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

It is currently 02 Aug 2015, 12:54
GMAT Club Tests

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 5^(x+2)/25<1 ?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28782
Followers: 4595

Kudos [?]: 47523 [0], given: 7123

Is 5^(x+2)/25<1 ? [#permalink] New post 25 Jun 2012, 02:07
Expert's post
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

76% (01:49) correct 24% (00:51) wrong based on 320 sessions
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28782
Followers: 4595

Kudos [?]: 47523 [0], given: 7123

Re: Is 5^(x+2)/25<1 ? [#permalink] New post 25 Jun 2012, 02:07
Expert's post
2
This post was
BOOKMARKED
SOLUTION

Is \(\frac{5^{x+2}}{25}<1\) ?

Is \(\frac{5^{x+2}}{25} <1\)? --> is \(\frac{5^{x+2}}{5^2}<1\)? --> is \(5^x<1\)? --> is \(x<0\)?

Or: is \(\frac{5^{x+2}}{25} <1\)? --> is \(5^{x+2}<5^2\)? --> is \(x+2<2\)? --> is \(x<0\)?

(1) \(5^x < 1\) --> \(x<0\). Sufficient.

(2) \(x < 0\). Directly answers the question. Sufficient.

Answer: D.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Senior Manager
User avatar
Joined: 28 Mar 2012
Posts: 287
Concentration: Entrepreneurship
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 19

Kudos [?]: 227 [0], given: 23

GMAT ToolKit User
Re: Is 5^(x+2)/25<1 ? [#permalink] New post 25 Jun 2012, 07:35
Hi,

Difficulty level: 600

To check, \(\frac {5^{(x+2)}}{25}<1\)
or \((5^25^x)/25 < 1\)
or \(5^x < 1\)?

Using (1),
\(5^x<1\). Sufficient.

Using (2),
x < 0
or \(5^x < 1\). Sufficient.

Answer (D)

Regards,
_________________

My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules

My story: 640 What a blunder!

Vocabulary resource: EdPrep

Facebook page: fb.com/EdPrep

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28782
Followers: 4595

Kudos [?]: 47523 [0], given: 7123

Re: Is 5^(x+2)/25<1 ? [#permalink] New post 29 Jun 2012, 03:43
Expert's post
SOLUTION

Is \(\frac{5^{x+2}}{25}<1\) ?

Is \(\frac{5^{x+2}}{25} <1\)? --> is \(\frac{5^{x+2}}{5^2}<1\)? --> is \(5^x<1\)? --> is \(x<0\)?

Or: is \(\frac{5^{x+2}}{25} <1\)? --> is \(5^{x+2}<5^2\)? --> is \(x+2<2\)? --> is \(x<0\)?

(1) \(5^x < 1\) --> \(x<0\). Sufficient.

(2) \(x < 0\). Directly answers the question. Sufficient.

Answer: D.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 5716
Followers: 323

Kudos [?]: 63 [0], given: 0

Premium Member
Re: Is 5^(x+2)/25<1 ? [#permalink] New post 06 Jul 2014, 03:10
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

Senior Manager
Senior Manager
User avatar
Joined: 03 Aug 2011
Posts: 262
GMAT 1: 640 Q44 V34
GMAT 2: 700 Q42 V44
GPA: 3.7
WE: Project Management (Energy and Utilities)
Followers: 11

Kudos [?]: 36 [0], given: 773

GMAT ToolKit User
Is 5^(x+2)/25<1 ? [#permalink] New post 30 Jun 2015, 01:02
What would happen if we would have \(x=\frac{-1}{10}\)?

Am I correct that \(5^\frac{-1}{10} = \frac{1}{5^(1/10)} = \frac{1}{\sqrt[10]{5^1}}\), but the denominator would still be always greater than the numerator?

Thank you!
_________________

Thank you very much for reading this post till the end! Kudos?

1 KUDOS received
Math Forum Moderator
User avatar
Joined: 06 Jul 2014
Posts: 471
Location: Ukraine
GMAT 1: 660 Q48 V33
Followers: 14

Kudos [?]: 271 [1] , given: 108

GMAT ToolKit User Premium Member CAT Tests
Is 5^(x+2)/25<1 ? [#permalink] New post 30 Jun 2015, 02:31
1
This post received
KUDOS
bgpower wrote:
What would happen if we would have \(x=\frac{-1}{10}\)?

Am I correct that \(5^\frac{-1}{10} = \frac{1}{5^(1/10)} = \frac{1}{\sqrt[10]{5^1}}\), but the denominator would still be always greater than the numerator?

Thank you!


