Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 29 Apr 2016, 17:32

### 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

# Which of the following fractions has a decimal equivalent

Author Message
TAGS:

### Hide Tags

Intern
Joined: 28 Jan 2011
Posts: 22
Followers: 1

Kudos [?]: 9 [0], given: 15

Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

07 Sep 2013, 03:57
4
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

65% (01:38) correct 35% (01:02) wrong based on 185 sessions

### HideShow timer Statictics

Which of the following fractions has a decimal equivalent that is a terminating decimal?

a) 10/189
b) 15/196
c) 16/225
d) 25/144
e) 39/128
[Reveal] Spoiler: OA
Manager
Joined: 20 Jul 2012
Posts: 169
Location: India
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 17 [1] , given: 499

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

07 Sep 2013, 05:25
1
KUDOS
salsal wrote:
Which of the following fractions has a decimal equivalent that is a terminating decimal?

a) 10/189
b) 15/196
c) 16/225
d) 25/144
e) 39/128

is there any simple method to find it?
Intern
Joined: 14 Aug 2013
Posts: 35
Location: United States
Concentration: Finance, Strategy
GMAT Date: 10-31-2013
GPA: 3.2
WE: Consulting (Consumer Electronics)
Followers: 2

Kudos [?]: 54 [3] , given: 4

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

07 Sep 2013, 06:48
3
KUDOS
akankshasoneja wrote:
salsal wrote:
Which of the following fractions has a decimal equivalent that is a terminating decimal?

a) 10/189
b) 15/196
c) 16/225
d) 25/144
e) 39/128

is there any simple method to find it?

Denominators of options a,c,d contains powers of 3...numerators of these options when divided by 3 will have non-terminating decimals
Denominator of option b contains power of 7...numerator 15 when divided by 7 will give non terminating decimal
Option E has denominator in powers of 2...so when 39 divided by 2 will give a terminating decimal

Hope it helps
Math Expert
Joined: 02 Sep 2009
Posts: 32539
Followers: 5625

Kudos [?]: 68235 [5] , given: 9797

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

07 Sep 2013, 09:13
5
KUDOS
Expert's post
6
This post was
BOOKMARKED
salsal wrote:
Which of the following fractions has a decimal equivalent that is a terminating decimal?

a) 10/189
b) 15/196
c) 16/225
d) 25/144
e) 39/128

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 $$2*5^3$$. 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.

BACK TO THE QUESTION:

Only option E (when reduced to its lowest form) has the denominator of the form $$2^n5^m$$: 39/128=39/2^7.

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.
_________________
Director
Joined: 29 Nov 2012
Posts: 901
Followers: 12

Kudos [?]: 774 [0], given: 543

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

07 Sep 2013, 10:07
You can solve this question in less than 30 seconds if you understand the concept of terminating decimal. The denominator must have only power's of 2 or 5 in the denominator no other powers ( if it has any other prime factors like 3,7, etc it won't be terminating). 2's and 5's can be in any possible combination but it must only have 2's and 5's

a) 10/189

denominator sum of digits is 18 so its divisible by 3 eliminate

b) 15/196

This has a prime factor of 7 when do the prime factorization of the denominator.. Eliminate

c) 16/225

denominator sum of digits is 9 so its divisible by 3 eliminate

d) 25/144

denominator sum of digits is 9 so its divisible by 3 eliminate

_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Math Expert
Joined: 02 Sep 2009
Posts: 32539
Followers: 5625

Kudos [?]: 68235 [0], given: 9797

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

07 Sep 2013, 10:13
Expert's post
fozzzy wrote:
You can solve this question in less than 30 seconds if you understand the concept of terminating decimal. The denominator must have only power's of 2 or 5 in the denominator no other powers ( if it has any other prime factors like 3,7, etc it won't be terminating). 2's and 5's can be in any possible combination but it must only have 2's and 5's

This is true if a fraction is reduced to its lowest term.

