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

 It is currently 22 Oct 2019, 04:21 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

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.  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 V
Joined: 02 Sep 2009
Posts: 58428
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 00:00

Difficulty:   25% (medium)

Question Stats: 78% (01:40) correct 22% (01:31) wrong based on 50 sessions

HideShow timer Statistics

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

(A) 0

(B) 1

(C) 2

(D) a

(E) abc

Source: Nova GMAT
Difficulty Level: 600

_________________

Originally posted by Bunuel on 07 Apr 2019, 21:39.
Last edited by SajjadAhmad on 23 Jul 2019, 10:18, edited 1 time in total.
Intern  B
Joined: 09 Apr 2018
Posts: 32
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

Since a,b and c can't be 0 or 1, x, y and z have to be 1.
Hence xyz=1

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  B
Joined: 24 Jun 2018
Posts: 35
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

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
Senior Manager  S
Joined: 12 Sep 2017
Posts: 302
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

1
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 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] 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

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