Hello bgpower

You are correct that \(5^\frac{-1}{10} = \frac{1}{5^(1/10)} = \frac{1}{\sqrt[10]{5^1}}\)

But this statement "the denominator would still be always greater than the numerator?" is suspicious.
If you talk about this fraction: \(\frac{1}{\sqrt[10]{5^1}}\) than you are wrong because in this fraction denominator \(\sqrt[10]{5^1}\) is less than nominator \(1\)
If you talk about fraction from initial task then you are right denominator \(25\) is bigger than nominator \(\sqrt[10]{5^1}\)
Senior Manager
Senior Manager
User avatar
Joined: 03 Aug 2011
Posts: 262
GMAT 1: 640 Q44 V34
GMAT 2: 700 Q42 V44
GPA: 3.7
WE: Project Management (Energy and Utilities)
Followers: 11

Kudos [?]: 36 [0], given: 773

GMAT ToolKit User
Is 5^(x+2)/25<1 ? [#permalink] New post 30 Jun 2015, 02:42
Hi, Thanks for your reply!

I was actually talking about: \(\frac{1}{\sqrt[10]{5^1}}\). So in this case I am wrong, as the numerator of 1 would clearly be greater than the denominator. But doesn't this mean that \(5^x\) is not always <1. The question does not define x to be positive and as shown above if x is a negative fraction (as \(-\frac{1}{10}\)) then the result is greater than 1.

Thanks for the clarification!
_________________

Thank you very much for reading this post till the end! Kudos?

1 KUDOS received
Math Forum Moderator
User avatar
Joined: 06 Jul 2014
Posts: 471
Location: Ukraine
GMAT 1: 660 Q48 V33
Followers: 14

Kudos [?]: 271 [1] , given: 108

GMAT ToolKit User Premium Member CAT Tests
Re: Is 5^(x+2)/25<1 ? [#permalink] New post 30 Jun 2015, 03:39
1
This post received
KUDOS
bgpower wrote:
Hi, Thanks for your reply!

I was actually talking about: \(\frac{1}{\sqrt[10]{5^1}}\). So in this case I am wrong, as the numerator of 1 would clearly be greater than the denominator. But doesn't this mean that \(5^x\) is not always <1. The question does not define x to be positive and as shown above if x is a negative fraction (as \(-\frac{1}{10}\)) then the result is greater than 1.

Thanks for the clarification!


I think you leave out last step of task (dividing on 25) and this confuse you.

You are absolutely right that \(\frac{1}{\sqrt[10]{5^1}}\) greater than 1
but if we divide this result on 25 (as tasks asks) then result will be less than 1

----

This task can be solved in much faster way:

Tasks asks if \(\frac{5^{(x+2)}}{25}\) will be less than 1

Let's transform this equation to \(5^{(x+2)} < 25\) --> \(5^{(x+2)} < 5^2\) from this view we see that this equation will be true if x will be less than 0

1) \(5^x<1\) this is possible only if \(x < 0\) - Sufficient
2) \(x<0\) - this is exactly what we seek - Sufficient

Sometimes picking numbers is good but in this case algebraic way is much faster and at the end you will not have any hesitations in answer
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 03 Aug 2011
Posts: 262
GMAT 1: 640 Q44 V34
GMAT 2: 700 Q42 V44
GPA: 3.7
WE: Project Management (Energy and Utilities)
Followers: 11

Kudos [?]: 36 [1] , given: 773

GMAT ToolKit User
Is 5^(x+2)/25<1 ? [#permalink] New post 30 Jun 2015, 04:10
1
This post received
KUDOS
I actually did it the following way:

\(\frac{5^(x+2)}{25}<1\)
\(\frac{(5^x)(5^2)}{5^2}<1\) => Here you can basically cancel out \(5^2\) and are left with \(5^x<1\)

Here we come to the point we have already discussed.

(1) is clearly SUFFICIENT as it says exactly \(5^x<1\).
(2) I thought (2) is NOT SUFFICIENT as for negative fractions (think \(-\frac{1}{10}\)), IMO this does NOT hold true, while for other negative values it does.
_________________

Thank you very much for reading this post till the end! Kudos?

Expert Post
Optimus Prep Instructor
User avatar
Joined: 06 Nov 2014
Posts: 416
Followers: 6

Kudos [?]: 78 [0], given: 2

Re: Is 5^(x+2)/25<1 ? [#permalink] New post 30 Jun 2015, 10:40
Expert's post
Is (5^x+2)/25<1 ?
Multiply both sides by 25 to yield 5^x+2>25. Rewrite 25 so that we have 5 as a base on both sides, so we want to know if 5^x+2> 5^2. The question is now is x+2>2. This will be true if x is negative.
(1) 5^x<1
1 can be rewritten so as 5^0 so as to give the same base. x<0 Sufficient.
(2) x<0
This is the same information as we derived from Statement 1 (x is negative). Therefore it is also sufficient.

