It is currently 17 Oct 2017, 12:17

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

  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: 41873

Kudos [?]: 128579 [0], given: 12180

Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 25 Jun 2012, 03:07
Expert's post
9
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

77% (00:50) correct 23% (00:49) wrong based on 694 sessions

HideShow timer Statistics

Kudos [?]: 128579 [0], given: 12180

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128579 [2], given: 12180

Re: Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 25 Jun 2012, 03:07
2
This post received
KUDOS
Expert's post
5
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 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

Kudos [?]: 128579 [2], given: 12180

Kellogg MMM ThreadMaster
User avatar
B
Joined: 29 Mar 2012
Posts: 322

Kudos [?]: 512 [0], given: 23

Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
GMAT ToolKit User
Re: Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 25 Jun 2012, 08:35
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,

Kudos [?]: 512 [0], given: 23

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128579 [0], given: 12180

Re: Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 29 Jun 2012, 04:43
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 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

Kudos [?]: 128579 [0], given: 12180

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16758

Kudos [?]: 273 [0], given: 0

Premium Member
Re: Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 06 Jul 2014, 04:10
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

Kudos [?]: 273 [0], given: 0

Senior Manager
Senior Manager
User avatar
Joined: 03 Aug 2011
Posts: 296

Kudos [?]: 72 [0], given: 916

Concentration: Strategy, Finance
GMAT 1: 640 Q44 V34
GMAT 2: 700 Q42 V44
GMAT 3: 680 Q44 V39
GMAT 4: 740 Q49 V41
GPA: 3.7
WE: Project Management (Energy and Utilities)
GMAT ToolKit User Reviews Badge
Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 30 Jun 2015, 02:02
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?

Kudos [?]: 72 [0], given: 916

1 KUDOS received
Math Forum Moderator
User avatar
Joined: 06 Jul 2014
Posts: 1272

Kudos [?]: 2311 [1], given: 178

Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT ToolKit User Premium Member
Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 30 Jun 2015, 03:31
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 \(\sqrt[10]{5^1}\)
_________________

Simple way to always control time during the quant part.
How to solve main idea questions without full understanding of RC.
660 (Q48, V33) - unpleasant surprise
740 (Q50, V40, IR3) - anti-debrief ;)

Kudos [?]: 2311 [1], given: 178

Senior Manager
Senior Manager
User avatar
Joined: 03 Aug 2011
Posts: 296

Kudos [?]: 72 [0], given: 916

Concentration: Strategy, Finance
GMAT 1: 640 Q44 V34
GMAT 2: 700 Q42 V44
GMAT 3: 680 Q44 V39
GMAT 4: 740 Q49 V41
GPA: 3.7
WE: Project Management (Energy and Utilities)
GMAT ToolKit User Reviews Badge
Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 30 Jun 2015, 03:42
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?

Kudos [?]: 72 [0], given: 916

1 KUDOS received
Math Forum Moderator
User avatar
Joined: 06 Jul 2014
Posts: 1272

Kudos [?]: 2311 [1], given: 178

Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT ToolKit User Premium Member
Re: Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 30 Jun 2015, 04:39
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
_________________

Simple way to always control time during the quant part.
How to solve main idea questions without full understanding of RC.
660 (Q48, V33) - unpleasant surprise
740 (Q50, V40, IR3) - anti-debrief ;)

Kudos [?]: 2311 [1], given: 178

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 03 Aug 2011
Posts: 296

Kudos [?]: 72 [1], given: 916

Concentration: Strategy, Finance
GMAT 1: 640 Q44 V34
GMAT 2: 700 Q42 V44
GMAT 3: 680 Q44 V39
GMAT 4: 740 Q49 V41
GPA: 3.7
WE: Project Management (Energy and Utilities)
GMAT ToolKit User Reviews Badge
Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 30 Jun 2015, 05:10
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?

Kudos [?]: 72 [1], given: 916

Expert Post
Optimus Prep Instructor
User avatar
B
Joined: 06 Nov 2014
Posts: 1905

Kudos [?]: 522 [0], given: 23

Re: Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 30 Jun 2015, 11:40
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
_________________

Janielle Williams

Customer Support

Special Offer: $80-100/hr. Online Private Tutoring
GMAT On Demand Course $299
Free Online Trial Hour

Kudos [?]: 522 [0], given: 23

Expert Post
1 KUDOS received
Optimus Prep Instructor
User avatar
B
Joined: 06 Nov 2014
Posts: 1905

Kudos [?]: 522 [1], given: 23

Re: Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 30 Jun 2015, 11:41
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
_________________