Consider this: the denominator of 3/30 has other primes than 2 or 5, but 3/30 IS a terminating decimal because 3 in the denominator gets reduced: 3/30=1/10=0.1.

Hope it's clear.
_________________
Director
Joined: 29 Nov 2012
Posts: 901
Followers: 12

Kudos [?]: 774 [0], given: 543

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

07 Sep 2013, 10:18
That's true bunuel. Thanks for pointing out
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Math Expert
Joined: 02 Sep 2009
Posts: 32539
Followers: 5625

Kudos [?]: 68235 [0], given: 9797

Re: Which of the following fractions has a decimal equivalent th [#permalink]

### Show Tags

27 Sep 2013, 08:37
Expert's post
Dmitriy wrote:
Which of the following fractions has a decimal equivalent that is a terminating decimal?

a) 10/189
b) 15/196
c) 16/225
d) 25/144
e) 39/128

How deal with a such kind of problems efficiently?

Merging similar topics. Please refer to the solutions above.

_________________
Manager
Joined: 26 Feb 2013
Posts: 184
Followers: 0

Kudos [?]: 34 [1] , given: 25

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

01 Oct 2013, 12:54
1
KUDOS
Bunuel wrote:
salsal wrote:
Which of the following fractions has a decimal equivalent that is a terminating decimal?

a) 10/189
b) 15/196
c) 16/225
d) 25/144
e) 39/128

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.

BACK TO THE QUESTION:

Only option E (when reduced to its lowest form) has the denominator of the form $$2^n5^m$$: 39/128=39/2^7.

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.

Typo? you mean $$2*5^3$$ ?
Current Student
Joined: 26 Sep 2013
Posts: 221
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Followers: 4

Kudos [?]: 102 [1] , given: 40

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

01 Oct 2013, 19:02
1
KUDOS
Bunuel wrote:
salsal wrote:
Which of the following fractions has a decimal equivalent that is a terminating decimal?

a) 10/189
b) 15/196
c) 16/225
d) 25/144
e) 39/128

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.

BACK TO THE QUESTION:

Only option E (when reduced to its lowest form) has the denominator of the form $$2^n5^m$$: 39/128=39/2^7.

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.

I'm confused, 128 is 2^7, you said it had to be 2^n*5^m....there is no 5^m in 128
Math Expert
Joined: 02 Sep 2009
Posts: 32539
Followers: 5625

Kudos [?]: 68235 [1] , given: 9797

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

02 Oct 2013, 03:18
1
KUDOS
Expert's post
AccipiterQ wrote:
Bunuel wrote:
salsal wrote:
Which of the following fractions has a decimal equivalent that is a terminating decimal?

a) 10/189
b) 15/196
c) 16/225
d) 25/144
e) 39/128

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.

BACK TO THE QUESTION:

Only option E (when reduced to its lowest form) has the denominator of the form $$2^n5^m$$: 39/128=39/2^7.

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.

I'm confused, 128 is 2^7, you said it had to be 2^n*5^m....there is no 5^m in 128

Yes, it is 128 = 2^7*5^0.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 32539
Followers: 5625

Kudos [?]: 68235 [0], given: 9797

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

02 Oct 2013, 03:19
Expert's post
Skag55 wrote:
Bunuel wrote:
salsal wrote:
Which of the following fractions has a decimal equivalent that is a terminating decimal?

a) 10/189
b) 15/196
c) 16/225
d) 25/144
e) 39/128

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.

BACK TO THE QUESTION:

Only option E (when reduced to its lowest form) has the denominator of the form $$2^n5^m$$: 39/128=39/2^7.

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.

Typo? you mean $$2*5^3$$ ?

Yes. Edited. Thank you. +1.
_________________
Current Student
Joined: 26 Sep 2013
Posts: 221
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Followers: 4

Kudos [?]: 102 [0], given: 40

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

02 Oct 2013, 07:12
Bunuel wrote:
AccipiterQ wrote:

I'm confused, 128 is 2^7, you said it had to be 2^n*5^m....there is no 5^m in 128

Yes, it is 128 = 2^7*5^0.

