Aug 22 09:00 PM PDT  10:00 PM PDT What you'll gain: Strategies and techniques for approaching featured GMAT topics, and much more. Thursday, August 22nd at 9 PM EDT Aug 24 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Aug 25 09:00 AM PDT  12:00 PM PDT Join a FREE 1day verbal workshop and learn how to ace the Verbal section with the best tips and strategies. Limited for the first 99 registrants. Register today! Aug 25 08:00 PM PDT  11:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE. Aug 28 08:00 AM PDT  09:00 AM PDT Join a FREE live webinar with examPAL and Admissionado and learn how to master GMAT Critical Reasoning questions and the 6pointed star of MBA application essay glory. Save your spot today! Aug 30 08:00 PM PDT  11:00 PM PDT We'll be posting questions in DS/PS/SC/CR in competition mode. Detailed and quickest solution will get kudos. Will be collecting new links to all questions in this topic. Here you can also check links to fresh questions posted.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 22 Jun 2019
Posts: 41
Location: Canada
Concentration: Operations, Organizational Behavior

Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
19 Jul 2019, 22:05
see the picture
Attachments
terminating  Copy.jpg [ 2.55 MiB  Viewed 282 times ]



Manager
Joined: 10 Nov 2014
Posts: 59
Location: United States
Concentration: Marketing, Strategy

Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
19 Jul 2019, 22:40
Soln:
Concept to apply: A fraction will always be terminating if the denominator of fraction in the least form has NO PRIME FACTOR other than 2,5, or both 2 and 5 Now lets check each option :
I) 83/80 80 has prime factors  2,2,2,2,5 (2^4 * 5^1) only 2 and 5 in denominator. So 83/80 is terminating decimal
II) 23/120 120 has prime factors  2,2,2,5,3 (2^3*5^1*3^1)  since prime factors includes 3 , other than 2 and 5 . 23/120 is non terminating decimal.
III) 33/480  We can reduce 33/480 to 11/160 ( by dividing by 3). This is final reduced form, now check denominator.  Prime Factors of 160 are 2,2,2,2,2,5 (2^5*5^1)  Applying concept mentioned above since only 2 and 5 in denominator 33/480 is terminating decimal
Ans choice D is CORRECT[



Manager
Joined: 31 May 2018
Posts: 186
Location: United States
Concentration: Finance, Marketing

Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
19 Jul 2019, 23:36
I. \(\frac{83}{80}\) \(\frac{83}{8}\)*\(\frac{1}{10}\) 1.0375*\(\frac{1}{10}\) = 0.10375 (yes this is a terminating decimal since this has finite number of digits after decimal point)
II. \(\frac{23}{120}\) \(\frac{23}{40}\)*\(\frac{1}{3}\) = 0.575 *\(\frac{1}{3}\) =0.19166666666......(this will not end in a finite number of digits) so this is not a terminating decimal
III. \(\frac{33}{480}\) = \(\frac{33}{3}\)*\(\frac{1}{160}\) = 11*\(\frac{1}{160}\) = 11*\(\frac{1}{2}\)*\(\frac{1}{2}\)*\(\frac{1}{2}\)*\(\frac{1}{2}\)*\(\frac{1}{10}\)
=0.6875 (yes this is a terminating decimal)
D is the answer



Manager
Joined: 12 Mar 2018
Posts: 83
Location: United States

Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
19 Jul 2019, 23:39
Which of the following fractions will lead to a terminating decimal?
I. 83/80
II. 23/120
III. 33/480
A. None B. I only C. I and II only D. I and III only E. I, II, and III
A simple condition that can be used to check for terminating decimals is to check for the presence of 2*5 as factors in the denominator. In this case, I II and III all of them have multiples of 10 in the denominator, so all of them will lead to a terminating decimal.
Hence, correct answer E



