

Bunuel wrote:
gmatcracker2017 wrote:
Bunuel wrote:
If 0 < x < 1, is it possible to write x as a terminating decimal?

(1) 24x is an integer --> $$24x=m$$, where m an integer --> $$x=\frac{m}{24}=\frac{m}{2^3*3}$$, If m is a multiple of 3, then the answer is YES, else the answer is NO. Not sufficient.

(2) 28x is an integer --> $$28x=n$$, where n an integer --> $$x=\frac{n}{28}=\frac{n}{2^2*7}$$, If n is a multiple of 7, then the answer is YES, else the answer is NO. Not sufficient.

(1)+(2) $$x=\frac{m}{2^3*3}=\frac{n}{2^2*7}$$ --> $$\frac{m}{n}=\frac{2*3}{7}$$ --> m IS a multiple of 3 (as well as n IS multiple of 7). Sufficient.

Theory:
Reduced fraction $$\frac{a}{b}$$ (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only $$b$$ (denominator) is of the form $$2^n5^m$$, where $$m$$ and $$n$$ are non-negative integers. For example: $$\frac{7}{250}$$ is a terminating decimal $$0.028$$, as $$250$$ (denominator) equals to $$2*5^2$$. Fraction $$\frac{3}{30}$$ is also a terminating decimal, as $$\frac{3}{30}=\frac{1}{10}$$ and denominator $$10=2*5$$.

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example $$\frac{x}{2^n5^m}$$, (where x, n and m are integers) will always be the terminating decimal.

We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction $$\frac{6}{15}$$ has 3 as prime in denominator and we need to know if it can be reduced.

Questions testing this concept:
http://gmatclub.com/forum/does-the-deci ... 89566.html
http://gmatclub.com/forum/any-decimal-t ... 01964.html
http://gmatclub.com/forum/if-a-b-c-d-an ... 25789.html
http://gmatclub.com/forum/700-question-94641.html
http://gmatclub.com/forum/is-r-s2-is-a- ... 91360.html
http://gmatclub.com/forum/pl-explain-89566.html
http://gmatclub.com/forum/which-of-the- ... 88937.html

Hope it helps.

hi man

since 0<x<1, say x is a proper fraction ....

taking 2 statements together,

x cannot be 1/3, as 3 can divide 24, but cannot divide 28...
in the same line of reasoning, x cannot be 1/7, as 7 can divide 28, but cannot divide 24...
So, for both of the two statements to hold true, x cannot be 3 and/or 7, thus we are left with only 2s in the denominator. Sufficient ....

please say to me whether the reasoning is okay.... Yes, x, when reduced to its simplest form must have 2 or 2^2 in the denominator.

thanks man .. you are great ..
Intern  B
Joined: 12 Nov 2016
Posts: 7
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

Bunuel wrote:
If 0 < x < 1, is it possible to write x as a terminating decimal?

(1) 24x is an integer --> $$24x=m$$, where m an integer --> $$x=\frac{m}{24}=\frac{m}{2^3*3}$$, If m is a multiple of 3, then the answer is YES, else the answer is NO. Not sufficient.

(2) 28x is an integer --> $$28x=n$$, where n an integer --> $$x=\frac{n}{28}=\frac{n}{2^2*7}$$, If n is a multiple of 7, then the answer is YES, else the answer is NO. Not sufficient.

(1)+(2) $$x=\frac{m}{2^3*3}=\frac{n}{2^2*7}$$ --> $$\frac{m}{n}=\frac{2*3}{7}$$ --> m IS a multiple of 3 (as well as n IS multiple of 7). Sufficient.

Theory:
Reduced fraction $$\frac{a}{b}$$ (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only $$b$$ (denominator) is of the form $$2^n5^m$$, where $$m$$ and $$n$$ are non-negative integers. For example: $$\frac{7}{250}$$ is a terminating decimal $$0.028$$, as $$250$$ (denominator) equals to $$2*5^2$$. Fraction $$\frac{3}{30}$$ is also a terminating decimal, as $$\frac{3}{30}=\frac{1}{10}$$ and denominator $$10=2*5$$.

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example $$\frac{x}{2^n5^m}$$, (where x, n and m are integers) will always be the terminating decimal.

We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction $$\frac{6}{15}$$ has 3 as prime in denominator and we need to know if it can be reduced.

Hope it helps.

Hello Bunuel

For the above question, could you see if below method works :
Since both 28x and 24 x are integers ; their difference should be an integer as well; which means 4x is an integer
Hence: x = integer /2square (always terminating )
Manager  S
Joined: 23 Sep 2016
Posts: 232
Re: If 0 < x < 1, is it possible to write x as a terminating dec  [#permalink]

### Show Tags

Sneakysam wrote:
thebloke wrote:
since the question asks "is it possible", wouldn't the answer be D since .5 is a terminating decimal and 24*.5=12, and 28*.5=24?

i agree with this. The way it is phrased, it should be D. I understand how the answer C is achieved, but I don't think this question is worded well....

The fact that a terminating decimal is possible should be enough. The only way, in my mind that C is correct is if the question asks "is X a terminating decimal?".

even i agree with you possibility doesn't means that you need to be certain. This question need to be phrased properly. Re: If 0 < x < 1, is it possible to write x as a terminating dec   [#permalink] 20 Jun 2019, 23:21

Go to page    1   2    Next  [ 21 posts ]

Display posts from previous: Sort by

# If 0 < x < 1, is it possible to write x as a terminating dec  