It is currently 22 Feb 2018, 14:42

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

If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1}

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

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43867
If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1} [#permalink]

Show Tags

New post 13 Mar 2015, 06:55
1
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

78% (01:28) correct 22% (02:20) wrong based on 92 sessions

HideShow timer Statistics

1 KUDOS received
Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 578
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1} [#permalink]

Show Tags

New post 13 Mar 2015, 07:11
1
This post received
KUDOS
Bunuel wrote:
If \((25\sqrt{5})^x=(\sqrt[3]{5})^{x+1}\), what does x equal

(A) 1/5
(B) 2/13
(C) 2/15
(D) 5/3
(E) 15/2

Kudos for a correct solution.



\((5/2)X=1/3 (X+1)\)
\(X=2/13\)
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the Image to appreciate my post !! :-)

Senior Manager
Senior Manager
User avatar
B
Joined: 28 Feb 2014
Posts: 296
Location: United States
Concentration: Strategy, General Management
Reviews Badge
Re: If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1} [#permalink]

Show Tags

New post 13 Mar 2015, 07:20
Bunuel wrote:
If \((25\sqrt{5})^x=(\sqrt[3]{5})^{x+1}\), what does x equal

(A) 1/5
(B) 2/13
(C) 2/15
(D) 5/3
(E) 15/2

Kudos for a correct solution.


25^x × 5^x/2 = (5^1/3)^(x+1)
(25^x × 5^x/2)/(5^x/3 +1/3) = 1
5^(x/6 - 1/3) = 5^-2x
13x/6 = 1/3
x = 2/13

Answer: B
1 KUDOS received
Director
Director
avatar
G
Joined: 21 May 2013
Posts: 581
Re: If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1} [#permalink]

Show Tags

New post 15 Mar 2015, 04:34
1
This post received
KUDOS
Bunuel wrote:
If \((25\sqrt{5})^x=(\sqrt[3]{5})^{x+1}\), what does x equal

(A) 1/5
(B) 2/13
(C) 2/15
(D) 5/3
(E) 15/2

Kudos for a correct solution.


+1 for B. (5^2*5^1/2)^X=5^X+1/3
5/2X=X+1/3
15X=2X+2
X=2/13
Manager
Manager
User avatar
Joined: 18 Aug 2014
Posts: 129
Location: Hong Kong
Schools: Mannheim
Re: If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1} [#permalink]

Show Tags

New post 15 Mar 2015, 05:24
KS15 wrote:
Bunuel wrote:
If \((25\sqrt{5})^x=(\sqrt[3]{5})^{x+1}\), what does x equal

(A) 1/5
(B) 2/13
(C) 2/15
(D) 5/3
(E) 15/2

Kudos for a correct solution.


+1 for B. (5^2*5^1/2)^X=5^X+1/3
5/2X=X+1/3
15X=2X+2
X=2/13


Hi, how do you get from first step to the second one? (5/2x = x + 1/3)
1 KUDOS received
Intern
Intern
avatar
Joined: 13 Mar 2015
Posts: 4
If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1} [#permalink]

Show Tags

New post 15 Mar 2015, 19:50
1
This post received
KUDOS
(25^x)(\(\sqrt{5}\)^x)= \(\sqrt[3]{5}\)^x+1
(5^2x)(5^x/2)= (5^(x+1/3))
(5^(4x/2))(5^x/2)= (5^(x+1/3))
(5^(5x/2))= (5^(x+1/3))

5x/2=x+1/3 cross multiply
15x=2x+2
13x=2
x=2/13
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43867
Re: If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1} [#permalink]

Show Tags

New post 15 Mar 2015, 22:00
Expert's post
2
This post was
BOOKMARKED
Bunuel wrote:
If \((25\sqrt{5})^x=(\sqrt[3]{5})^{x+1}\), what does x equal

(A) 1/5
(B) 2/13
(C) 2/15
(D) 5/3
(E) 15/2

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

We need to express each side as a power of 5. We will use fractional exponents for the roots.
Attachment:
cgpwe_img34.png
cgpwe_img34.png [ 3.83 KiB | Viewed 1512 times ]

Equate the exponents.
Attachment:
cgpwe_img35.png
cgpwe_img35.png [ 937 Bytes | Viewed 1512 times ]

Multiply both sides by 6 to clear the fractions.
Attachment:
cgpwe_img36.png
cgpwe_img36.png [ 2.07 KiB | Viewed 1512 times ]


Answer = (B).
_________________

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

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1839
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1} [#permalink]

Show Tags

New post 17 Mar 2015, 02:07
Making bases of both the sides 5, so that the powers can be equated

\((5^2 * 5^{\frac{1}{2}})^x = 5^{\frac{1}{3} * (x+1)}\)

Equating the powers

\(\frac{5}{2} * x = \frac{1}{3} *(x+1)\)

\(x = \frac{2}{13}\)

Answer = B
_________________

Kindly press "+1 Kudos" to appreciate :)

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13801
Premium Member
Re: If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1} [#permalink]

Show Tags

New post 16 Apr 2017, 00:45
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: If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1}   [#permalink] 16 Apr 2017, 00:45
Display posts from previous: Sort by

If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+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®.