D
_________________

Cassandra Wolff
Customer Support | Optimus Prep
 
Facebook Linkedin Youtube Twitter slideshare Google+
 

Expert Post
1 KUDOS received
Optimus Prep Instructor
User avatar
Joined: 06 Nov 2014
Posts: 416
Followers: 6

Kudos [?]: 78 [1] , given: 2

Re: Is 5^(x+2)/25<1 ? [#permalink] New post 30 Jun 2015, 10:41
1
This post received
KUDOS
Expert's post
Is (5^x+2)/25<1 ?
Multiply both sides by 25 to yield 5^x+2<25. Rewrite 25 so that we have 5 as a base on both sides, so we want to know if 5^x+2< 5^2. The question is now is x+2<2. This will be true if x is negative.
(1) 5^x<1
1 can be rewritten so as 5^0 so as to give the same base. x<0 Sufficient.
(2) x<0
This is the same information as we derived from Statement 1 (x is negative). Therefore it is also sufficient.

D
_________________

Cassandra Wolff
Customer Support | Optimus Prep
 
Facebook Linkedin Youtube Twitter slideshare Google+
 

Senior Manager
Senior Manager
User avatar
Joined: 03 Aug 2011
Posts: 262
GMAT 1: 640 Q44 V34
GMAT 2: 700 Q42 V44
GPA: 3.7
WE: Project Management (Energy and Utilities)
Followers: 11

Kudos [?]: 36 [0], given: 773

GMAT ToolKit User
Is 5^(x+2)/25<1 ? [#permalink] New post 01 Jul 2015, 02:56
OptimusPrepJanielle

Thank you for your explanation! I fully get your explanation. Nevertheless, I still don't see anyone addressing my questions, which basically asks what happens when x is a negative fraction as \(-\frac{1}{10}\)? I may be the one with an error here, but please explain it to me.

Thanks!
_________________

Thank you very much for reading this post till the end! Kudos?

Expert Post
1 KUDOS received
Optimus Prep Instructor
User avatar
Joined: 06 Nov 2014
Posts: 416
Followers: 6

Kudos [?]: 78 [1] , given: 2

Re: Is 5^(x+2)/25<1 ? [#permalink] New post 01 Jul 2015, 03:09
1
This post received
KUDOS
Expert's post
Hi bgpower,

The issue is whether or not x is negative. If x is a negative fraction such as -1/10 the expression should still hold true. I hope that helps.
_________________

Cassandra Wolff
Customer Support | Optimus Prep
 
Facebook Linkedin Youtube Twitter slideshare Google+
 

1 KUDOS received
Math Forum Moderator
User avatar
Joined: 06 Jul 2014
Posts: 471
Location: Ukraine
GMAT 1: 660 Q48 V33
Followers: 14

Kudos [?]: 271 [1] , given: 108

GMAT ToolKit User Premium Member CAT Tests
Re: Is 5^(x+2)/25<1 ? [#permalink] New post 01 Jul 2015, 03:12
1
This post received
KUDOS
bgpower wrote:
OptimusPrepJanielle

Thank you for your explanation! I fully get your explanation. Nevertheless, I still don't see anyone addressing my questions, which basically asks what happens when x is a negative fraction as \(-\frac{1}{10}\)? I may be the one with an error here, but please explain it to me.

Thanks!


Hello bgpower

When x = -1/10 then \(5^{-1/10+2} = 5^{19/10}\)
We need to check whether this \(5^{19/10}\) less than \(5^2\)
19/10 less than 2
so \(5^{x+2} < 5^2\)
Re: Is 5^(x+2)/25<1 ?   [#permalink] 01 Jul 2015, 03:12
    Similar topics Author Replies Last post
Similar
Topics:
5 Experts publish their posts in the topic Is rst <= 1? gmatpapa 6 30 Dec 2010, 05:23
Experts publish their posts in the topic Is x+y<1? vigneshpandi 6 21 Sep 2010, 21:57
29 Experts publish their posts in the topic Is |x|<1? mn2010 33 28 Jul 2010, 02:56
1 Experts publish their posts in the topic Is |x| < 1? boros2203 4 12 Feb 2010, 03:20
16 Experts publish their posts in the topic Is |x|<1 ? msand 11 31 Dec 2009, 07:24
Display posts from previous: Sort by

Is 5^(x+2)/25<1 ?

  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®.