Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Sep 2014, 22:36

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is \frac{r}{s^2} a terminating decimal? 1. s = 225 2. r = 81

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Retired Moderator
User avatar
Joined: 18 Jul 2008
Posts: 997
Followers: 8

Kudos [?]: 71 [0], given: 5

GMAT Tests User
Is \frac{r}{s^2} a terminating decimal? 1. s = 225 2. r = 81 [#permalink] New post 06 Nov 2008, 11:46
Is \frac{r}{s^2} a terminating decimal?

1. s = 225
2. r = 81


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
Intern
Intern
avatar
Joined: 30 Oct 2008
Posts: 30
Followers: 0

Kudos [?]: 2 [0], given: 0

Re: Terminating Decimal [#permalink] New post 06 Nov 2008, 12:15
C.
When r = 81, if s = 2 will lead to terminating decimal. If s=21 will lead to non terminating.
When s = 225, if r = 81 will lead to terminating decimal. If r=1 will lead to non terminating.

When s=225, r=81 then
r/s^2 = 9*9/(25*25*9*9) = 0.04*0.04 a terminating decimal.
1 KUDOS received
VP
VP
User avatar
Joined: 05 Jul 2008
Posts: 1436
Followers: 33

Kudos [?]: 219 [1] , given: 1

GMAT Tests User
Re: Terminating Decimal [#permalink] New post 06 Nov 2008, 20:03
1
This post received
KUDOS
bigfernhead wrote:
Is \frac{r}{s^2} a terminating decimal?

1. s = 225
2. r = 81


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


terminating decimal is one in which the denominator has only 2's and 5's

s=225. means 5 ^ 4 X 3 ^ 4 Insuff because we dont know what numerator can be

r = 81 we dont know what the denominator is

use both, we get 5 ^ 4 and 2 ^ 0 in the denominator. Yes it is terminating.
Retired Moderator
User avatar
Joined: 18 Jul 2008
Posts: 997
Followers: 8

Kudos [?]: 71 [0], given: 5

GMAT Tests User
Re: Terminating Decimal [#permalink] New post 07 Nov 2008, 06:23
When you say "it only has 2's and 5's in the denominator"

Does that mean prime factors of 2's and 5's?

Let's say the denominator is 50.

Prime factors are 5*5*2, therefore it is terminating?

Also, what does this mean?

s=225. means 5 ^ 4 X 3 ^ 4 Insuff because we dont know what numerator can be

icandy wrote:
bigfernhead wrote:
Is \frac{r}{s^2} a terminating decimal?

1. s = 225
2. r = 81


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


terminating decimal is one in which the denominator has only 2's and 5's

s=225. means 5 ^ 4 X 3 ^ 4 Insuff because we dont know what numerator can be

r = 81 we dont know what the denominator is

use both, we get 5 ^ 4 and 2 ^ 0 in the denominator. Yes it is terminating.
1 KUDOS received
SVP
SVP
avatar
Joined: 17 Jun 2008
Posts: 1579
Followers: 12

Kudos [?]: 184 [1] , given: 0

GMAT Tests User
Re: Terminating Decimal [#permalink] New post 07 Nov 2008, 10:57
1
This post received
KUDOS
bigfernhead wrote:
When you say "it only has 2's and 5's in the denominator"

Does that mean prime factors of 2's and 5's?

Let's say the denominator is 50.

Prime factors are 5*5*2, therefore it is terminating?

Also, what does this mean?

s=225. means 5 ^ 4 X 3 ^ 4 Insuff because we dont know what numerator can be



To make it simpler, a fraction will be a terminating decimal when the decimal point terminates (e.g. 1/3 cannot be a terminating decimal as it will be 0.3333333333333 without any termination. However, 9/3 is a terminating decimal as it is 3.0).

With this, in order to find out whether a fraction is a terminating decimal, we need to know the values of numerator as well as denominator. Additionally, if the denominator contains only 2's (e.g. 2, 2^2, 2^10, etc.), only 5's or a combination of 2's and 5's, then the fraction will always be a terminating decimal irrespective of the numerator.

However, from stmt1, we know that denominator = 5^2 * 3^2 and the presence of 3^2 adds to the complexity. We do not know whether the numerator is a multiple of 3^2. If it is, the fraction is a terminating decimal. Else, it is not.

Similarly, from stmt2 only, we do not know what denominator is.

