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

It is currently 07 Dec 2019, 08:07

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

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

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59588
If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1}  [#permalink]

Show Tags

New post 13 Mar 2015, 07:55
1
4
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

78% (01:58) correct 22% (02:33) wrong based on 109 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
User avatar
Joined: 07 Aug 2011
Posts: 499
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, 08:11
1
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.



\((5/2)X=1/3 (X+1)\)
\(X=2/13\)
Senior Manager
Senior Manager
User avatar
B
Joined: 28 Feb 2014
Posts: 289
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, 08:20
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
Director
Director
avatar
P
Joined: 21 May 2013
Posts: 633
Re: If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1}  [#permalink]

Show Tags

New post 15 Mar 2015, 05:34
1
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: 111
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, 06:24
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)
Intern
Intern
avatar
Joined: 13 Mar 2015
Posts: 3
If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1}  [#permalink]

Show Tags

New post 15 Mar 2015, 20:50
2
(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
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59588
Re: If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1}  [#permalink]

Show Tags

New post 15 Mar 2015, 23:00
1
2
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 2041 times ]

Equate the exponents.
Attachment:
cgpwe_img35.png
cgpwe_img35.png [ 937 Bytes | Viewed 2041 times ]

Multiply both sides by 6 to clear the fractions.
Attachment:
cgpwe_img36.png
cgpwe_img36.png [ 2.07 KiB | Viewed 2041 times ]


Answer = (B).
_________________
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1727
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, 03:07
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
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13721
Re: If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1}  [#permalink]

Show Tags

New post 24 Mar 2019, 07:43
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 Club Bot
Re: If (25[square_root]5[/square_root])^x=(\sqrt[3]{5})^{x+1}   [#permalink] 24 Mar 2019, 07:43
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  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne