Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 28 Jan 2011
Posts: 22

Which of the following fractions has a decimal equivalent
[#permalink]
Show Tags
07 Sep 2013, 03:57
Question Stats:
65% (00:43) correct 35% (00:51) wrong based on 413 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 49206

Re: Which of the following fractions has a decimal equivalent
[#permalink]
Show Tags
07 Sep 2013, 09:13
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 nonnegative 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 2s and/or 5s 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. Answer: E. Questions testing this concept:doesthedecimalequivalentofpqwherepandqare89566.htmlanydecimalthathasonlyafinitenumberofnonzerodigits101964.htmlifabcdandeareintegersandp2a3bandq2c3d5eispqaterminatingdecimal125789.html700question94641.htmlisrs2isaterminatingdecimal91360.htmlplexplain89566.htmlwhichofthefollowingfractions88937.htmlHope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Intern
Joined: 14 Aug 2013
Posts: 34
Location: United States
Concentration: Finance, Strategy
GMAT Date: 10312013
GPA: 3.2
WE: Consulting (Consumer Electronics)

Re: Which of the following fractions has a decimal equivalent
[#permalink]
Show Tags
07 Sep 2013, 06:48
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 nonterminating 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




Director
Joined: 29 Nov 2012
Posts: 802

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 e) 39/128 Jackpot Correct answer
_________________
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 http://gmatclub.com/forum/gmatprepsoftwareanalysisandwhatifscenarios146146.html



Math Expert
Joined: 02 Sep 2009
Posts: 49206

Re: Which of the following fractions has a decimal equivalent
[#permalink]
Show Tags
07 Sep 2013, 10:13



Director
Joined: 29 Nov 2012
Posts: 802

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 http://gmatclub.com/forum/gmatprepsoftwareanalysisandwhatifscenarios146146.html



Manager
Joined: 26 Sep 2013
Posts: 198
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

Re: Which of the following fractions has a decimal equivalent
[#permalink]
Show Tags
01 Oct 2013, 19:02
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 nonnegative 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 2s and/or 5s 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. Answer: E. Questions testing this concept:doesthedecimalequivalentofpqwherepandqare89566.htmlanydecimalthathasonlyafinitenumberofnonzerodigits101964.htmlifabcdandeareintegersandp2a3bandq2c3d5eispqaterminatingdecimal125789.html700question94641.htmlisrs2isaterminatingdecimal91360.htmlplexplain89566.htmlwhichofthefollowingfractions88937.htmlHope 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: 49206

Re: Which of the following fractions has a decimal equivalent
[#permalink]
Show Tags
02 Oct 2013, 03:18
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 nonnegative 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 2s and/or 5s 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. Answer: E. Questions testing this concept:doesthedecimalequivalentofpqwherepandqare89566.htmlanydecimalthathasonlyafinitenumberofnonzerodigits101964.htmlifabcdandeareintegersandp2a3bandq2c3d5eispqaterminatingdecimal125789.html700question94641.htmlisrs2isaterminatingdecimal91360.htmlplexplain89566.htmlwhichofthefollowingfractions88937.htmlHope 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 26 Sep 2013
Posts: 198
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

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: 49206

Re: Which of the following fractions has a decimal equivalent
[#permalink]
Show Tags
02 Oct 2013, 08:35



Manager
Joined: 26 Sep 2013
Posts: 198
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

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!



Manager
Joined: 12 Sep 2015
Posts: 89

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?



Current Student
Joined: 20 Mar 2014
Posts: 2639
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Which of the following fractions has a decimal equivalent
[#permalink]
Show Tags
12 Feb 2016, 15:09
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.



Director
Joined: 23 Jan 2013
Posts: 592

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



CEO
Joined: 12 Sep 2015
Posts: 2844
Location: Canada

Re: Which of the following fractions has a decimal equivalent
[#permalink]
Show Tags
28 Sep 2016, 16:22
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 NOTE: this is one of those questions that require us to check/test each answer choice. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top. For more on this strategy, see my article: http://www.gmatprepnow.com/articles/han ... questions Cheers, Brent
_________________
Brent Hanneson – GMATPrepNow.com
Sign up for our free Question of the Day emails



Senior Manager
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 450
Location: India

Re: Which of the following fractions has a decimal equivalent
[#permalink]
Show Tags
01 Mar 2017, 00:59
If numerator and denominator in fraction doesn’t have any common factor and the denominator has a prime factor except 2 and 5, then it is going to be non terminating decimal. Out of every option only Option E has 2 as the prime factor. Rest all have 3also. Hence option E s the answer
_________________
GMAT Mentors



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8278
Location: Pune, India

Re: Which of the following fractions has a decimal equivalent
[#permalink]
Show Tags
01 Mar 2017, 02:08
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 Check out this post for a detailed discussion on terminating decimals: https://www.veritasprep.com/blog/2013/1 ... thegmat/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3484
Location: United States (CA)

Re: Which of the following fractions has a decimal equivalent
[#permalink]
Show Tags
13 Mar 2018, 17:01
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 A decimal will terminate when the equivalent fraction in lowest terms has a denominator that breaks down to primes of 2’s only, 5’s only, or both 2’s and 5’s only. Looking at our answer choices we see that 39/128 is a terminating decimal since 128 = 2^7. Answer: E
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: Which of the following fractions has a decimal equivalent &nbs
[#permalink]
13 Mar 2018, 17:01