Manager
Joined: 03 Aug 2009
Posts: 58

Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
19 Jul 2019, 23:56
Which of the following fractions will lead to a terminating decimal?
I. \(\frac{83}{80}\)
II. \(\frac{23}{120}\)
III. \(\frac{33}{480}\)
Now, there is theorem (rarely published in GMAT materials) on which this questions is based: A fraction has terminating decimal if its denominator has prime factors of only 2 and 5 in any power.
Now, need to prime factorize denominators in the answers: 1. \(80 = 5*2*2*2*2\)  only 2 and 5, therefore has terminating decimal 1. \(120 = 3*2*2*2*5\)  there is 3 in it , therefore out 1. \(480 = 120*4\)  as we seen, 120 has 3 in it, therefore out
Answer is B



Manager
Joined: 18 May 2019
Posts: 164

Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
Updated on: 20 Jul 2019, 05:49
We are to determine which of the following will lead to a terminating decimal.
I. 83/80 83/80=8.3/8 but we know 1/8=0.125. Hence 8.3/8 = 8.3*0.125 = 83*125*10^4 Since 83*125 leads to an integer, which is 10375, then 83*125*10^4 = 10375/10000 = 1.0375. therefore I leads to a terminating decimal.
II. 23/120. 23/120 = 23/(10*4*3) = 23*[(1/10*1/4*1/3)]. We know that 1/4 = 0.25 and 1/10 = 0.1. hence 1/4*1/10=0.025. However, 1/3 leads to a nonterminating decimal, and multiplying 0.025 by 1/3 leads to a nonterminating decimal. Therefore II does not lead to a terminating decimal
III. 33/480 33/480 = 11/160 = 11*1/160 = 11/[(1/10*1/16)]. We know 1/10 = 0.1. and 1/16 = 1/2*1/8 0.5*0.125 = 0.0625 hence 11/60 = 11*0.1*0.0625 = 0.06875, which is a terminating decimal.
The answer therefore is D. since only I and III leads to a terminating decimal.
Originally posted by eakabuah on 20 Jul 2019, 00:40.
Last edited by eakabuah on 20 Jul 2019, 05:49, edited 1 time in total.



Manager
Joined: 24 Jan 2019
Posts: 103
Location: India
Concentration: Strategy, Finance
GPA: 4

Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
20 Jul 2019, 00:52
I. 83/80
83/80 = 1 + (3/80) 1/80 = 0.0125 , So (3/80) is also terminating. No need to do the further calculation, from the above result we can directly say the (83/80) will lead to the terminating decimal.
II. 23/120
1/120 = 0.0083333..... (non terminating) So, 23/120 is also nonterminating decimal. Note: (a/120) will be terminating decimal if 'a' is multiple of '3'. Here, 23 is not a multiple of 3.
III. 33/480
33/480= 11/160 1/160 = 0.00625 1/160 is leading to terminating decimal. So, 11/160 will also lead to terminating decimal.
ANSWER: D



Manager
Joined: 07 Jul 2019
Posts: 54

Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
20 Jul 2019, 00:53
Task is to find denominators with either 2 or 5 or both. Only I and III have 2 and 5. II has 2, 5, and 3 in its denominator (infinite number of digits). D answer



Manager
Joined: 18 Jun 2013
Posts: 141
Location: India
Concentration: Technology, General Management
GPA: 3.2
WE: Information Technology (Consulting)

Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
20 Jul 2019, 01:01
Rule for Terminating or NonTerminating Recurring decimals,
=> For fractions in their simplest form, if the denominator has only powers of 2 and 5 then the fraction will be terminating.
=> For fractions in their simplest form, if the denominator has powers other than for 2 and 5 then the fraction will be non terminating recurring.
Let us now check the 3 options given,
Option 1: 83/80
This fraction is in it's lowert form.
Also, 80 = 2^4 * 5
=> 83/80 will be terminating.
Option 2: 23/120
This fraction is in it's lowest form.
Also, 120 = 2^3 * 3 * 5
=> 23/120 will be nonterminating recurring.
Option 3: 33/480
33/480 => 11/160
This fraction is in it's lowet form now.
Also, 160 = 2^5 * 5
=> 33/480 will be terminating.
Answer: D



