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

It is currently 19 Jun 2018, 03:01

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

Events & Promotions in June
Open Detailed Calendar

Is r/s^2 a terminating decimal?

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46161
Re: Is r/s^2 a terminating decimal? [#permalink]

Show Tags

New post 16 Nov 2014, 12:25
davidfrank wrote:
Bunuel wrote:
SudiptoGmat wrote:
Is r/s^2 a terminating decimal?

1. s=225
2. r=81f t 5r y t5

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

Statement (1) by itself is insufficient. Knowing only without is not enough information to answer the question.

Statement (2) by itself is insufficient. Knowing only without is not enough information to answer the question.

Statements (1) and (2) combined are sufficient. We know both and , so we can calculate the given expression.

The correct answer is C.

But I think answer is A. ST 1 is sufficient. Any comment ??


Several questions have been posted about terminating decimals lately. Below is the theory about this issue:

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.

Now:

For (1) \(\frac{r}{s^2}=\frac{r}{225^2}=\frac{r}{9^2*5^4}\), we can not say whether this fraction will be terminating, as 9^2 can be reduced or not.

(2) is clearly insufficient.

(1)+(2) \(\frac{r}{s^2}=\frac{9^2}{9^2*5^4}=\frac{1}{5^4}\), as denominator has only 5 as prime, hence this fraction is terminating decimal.

Answer: C.


Hey Bunuel,

As per the theory if the denominator can be expressed in the form of 2^m*5^n, then the numerator is a terminating decimal. However, in the question above after reducing the fraction we are left only with 5^n and hence not sure why in theory we are mentioning 2^n when any integer when divided by 5 will always be terminating. I might be asking a very stupid question but really now want to understand what is the missing link here.


You are not reading carefully...

The denominator should be in the form of 2^m*5^n, where \(m\) and \(n\) are non-negative integers. Thus n and m could be 0, meaning that the denominator could have only 2's, only 5's or both.

For more check Terminating and Recurring Decimals Problems in our Special Questions Directory.

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

Manager
Manager
avatar
S
Joined: 11 Apr 2016
Posts: 50
Location: India
Concentration: Marketing, Technology
WE: Business Development (Computer Software)
Premium Member Reviews Badge
Re: Is r/s^2 a terminating decimal? [#permalink]

Show Tags

New post 27 Aug 2016, 09:49
Hi, I had a doubt in this question. Using the same logic of denominator needs to be in a ratio of 2^n * 5^m, with option 1 we clearly know its not the case regardless of the numerator.

s^2 = 225 ^ 2 = 3^ 4 * 5^4

So how does it matter what the numerator is? It will never be a terminating decimal and the answer should be A. Brunel can you please explain this
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46161
Re: Is r/s^2 a terminating decimal? [#permalink]

Show Tags

New post 27 Aug 2016, 09:54
varunjoshi31 wrote:
Hi, I had a doubt in this question. Using the same logic of denominator needs to be in a ratio of 2^n * 5^m, with option 1 we clearly know its not the case regardless of the numerator.

s^2 = 225 ^ 2 = 3^ 4 * 5^4

So how does it matter what the numerator is? It will never be a terminating decimal and the answer should be A. Brunel can you please explain this


Let me ask you: what id the numerator is 3^4?
_________________

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

Manager
Manager
avatar
S
Joined: 11 Apr 2016
Posts: 50
Location: India
Concentration: Marketing, Technology
WE: Business Development (Computer Software)
Premium Member Reviews Badge
Re: Is r/s^2 a terminating decimal? [#permalink]

Show Tags

New post 27 Aug 2016, 19:19
Thanks Brunel for the clarification, missed out that 2^m could be 1 where m is 0 i.e. non negative. Always thought that the decimal to be terminating should be a multiple of 10, but now realize it could be a multiple of 5 or even 2 (2^m * 5^n) where m and n are non negative.
Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 398
Re: Is r/s^2 a terminating decimal? [#permalink]

Show Tags

New post 26 Sep 2016, 07:29
C


(1) s=225 --> NOT SUFFICIENT - we don't know the value of r to make that determination


(2) r=81 --> NOT SUFFICIENT - we don't know value of s

A,B,D eliminated

(1) + (2) - SUFFICIENT - we can determine if 81/(225^2) is a terminating decimal or not
Director
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 597
Schools: Cambridge'16
Re: Is r/s^2 a terminating decimal? [#permalink]

Show Tags

New post 27 Apr 2017, 22:32
davidfrank wrote:
Bunuel wrote:
SudiptoGmat wrote:
Is r/s^2 a terminating decimal?

1. s=225
2. r=81f t 5r y t5

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

Statement (1) by itself is insufficient. Knowing only without is not enough information to answer the question.

Statement (2) by itself is insufficient. Knowing only without is not enough information to answer the question.

Statements (1) and (2) combined are sufficient. We know both and , so we can calculate the given expression.

The correct answer is C.

But I think answer is A. ST 1 is sufficient. Any comment ??


Several questions have been posted about terminating decimals lately. Below is the theory about this issue:

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.

Now:

For (1) \(\frac{r}{s^2}=\frac{r}{225^2}=\frac{r}{9^2*5^4}\), we can not say whether this fraction will be terminating, as 9^2 can be reduced or not.

(2) is clearly insufficient.

(1)+(2) \(\frac{r}{s^2}=\frac{9^2}{9^2*5^4}=\frac{1}{5^4}\), as denominator has only 5 as prime, hence this fraction is terminating decimal.

Answer: C.


Hey Bunuel,

As per the theory if the denominator can be expressed in the form of 2^m*5^n, then the numerator is a terminating decimal. However, in the question above after reducing the fraction we are left only with 5^n and hence not sure why in theory we are mentioning 2^n when any integer when divided by 5 will always be terminating. I might be asking a very stupid question but really now want to understand what is the missing link here.





You can always do like in this case: 5^4*2^0
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 6997
Premium Member
Re: Is r/s^2 a terminating decimal? [#permalink]

Show Tags

New post 18 Jun 2018, 04:08
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Is r/s^2 a terminating decimal?   [#permalink] 18 Jun 2018, 04:08

Go to page   Previous    1   2   [ 27 posts ] 

Display posts from previous: Sort by

Is r/s^2 a terminating decimal?

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


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®.