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

It is currently 16 Nov 2018, 06:10

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • GMATbuster's Weekly GMAT Quant Quiz # 9

     November 17, 2018

     November 17, 2018

     09:00 AM PST

     11:00 AM PST

    Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

Any decimal that has only a finite number of nonzero digits

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Joined: 02 Dec 2012
Posts: 177
Any decimal that has only a finite number of nonzero digits  [#permalink]

Show Tags

New post 18 Dec 2012, 04:27
2
17
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

75% (00:57) correct 25% (01:46) wrong based on 855 sessions

HideShow timer Statistics

Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?

(1) 90 < r < 100
(2) s = 4
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50617
Re: Any decimal that has only a finite number of nonzero digits  [#permalink]

Show Tags

New post 18 Dec 2012, 04:32
18
33
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 \(b\) (the 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 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:
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?

(1) 90 < r < 100. Nothing about the denominator. Not sufficient.

(2) s = 4. According to the above, any fraction r/4=r/2^2 when expressed as a decimal will be a terminating decimal. Sufficient.

Answer: B.

Questions testing this concept:
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.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
VP
VP
User avatar
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1151
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
GMAT ToolKit User Premium Member
Re: Any decimal that has only a finite number of nonzero digits  [#permalink]

Show Tags

New post 18 Dec 2012, 04:33
A fraction r/s will only be a terminating decimal ONLY if it is of the form \(Numerator/ 2^m 5^n\), where n and m are non-negative.
Statement 1 gives the range of numerators, of which we are not concerned at all. Insufficient
Statement 2 gives the value of denominator which is of the form \(2^2\). Hence the fraction has to be a terminating decimal.
+1B
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

VP
VP
User avatar
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1151
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
GMAT ToolKit User Premium Member
Re: Any decimal that has only a finite number of nonzero digits  [#permalink]

Show Tags

New post 18 Dec 2012, 04:33
2
Manager
Manager
avatar
Joined: 29 Mar 2010
Posts: 121
Location: United States
Concentration: Finance, International Business
GMAT 1: 590 Q28 V38
GPA: 2.54
WE: Accounting (Hospitality and Tourism)
GMAT ToolKit User
Re: Any decimal that has only a finite number of nonzero digits  [#permalink]

Show Tags

New post 29 Jul 2013, 17:43
Question, I understand that a terminating decimal has to be of the form \(2^x5^x\) but four is only in the form of \(2^n\) to be a terminating decimal it can meet either of the requirements?

Thanks,
Hunter
_________________

4/28 GMATPrep 42Q 36V 640

Director
Director
User avatar
Joined: 14 Dec 2012
Posts: 766
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
GMAT ToolKit User
Re: Any decimal that has only a finite number of nonzero digits  [#permalink]

Show Tags

New post 29 Jul 2013, 17:51
2
1
hfbamafan wrote:
Question, I understand that a terminating decimal has to be of the form \(2^x5^x\) but four is only in the form of \(2^n\) to be a terminating decimal it can meet either of the requirements?

Thanks,
Hunter


for a fraction to be terminating two condition must satisfy:
1) numerator is an INTEGER.
2) denominator should be of form \(2^x 5^y\) \((x,y\)==>integers which also includes 0)

now in this question
denominator is \(2^2 5^0\)
hence it satisfies.

hope it helps
_________________

When you want to succeed as bad as you want to breathe ...then you will be successfull....

GIVE VALUE TO OFFICIAL QUESTIONS...



GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabulary-list-for-gmat-reading-comprehension-155228.html
learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment
: http://www.youtube.com/watch?v=APt9ITygGss

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4170
Location: United States (CA)
Re: Any decimal that has only a finite number of nonzero digits  [#permalink]

Show Tags

New post 03 Oct 2016, 09:33
1
1
Walkabout wrote:
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?

(1) 90 < r < 100
(2) s = 4


This problem is testing us on our knowledge of terminating decimals.

