BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Terminated decimal

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Tue Jul 09, 2013 8:16 am
veenu08 wrote:Is r/s a terminated decimal?

1. r is a factor of 100
2. s is a factor of 100
Aside: A terminating decimal is one that does not repeat.
For example, 1/4 = 0.25 so this is a terminating decimal.
Conversely, 1/3 = 0.333333.... so this is a non-terminating decimal

Target question: Is r/s a terminating decimal?

Statement 1: r is a factor of 100
There are several pairs of values that meet this condition. Here are two:
Case a: r = 1 and s = 4, in which case r/s is a terminating decimal
Case b: r = 1 and s = 3, in which case r/s is not a terminating decimal
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: s is a factor of 100
There's a nice rule that says something like,
If the prime factorization of the denominator contains only 2's and/or 5's, then the decimal version of the fraction will be a terminating decimal.
Since 100 = 2x2x5x5, any factor of 100 will contain only 2's and/or 5's (or the denominator can be 1, in which case the decimal will definitely terminate).
Since the denominator of r/s must contain only 2's and/or 5's, r/s must be a terminating decimal
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Mon Oct 24, 2016 6:25 am, edited 1 time in total.
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Tue Jul 09, 2013 8:26 am
If r and s are positive integers, can the fraction r/s be expressed as a decimal with only a finite number of nonzero digits?

(1) s is a factor of 100.
(2) r is a factor of 100.
A TERMINATING decimal has a FINITE NUMBER OF DIGITS:
.5
.123
.8730253.

A NON-TERMINATING decimal has an INFINITE NUMBER OF DIGITS:
.33333....
.121212....
.871871871...

To determine whether a fraction will yield a terminating decimal:

1. Put the fraction in its MOST REDUCED FORM.
2. PRIME-FACTORIZE the denominator.

If the prime-factorization of the denominator includes ONLY 2'S AND/OR 5'S, the fraction will yield a TERMINATING decimal.
If the prime-factorization of the denominator includes ANY OTHER PRIME NUMBER, the fraction will yield a NON-TERMINATING decimal.

Case 1: 3/120
In its most reduced form, 3/120 = 1/40.
40 = 2² * 5.
Since the the prime-factorization of the denominator includes only 2's and 5's, 3/120 will yield a TERMINATING DECIMAL:
3/120 = .025

Case 2: 15/110
In its most reduced form, 15/110 = 3/22.
22 = 2*11.
Since the prime-factorization of the denominator includes 11 -- a prime number OTHER THAN 2 OR 5 -- 15/110 will yield a NON-TERMINATING DECIMAL:
15/110 = .1363636...

Onto the problem at hand.
Question rephrased: When r/s is in its most reduced form, will the prime-factorization of the denominator include only 2's and/or 5's?

Statement 1: s is a factor of 100
Since 100 = 2²5², the prime-factorization of s cannot include any prime number other than 2 and/or 5.
Thus, the value of r is IRRELEVANT:
Since the prime-factorization of s cannot include any prime number other than 2 and/or 5, the denominator of r/s in its most reduced form cannot include any prime number other than 2 and/or 5.
SUFFICIENT.

Statement 2: r is a factor of 100
No information about s.
If r=1 and s=2, then r/s = 1/2 = .5.
In this case, r/s is terminating.
If r=1 and s=3, then r/s = 1/3 = .33333...
In this case, r/s is NOT terminating.
INSUFFICIENT.

The correct answer is A.

Similar problems:

https://www.beatthegmat.com/real-number- ... 61902.html
https://www.beatthegmat.com/terminating- ... 08208.html
https://www.beatthegmat.com/terminating- ... 92476.html
Last edited by GMATGuruNY on Tue Jul 09, 2013 5:44 pm, edited 1 time in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Tue Jul 09, 2013 4:46 pm
As you've written the question, the answer is C, as we need to know that r is an integer. (If, for example, r = 1/3 and s = any factor of 100, r/s will not terminate.)

That said, I would imagine that GMAT would tell you that r is an integer, or that r/s is expressed in reduced form (which, by convention, means that both r and s are integers), in which case the logic given above is correct. I notice that GMATGuruNY changed the prompt to add this fact to the original question, and I'd say he was right to do so.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 358
Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members
Location: Jeddah, Saudi Arabia
Thanked: 42 times
GMAT Score:730

by faraz_jeddah » Wed Jul 10, 2013 11:34 am
Matt@VeritasPrep wrote:As you've written the question, the answer is C, as we need to know that r is an integer. (If, for example, r = 1/3 and s = any factor of 100, r/s will not terminate.)

That said, I would imagine that GMAT would tell you that r is an integer, or that r/s is expressed in reduced form (which, by convention, means that both r and s are integers), in which case the logic given above is correct. I notice that GMATGuruNY changed the prompt to add this fact to the original question, and I'd say he was right to do so.
Thanks! I was wondering the same.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 209
Joined: Thu Jan 12, 2012 12:59 pm

by dddanny2006 » Sat Mar 15, 2014 2:50 pm
Hey Brent
In this particular problem Statement 1 says r is a factor of 100

1,2,4,5,10,25,20,50 and 100 are factors of 100

Now let s be equal to 4 and let r be 100

Now we have (r/s)=100/25 =4

Next lets have s=10 and r=2 (r/s)=0.2(non recurring)


So I guess it should be insufficient because we could get an integer or we could also get a non recurring decimal.