Combining both, we know that numerator is a multiple of 3^2 and additionally, denominator contains only 5^2. Hence, the fraction will be a terminating decimal.
Retired Moderator
User avatar
Joined: 18 Jul 2008
Posts: 997
Followers: 8

Kudos [?]: 71 [0], given: 5

GMAT Tests User
Re: Terminating Decimal [#permalink] New post 07 Nov 2008, 11:10
+1 for the both of you. Awesome explanations!
Manager
Manager
avatar
Joined: 15 Oct 2008
Posts: 112
Followers: 1

Kudos [?]: 1 [0], given: 0

Re: Terminating Decimal [#permalink] New post 07 Nov 2008, 13:22
icandy wrote:
bigfernhead wrote:
Is \frac{r}{s^2} a terminating decimal?

1. s = 225
2. r = 81


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


terminating decimal is one in which the denominator has only 2's and 5's

s=225. means 5 ^ 4 X 3 ^ 4 Insuff because we dont know what numerator can be

r = 81 we dont know what the denominator is

use both, we get 5 ^ 4 and 2 ^ 0 in the denominator. Yes it is terminating.


I think you made a mistake here. 225 = 5^2 x 3^2 (instead of 5^4 x 3^4).
Senior Manager
Senior Manager
User avatar
Joined: 21 Apr 2008
Posts: 272
Location: Motortown
Followers: 0

Kudos [?]: 82 [0], given: 0

GMAT Tests User
Re: Terminating Decimal [#permalink] New post 08 Nov 2008, 08:44
scthakur wrote:
bigfernhead wrote:
When you say "it only has 2's and 5's in the denominator"

Does that mean prime factors of 2's and 5's?

Let's say the denominator is 50.

Prime factors are 5*5*2, therefore it is terminating?

Also, what does this mean?

s=225. means 5 ^ 4 X 3 ^ 4 Insuff because we dont know what numerator can be



To make it simpler, a fraction will be a terminating decimal when the decimal point terminates (e.g. 1/3 cannot be a terminating decimal as it will be 0.3333333333333 without any termination. However, 9/3 is a terminating decimal as it is 3.0).

With this, in order to find out whether a fraction is a terminating decimal, we need to know the values of numerator as well as denominator. Additionally, if the denominator contains only 2's (e.g. 2, 2^2, 2^10, etc.), only 5's or a combination of 2's and 5's, then the fraction will always be a terminating decimal irrespective of the numerator.

However, from stmt1, we know that denominator = 5^2 * 3^2 and the presence of 3^2 adds to the complexity. We do not know whether the numerator is a multiple of 3^2. If it is, the fraction is a terminating decimal. Else, it is not.

Similarly, from stmt2 only, we do not know what denominator is.

Combining both, we know that numerator is a multiple of 3^2 and additionally, denominator contains only 5^2. Hence, the fraction will be a terminating decimal.


scthakur : how is 81/225^2 = 81/50625 = .0016 a terminating decimal ?

As far as I know, a terminating decimal is one, with numerator as an integer and denominator must be an interger that can be expressed as 2^x * 5^y, where x and y are non-negative integers, that means they can't be zero.

Even though the answer to the above DS problem is C, isn't the answer to the question Is r/s^2, a clear No ?
VP
VP
User avatar
Joined: 05 Jul 2008
Posts: 1436
Followers: 33

Kudos [?]: 219 [0], given: 1

GMAT Tests User
Re: Terminating Decimal [#permalink] New post 08 Nov 2008, 09:02
nganle08 wrote:

I think you made a mistake here. 225 = 5^2 x 3^2 (instead of 5^4 x 3^4).


The denominator is S^2 and NOT S. I made a mistake in writing the den as S.

225 ^2 = 15 ^4 = 5 ^4 X 3 ^4 ; numerator = 3 ^4
Re: Terminating Decimal   [#permalink] 08 Nov 2008, 09:02
    Similar topics Author Replies Last post
Similar
Topics:
11 Experts publish their posts in the topic If d=(1)/((2^3)(5^7)) is expressed as a terminating decimal wizard 4 02 Mar 2012, 03:20
10 Experts publish their posts in the topic Is r/s^2 a terminating decimal? SudiptoGmat 14 23 Feb 2010, 13:23
Is \frac{r}{s^2} a terminating decimal? 1. s = 225 2. r = 81 study 3 12 Jan 2010, 03:27
Experts publish their posts in the topic Is r/s^2 a terminating number? 1) s = 225 2) r = 81 seongbae 1 17 May 2008, 17:34
Is r/s^2 a terminating decimal? 1) s = 225 2) r = 81 yuefei 4 14 Nov 2007, 16:23
Display posts from previous: Sort by

Is \frac{r}{s^2} a terminating decimal? 1. s = 225 2. r = 81

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.