So ANY number with a 2^x or 5^x (where x is greater than or equal to 1) will fall into this then?

I'm confused though, so 6/15 a terminating decimal, because 15 is 5^1*3^1*2^0, but then why is 16/225 is not terminating? It follows the same pattern; 225 is 5^2*3^2*2^0
Math Expert
Joined: 02 Sep 2009
Posts: 32539
Followers: 5625

Kudos [?]: 68235 [1] , given: 9797

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

02 Oct 2013, 08:35
1
KUDOS
Expert's post
AccipiterQ wrote:
Bunuel wrote:
AccipiterQ wrote:

I'm confused, 128 is 2^7, you said it had to be 2^n*5^m....there is no 5^m in 128

Yes, it is 128 = 2^7*5^0.

So ANY number with a 2^x or 5^x (where x is greater than or equal to 1) will fall into this then?

I'm confused though, so 6/15 a terminating decimal, because 15 is 5^1*3^1*2^0, but then why is 16/225 is not terminating? It follows the same pattern; 225 is 5^2*3^2*2^0

6/15=6/(3*5) is a terminating decimal because extra 3 in the denominator is reduced and we get 2/5 (the denominator is in the form of 2^n*5^m).

16/225=16/(3^2*5^2) is not a terminating decimal because extra 3^2 in the denominator is not reduced to get the denominator in the form of 2^n*5^m.

Hope it's clear.
_________________
Current Student
Joined: 26 Sep 2013
Posts: 221
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Followers: 4

Kudos [?]: 102 [0], given: 40

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

02 Oct 2013, 09:36
I'm a dummy! I forgot my 4th grade teachers directive to always make sure fractions are reduced haha

Thanks!
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 9224
Followers: 454

Kudos [?]: 114 [1] , given: 0

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

03 Jan 2015, 17:05
1
KUDOS
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.
_________________
Manager
Joined: 12 Sep 2015
Posts: 112
Followers: 0

Kudos [?]: 4 [0], given: 24

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

12 Feb 2016, 14:21
So the numerator in this situation is irrelevant?
Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2599
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 93

Kudos [?]: 1062 [0], given: 775

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

12 Feb 2016, 15:09
Expert's post
MrSobe17 wrote:
So the numerator in this situation is irrelevant?

Yes, but only after making sure that the fraction is reduced to the lowest terms ie the LCM of the numerator and denominator is = 1.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Director
Joined: 23 Jan 2013
Posts: 505
Schools: Cambridge'16
Followers: 2

Kudos [?]: 49 [0], given: 37

Re: Which of the following fractions has a decimal equivalent [#permalink]

### Show Tags

13 Feb 2016, 05:16
every terminating decimal has 10,100,1000,10000 etc. in denominator when written as fraction.
So, all fractions should have only 2 and/or 5 as a factors in their reduced state

a) 10/189, it is reduced, and 189 does not have any 2 or 5
b) 15/196, reduced, and 196=(2*7)^2, so does not fit
c) 16/225, reduced, and 225=(3*5)^2, so does not fit
d) 25/144, reduced, and 144=(3*4)^2, so does not fit
e) 39/128, reduced, and 128=2^7, so can have 10^7 in denominator and fits

E
Re: Which of the following fractions has a decimal equivalent   [#permalink] 13 Feb 2016, 05:16
Similar topics Replies Last post
Similar
Topics:
13 Which of the following has a decimal equivalent that is a 4 20 Oct 2013, 06:36
46 Which of the following fractions has a decimal equivalent 17 08 Jan 2010, 14:22
6 Which of the following fractions has a decimal equivalent th 11 22 Aug 2009, 11:09
54 Which of the following fractions has a decimal equivalent th 5 09 Jul 2009, 10:29
12 Which of the following fractions has a decimal equivalent 17 02 Apr 2007, 06:18
Display posts from previous: Sort by