When solving this problem, we should remember that there is a special property of fractions that allows their decimal equivalents to terminate. In its most-reduced form, any fraction with a denominator whose prime factorization contains only 2s, 5s, or both produces decimals that terminate. A denominator with any other prime factors produces decimals that do not terminate. So to determine whether r/s is expressed as a terminating decimal, we need to determine whether the prime factorization of s contains only 2s, 5s, or both.

Statement One Alone:

90 < r < 100

Since statement one does not provide any information about s, we cannot determine whether r/s is expressed as a terminating decimal. If r = 91 and s = 1, then r/s is a terminating decimal. On the other hand, if r = 91 and s = 3, then r/s = 30.3333… and thus, r/s is not a terminating decimal. Statement one alone is not sufficient. We can eliminate answer choices A and D.

Statement Two Alone:

s = 4

Since we know that s = 4, we know that the prime factorization of s (2^2) only contains 2’s. Thus, r/s is expressed as a terminating decimal.

Answer: B
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 477
Re: Any decimal that has only a finite number of nonzero digits  [#permalink]

Show Tags

New post 12 Sep 2018, 14:32
Walkabout wrote:
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?

(1) 90 < r < 100
(2) s = 4


\(r,s\,\, \geqslant 1\,\,\,{\text{ints}}\)

\(\frac{r}{s}\,\,\,\mathop = \limits^? \,\,\,\,{\text{terminating}}\)

\(\left( 1 \right)\,\,90 < r < 100\,\,\,\,\left\{ \begin{gathered}
\,\left( {r,s} \right) = \left( {95,5} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\,\left( {\frac{{95}}{5} = \operatorname{int} } \right) \hfill \\
\,\left( {r,s} \right) = \left( {91,3} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\,\left( {\frac{{91}}{3} = 30\frac{1}{3} = 30.333 \ldots } \right) \hfill \\
\end{gathered} \right.\)

\(\left( 2 \right)\,\,s = 4\)

\(\left( * \right)\,\,\,\,{\text{r/s}}\,\,\,{\text{division}}\,\,{\text{algorithm}}:\,\,\,\left\{ \begin{gathered}
\,r = qs + R\,\,\,\mathop = \limits^{s\, = \,4} \,\,\,4q + R \hfill \\
\,q\,\,\operatorname{int} \,\,\,,\,\,\,\,0\,\,\, \leqslant \,\,\,R\,\,\operatorname{int} \,\,\, \leqslant \,\,3\,\,\,\,\left( { = s - 1} \right) \hfill \\
\end{gathered} \right.\)

\(\frac{r}{s}\,\,\,\,\mathop = \limits^{\,\left( * \right)} \,\,\,\,\frac{{4q + R}}{4} = q + \frac{R}{4}\,\, = \,\,\operatorname{int} \,\, + \,\,\frac{R}{4}\,\,\,\,\,\,\,\)

\(\frac{R}{4} = \,\,\,\left\{ {\begin{array}{*{20}{c}}
{\,\,\frac{0}{4}} \\
{\,\,\frac{1}{4}} \\
{\,\,\frac{2}{4}} \\
{\,\,\frac{3}{4}}
\end{array}} \right.\begin{array}{*{20}{c}}
{\,\,{\text{if}}\,\,\,R = 0\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left( {\frac{r}{4} = \operatorname{int} } \right)} \\
{\,\,{\text{if}}\,\,\,R = 1\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left( {\frac{r}{4} = \operatorname{int} \,\, + \,\,0.25} \right)} \\
{\,\,{\text{if}}\,\,\,R = 2\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left( {\frac{r}{4} = \operatorname{int} \,\, + \,\,0.5} \right)} \\
{\,\,{\text{if}}\,\,\,R = 3\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left( {\frac{r}{4} = \operatorname{int} \,\, + \,\,0.75} \right)}
\end{array}\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

GMAT Club Bot
Re: Any decimal that has only a finite number of nonzero digits &nbs [#permalink] 12 Sep 2018, 14:32
Display posts from previous: Sort by

Any decimal that has only a finite number of nonzero digits

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron
Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.