Janielle Williams

Customer Support

Special Offer: $80-100/hr. Online Private Tutoring
GMAT On Demand Course $299
Free Online Trial Hour

Kudos [?]: 522 [1], given: 23

Senior Manager
Senior Manager
User avatar
Joined: 03 Aug 2011
Posts: 296

Kudos [?]: 72 [0], given: 916

Concentration: Strategy, Finance
GMAT 1: 640 Q44 V34
GMAT 2: 700 Q42 V44
GMAT 3: 680 Q44 V39
GMAT 4: 740 Q49 V41
GPA: 3.7
WE: Project Management (Energy and Utilities)
GMAT ToolKit User Reviews Badge
Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 01 Jul 2015, 03:56
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?

Kudos [?]: 72 [0], given: 916

Expert Post
1 KUDOS received
Optimus Prep Instructor
User avatar
B
Joined: 06 Nov 2014
Posts: 1905

Kudos [?]: 522 [1], given: 23

Re: Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 01 Jul 2015, 04:09
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.
_________________

Janielle Williams

Customer Support

Special Offer: $80-100/hr. Online Private Tutoring
GMAT On Demand Course $299
Free Online Trial Hour

Kudos [?]: 522 [1], given: 23

1 KUDOS received
Math Forum Moderator
User avatar
Joined: 06 Jul 2014
Posts: 1272

Kudos [?]: 2311 [1], given: 178

Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT ToolKit User Premium Member
Re: Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 01 Jul 2015, 04:12
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 \(5^{x+2} < 5^2\)
_________________

Simple way to always control time during the quant part.
How to solve main idea questions without full understanding of RC.
660 (Q48, V33) - unpleasant surprise
740 (Q50, V40, IR3) - anti-debrief ;)

Kudos [?]: 2311 [1], given: 178

Intern
Intern
avatar
Joined: 21 Mar 2013
Posts: 12

Kudos [?]: [0], given: 14

Re: Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 21 Jul 2016, 14:18
For\frac{\(5^(x+2)\)}{25} < 1, the numerator will have to be less than 25.

\(5^(x+2)\) < 25?

For \(5^(x+2)\) < 25, x will have to be less than 0.
x<0?

So statement B is straightforward. I am bungled up on the first statement.

\(5^x\) <1

Since \(5^0\) = 1, x != 0.
Also, \(5^1\) = 5 and hence x<1.

But what about x being a fraction i.e. 0<x<1?

If that is the case then Statement 1 is no sufficient.

Please tell me where I am wrong.

Kudos [?]: [0], given: 14

Top Contributor
Math Forum Moderator
User avatar
Joined: 06 Jul 2014
Posts: 1272

Kudos [?]: 2311 [0], given: 178

Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT ToolKit User Premium Member
Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 21 Jul 2016, 14:41
Top Contributor
Witchcrafts wrote:
For\frac{\(5^(x+2)\)}{25} < 1, the numerator will have to be less than 25.

\(5^(x+2)\) < 25?

For \(5^(x+2)\) < 25, x will have to be less than 0.
x<0?

So statement B is straightforward. I am bungled up on the first statement.

\(5^x\) <1

Since \(5^0\) = 1, x != 0.
Also, \(5^1\) = 5 and hence x<1.

But what about x being a fraction i.e. 0<x<1?

If that is the case then Statement 1 is no sufficient.

Please tell me where I am wrong.


Hello Witchcrafts
if x is fraction than it will be some root from 5 and result of any root will be always more than 1 so x can't be a fraction

if \(x = \frac{1}{2}\) then \(5^x = \sqrt{5}\)
_________________

Simple way to always control time during the quant part.
How to solve main idea questions without full understanding of RC.
660 (Q48, V33) - unpleasant surprise
740 (Q50, V40, IR3) - anti-debrief ;)

Kudos [?]: 2311 [0], given: 178

Intern
Intern
avatar
Joined: 21 Mar 2013
Posts: 12

Kudos [?]: [0], given: 14

Re: Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 21 Jul 2016, 15:38
Thanks Harley. I figured that after I posted the question :-)

The rule is:
If a x and y are positive integers then
y^(1/x) >1

Kudos [?]: [0], given: 14

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16758

Kudos [?]: 273 [0], given: 0

Premium Member
Re: Is 5^(x+2)/25<1 ? [#permalink]

Show Tags

New post 28 Sep 2017, 10:40
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

Kudos [?]: 273 [0], given: 0

Re: Is 5^(x+2)/25<1 ?   [#permalink] 28 Sep 2017, 10:40
Display posts from previous: Sort by

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

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.