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

It is currently 19 Apr 2019, 23:28

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 a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c and c^z

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54372
If a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c and c^z  [#permalink]

Show Tags

New post 07 Apr 2019, 21:39
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (01:44) correct 31% (01:29) wrong based on 32 sessions

HideShow timer Statistics

Intern
Intern
avatar
B
Joined: 09 Apr 2018
Posts: 25
Location: India
Concentration: Strategy, Finance
If a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c and c^z  [#permalink]

Show Tags

New post 07 Apr 2019, 21:56
Since a,b and c can't be 0 or 1, x, y and z have to be 1.
Hence xyz=1

Answer: B

Alternately,

Since we have a^x=b & b^y=c, (a^x)^y=c
a^xy=c
Again,
c^z=a And hence (a^xy)^z=a
a^xyz=a
Intern
Intern
avatar
B
Joined: 24 Jun 2018
Posts: 27
Re: If a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c and c^z  [#permalink]

Show Tags

New post 08 Apr 2019, 11:42
Simple substitution can give us the answer:

Given:
a^x = b
b^y=c
c^z=a

Now,
b^y=c
=> (a^x)^y=c
=> a^xy=c ------> (1)

Now,
c^z=a
From 1
(a^xy)^z=a
Hence, a^xyz=a

Since a is not equal to 0 or 1, for both sides to be equal

xyz must be equal to 1
hence xyz = 1
Manager
Manager
User avatar
B
Joined: 12 Sep 2017
Posts: 214
If a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c and c^z  [#permalink]

Show Tags

New post 09 Apr 2019, 18:01
I did it this way, just keep adding the exponents, given:

\(a^x = b\)
\(b^y = c\)
\(c^z = a\)

Take the first one and add ^y to both sides.

\(a^x^y = b^y = c\) Now add the ^z so the whole term can be equal to a.

\(a^x^y^z = b^y^z = c^y^z = a\)

so

\(a^x^y^z = a^1\)

\(xyz = 1\)

B
GMAT Club Bot
If a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c and c^z   [#permalink] 09 Apr 2019, 18:01
Display posts from previous: Sort by

If a, b, and c are not equal to 0 or 1 and if a^x = b, b^y = c and c^z

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


Copyright

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