Manager
Joined: 22 Oct 2018
Posts: 74

Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
20 Jul 2019, 02:57
Which of the following fractions will lead to a terminating decimal?
I. 83 80
8380
II. 23 120
23120
III. 33 480
33480
A. None B. I only C. I and II only D. I and III only E. I, II, and III
Solution:
The concept in this question is that a fraction will lead to a terminating decimal if and only if the reduced fraction has a prime factorization that contains only 2's or5's or both.If the prime factorization of the reduced fraction contains denominatior anything other than 2s or 5s,the decimal equivalent will not terminate. So considering the various options:
2 ) 23/120 = 23/(\(2^3\)*3*5)
3)\(\frac{33}{480}\) = \(\frac{11}{(2^5*5)}\)
1) \(\frac{83}{80}\) = 83 /\((2^4\)*5)
As we see that only 1 and 3 option have 5 and 2 in their denominators and hence they will lead to a terminating decimal. Optionn 2 have 3 also in its denominator hence it will not be a terminating decimal.Hence D is the answer IMO.



Intern
Joined: 24 Sep 2014
Posts: 39
Concentration: General Management, Technology

Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
20 Jul 2019, 03:35
(i) 83/80 > 83/(8*10) > 83/(2^4*5), 1/(2^4*5) gives terminating decimal (ii) 23/120 > 23/(12*10) > 23/(2^2*3*2*5) > 23/(2^3*3*5) doesn't give a terminating decimal because of 3 (iii) 33/480 > 3*11/(2^5*3*5) > 11/(2^5*5), 1/(2^5*5) gives terminating decimal
Answer is D



Intern
Joined: 24 Mar 2018
Posts: 48
Location: India
Concentration: Operations, Strategy
WE: Project Management (Energy and Utilities)

Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
20 Jul 2019, 03:48
A fraction leads to a terminating decimal only if its denominator has 2 or 5 as its prime factors. Any other prime factor in the denominator will make the decimal nonterminating.
I. \(\frac{83}{80} = \frac{83}{2^4*5^1}\) As the denominator has only 2 and 5 as its factors, this is a terminating decimal.
II. \(\frac{23}{120} = \frac{23}{2^3*3^1*5^1}\) As the denominator has 3 as one of its prime factors, this is a nonterminating decimal.
III. \(\frac{33}{480} = \frac{33}{2^5*3^1*5^1}\) As the denominator has 3 as one of its prime factors, this is a nonterminating decimal.
Hence, Option (B)



Intern
Joined: 14 Mar 2017
Posts: 39
Location: United States (MD)
GPA: 2.9
WE: Science (Other)

Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
20 Jul 2019, 04:14
Question: Which of the following fractions will lead to a terminating decimal?If the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5, the decimal expression terminates.I. \(\frac{83}{80}\)\[\text{Prime Factorization Calculation }\\ \text{Example: 80} \\ \begin{pmatrix*} &&80&& \\ &\swarrow&&\searrow&\\ 2&&\downarrow&&2^3\\ &&5&&\\ &&&&\\ &&&& \end{pmatrix*} \rightarrow \text{Prime Factors of 80 are } 2,2,2,2,5\\ \text{Terminating!} \] II. \(\frac{23}{120}\)\[\text{Prime Factorization Calculation }\\ \text{Example: N = 120} \\ \begin{pmatrix*} &&120&& \\ &\swarrow&&\searrow&\\ 2^3&&\downarrow&&5\\ &&3&&\\ &&&&\\ &&&& \end{pmatrix*} \rightarrow \text{Prime Factors of 120 are } 2,2,2,3,5\\ \text{NOT Terminating!} \] III. \(\frac{33}{480}\)\[\text{Prime Factorization Calculation }\\ \text{Example: N = 480} \\ \begin{pmatrix*} &&480&& \\ &\swarrow&&\searrow&\\ 2^5&&\downarrow&&5\\ &&3&&\\ &&&&\\ &&&& \end{pmatrix*} \rightarrow \text{Prime Factors of 480 are } 2,2,2,2,2,3,5\\ \text{NOT Terminating!} \] Correct Answer: B. \(\implies\text{I only}\)
_________________
"What is my purpose?" "You pass butter." "Oh my god..." "Yeah, welcome to the club, pal."



Senior Manager
Joined: 25 Sep 2018
Posts: 396
Location: United States (CA)
Concentration: Finance, Strategy
GPA: 3.97
WE: Investment Banking (Investment Banking)

Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
20 Jul 2019, 04:15
Solution: General property: A fraction in its lowest term can be expressed as a terminating decimal if and only if the denominator has powers of only 2 and/or 5. Lets prime factorize the division. I. \(\frac{83}{2^4 X 5}\) , Hence we see that the division only contains 2 & 5. So this fraction will be terminating. II.\(\frac{23}{2^3 X 3 X 5}\)We observe that there is 3 in the prime factorization , Hence this fraction is non terminating III.\(\frac{33}{480}\) =\(\frac{{11 X 3}}{2^5 X 3 X 5}\), we observe that 3 gets cancelled with the 3 in the numerator leaving only 2 & 5 as factors in the denominator. Hence this fraction will be terminating. So the answer here must be D
_________________
Why do we fall?...So we can learn to pick ourselves up again



Manager
Joined: 01 Oct 2018
Posts: 111

Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
20 Jul 2019, 05:05
Which of the following fractions will lead to a terminating decimal?
I. 83/80 = 1.0375
II. 23/120 = 0.19166(6)
III. 33/480 = 0.06875
ANSWER D
A. None B. I only C. I and II only D. I and III only E. I, II, and III



Manager
Joined: 17 Jan 2017
Posts: 83

Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
20 Jul 2019, 05:13
Which of the following fractions will lead to a terminating decimal?
I. 83/80
II. 23/120
III. 33/480
For a decimal to be terminating, the denominator must be in power of 2's or 5's or both.
i) 80= 5*2^4 ii) 120= 5*3*2^3 iii) 160 = 5*2^5
so, the correct answer choice is (D)



Manager
Joined: 25 Jul 2018
Posts: 199

Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
20 Jul 2019, 05:33
As we know, we call the Terminating decimal if and only if the denominator has powers of only 2 and/or 5.
I. 83/80=83/(16*5)=83/(2^4*5) (yes, denominator consists of only powers of 2 and 5)
II. 23/120=23/(2^3*3*5) (No, it is not terminating decimal, denominator has power of 3.)
III. 33/480 (we can divide both parts of fraction by 3) > 11/160 > 11/160=11/(16*10)=11/(2^5*5) (yes, denominator consists of only powers of 2 and 5)
We got only I and III right The answer choice is D



Manager
Joined: 27 Mar 2018
Posts: 73
Location: India

Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
20 Jul 2019, 06:31
For a fraction to be a terminating decimal, the denominator must be in the form 2^m*5^n in reduced form. 1) 80 = 2^4*5. Hence it will be lead to a terminating decimal. 2) 120= 2^3 * 3 * 5. Non terminating 3) Reducing fraction further it can be written as \(\frac{11}{160}\). 160=2^5*5. Terminating Hence option D
_________________
Thank you for the kudos. You are awesome!



Intern
Joined: 09 Jul 2019
Posts: 38

Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
20 Jul 2019, 06:38
Only options 1 and 3 have denominators in forms of 2^a*5^b. Option 2 has 2^a*3^b*5^c. (D) is answer



Senior Manager
Joined: 18 Jan 2018
Posts: 308
Location: India
Concentration: General Management, Healthcare
GPA: 3.87
WE: Design (Manufacturing)

Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
Show Tags
20 Jul 2019, 06:38
I. 83/80 =83/8 *10 = 10.3875/10 = 1.03875 > Terminating decimal
II. 23/120 = 23/12*10 = 1.916666666.. /10 = 0.19166666666... > is not a terminating decimal
III. 33/480 = 11*3/4*3*4*10 = 11/16*10 =0.9=6875/10 = 0.06875> terminating decimal
D. I and III only Is the correct answer




Re: Which of the following fractions will lead to a terminating decimal?
[#permalink]
20 Jul 2019, 06:38



Go to page
Previous
1 2 3 4 5
Next
[ 81 posts ]