Please clear this sir,

Thanks

Brent@GMATPrepNow wrote:
veenu08 wrote:If r and s are positive integers, can the fraction r/s be expressed as a decimal with only a finite number of nonzero digits?

(1) s is a factor of 100.
(2) r is a factor of 100.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Sat Mar 15, 2014 8:01 pm
dddanny2006 wrote:Hey Brent
In this particular problem Statement 1 says r is a factor of 100

1,2,4,5,10,25,20,50 and 100 are factors of 100

Now let s be equal to 4 and let r be 100

Now we have (r/s)=100/25 = 4

Next lets have s=10 and r=2 (r/s)=0.2(non recurring)

So I guess it should be insufficient because we could get an integer or we could also get a non recurring decimal.
A terminating decimal is one that does not repeat.
For example, 1/4 = 0.25, so this is a terminating decimal.
Likewise, 6/3 = 2, so this is a terminating decimal
Conversely, 1/3 = 0.333333.... so this is a non-terminating decimal

Both of your examples result in terminating decimals.
100/25 = 4: 4 is a terminating decimal
2/10 = 0.2 : 0.2 is a terminating decimal

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 209
Joined: Thu Jan 12, 2012 12:59 pm

by dddanny2006 » Sun Mar 16, 2014 1:59 am
Thanks Sir.I was of the opinion that 4 was an integer.Do we represent that 4 as 4.0?Is this the mechanism that makes it a decimal?A little confused.Because everywhere I saw something relating to terminating decimals,it was just a 1/3 or a 25/4 and other similar decimals,never did I come across an integer.
Brent@GMATPrepNow wrote:
dddanny2006 wrote:Hey Brent
In this particular problem Statement 1 says r is a factor of 100

1,2,4,5,10,25,20,50 and 100 are factors of 100

Now let s be equal to 4 and let r be 100

Now we have (r/s)=100/25 = 4

Next lets have s=10 and r=2 (r/s)=0.2(non recurring)

So I guess it should be insufficient because we could get an integer or we could also get a non recurring decimal.
A terminating decimal is one that does not repeat.
For example, 1/4 = 0.25, so this is a terminating decimal.
Likewise, 6/3 = 2, so this is a terminating decimal
Conversely, 1/3 = 0.333333.... so this is a non-terminating decimal

Both of your examples result in terminating decimals.
100/25 = 4: 4 is a terminating decimal
2/10 = 0.2 : 0.2 is a terminating decimal

Cheers,
Brent
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Sun Mar 16, 2014 6:21 am
dddanny2006 wrote:Thanks Sir.I was of the opinion that 4 was an integer.Do we represent that 4 as 4.0?Is this the mechanism that makes it a decimal? A little confused. Because everywhere I saw something relating to terminating decimals, it was just a 1/3 or a 25/4 and other similar decimals,never did I come across an integer.
A decimal is just a framework one can use to represent numbers using powers of ten (this the prefix "dec"), whereby one position represents tenths, another position represents hundredths, and so on. This framework also includes tens, hundreds and thousands.

For this question, it really comes down to, "Can we write this number using decimal notation and be able to stop writing digits?"
So, if we convert 1/3 to decimal notation, we CANNOT STOP writing digits: 0.333333...
If we convert 1/4 to decimal notation, we CAN STOP writing digits: 0.25
Similarly, if we convert 12/4 to decimal notation, we CAN STOP writing digits: 3

For more, see page 110 of the OG13

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 209
Joined: Thu Jan 12, 2012 12:59 pm

by dddanny2006 » Sun Mar 16, 2014 10:53 am
So you mean 100/25 equals 4.This 4 can be represented as 0.4 *10 to the power of 1.And this 0.4 is a terminated decimal.Is my understanding correct now?
Brent@GMATPrepNow wrote:
dddanny2006 wrote:Thanks Sir.I was of the opinion that 4 was an integer.Do we represent that 4 as 4.0?Is this the mechanism that makes it a decimal? A little confused. Because everywhere I saw something relating to terminating decimals, it was just a 1/3 or a 25/4 and other similar decimals,never did I come across an integer.
A decimal is just a framework one can use to represent numbers using powers of ten (this the prefix "dec"), whereby one position represents tenths, another position represents hundredths, and so on. This framework also includes tens, hundreds and thousands.

For this question, it really comes down to, "Can we write this number using decimal notation and be able to stop writing digits?"
So, if we convert 1/3 to decimal notation, we CANNOT STOP writing digits: 0.333333...
If we convert 1/4 to decimal notation, we CAN STOP writing digits: 0.25
Similarly, if we convert 12/4 to decimal notation, we CAN STOP writing digits: 3

For more, see page 110 of the OG13

Cheers,
Brent
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1