NEW HERE? LEARN MORE
closeclose
Last visit was: 27 Apr 2024, 11:26 It is currently 27 Apr 2024, 11:26
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

The equation [m]((5-3-A)^2+3-6)^B=1[/m] can be made true for certain v

Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11182
Own Kudos [?]: 31990 [3]
Given Kudos: 291
Send PM
Reviews Badge
The equation [m]((5-3-A)^2+3-6)^B=1[/m] can be made true for certain v [#permalink] New post   28 Mar 2024, 06:43
2
Kudos
1
Bookmarks
Expert Reply
00:00

Difficulty:

45% (medium)

Question Stats:

76% (01:47) correct 24% (01:56) wrong based on 63 sessions
Hide Show timer Statistics
The equation \(((5-3-A)^2+3-6)^B=1\) can be made true for certain values of variables A and B independent of each other. The variables A and B are both integers.

Select for A a value that would make the equation true irrespective of whatever value B has, and select for B a value that would make the equation true irrespective of value of  A. Make only two selection, one for each column.
 
A B
-2
-1
0
1
2
3
Submit
Click Submit to add this question to your Error log
User avatar
P
MartyMurray
Tutor
Joined: 11 Aug 2023
Posts: 827
Own Kudos [?]: 1424 [3]
Given Kudos: 75
GMAT 1: 800 Q51 V51
Send PM
The equation [m]((5-3-A)^2+3-6)^B=1[/m] can be made true for certain v [#permalink] New post   28 Mar 2024, 12:50
3
Kudos
Expert Reply
The equation \(((5-3-A)^2+3-6)^B=1\) can be made true for certain values of variables A and B independent of each other. The variables A and B are both integers.

Select for A a value that would make the equation true irrespective of whatever value B has, and select for B a value that would make the equation true irrespective of value of  A. Make only two selection, one for each column.

The equation will be true for any \(B\) if the expression in the parentheses equals \(1\) since \(1\) raised to any power is \(1\). So, we can find the answer choice for \(A\) such that the expression in the parentheses equals \(1\).

The expression in the parentheses simplifies to

\(((2 - A)^2 - 3)\)

For \(((2 - A)^2 - 3)\) to equal \(1\), \((2 - A)^2\) must be \(4\), and thus \(2 - A\) must be \(2\), and \(A\) must be \(0\).

Select \(0\) for \(A\).

The equation can be true for any \(A\) if \(B\) equals \(0\) since any number to the \(0\) power equals \(1\).

Select \(0\) for \(B\).

Correct answer: 0, 0­
User avatar
S
Gemmie
Manager
Manager
Joined: 19 Dec 2021
Posts: 101
Own Kudos [?]: 41 [0]
Given Kudos: 2
Location: Viet Nam
GPA: 3.55
Send PM
Re: The equation [m]((5-3-A)^2+3-6)^B=1[/m] can be made true for certain v [#permalink] New post   29 Mar 2024, 21:29
\(­((5−3−A)^2+3−6)^B=1\)

=> \(((2-A)^2-3)^B = 1\)

A value of A that would make the equation true irrespective of whatever value B has
=> \((2-A)^2 - 3 = 1\)
=> \((2-A)^2 = 4\)
=> 2- A = 2 or 2-A=-2
=> A=0 of A =4

==> Given the answer choices, A = 0

A value of B that would make the equation true irrespective of value of A
=> B = 0­
User avatar
B
Aditya8624
Intern
Intern
Joined: 26 Jan 2024
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 17
Send PM
Re: The equation [m]((5-3-A)^2+3-6)^B=1[/m] can be made true for certain v [#permalink] New post   31 Mar 2024, 21:09
any number raised to the power of zero always equals 1
so why can't we take B=0 while A can have any value?
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11182
Own Kudos [?]: 31990 [0]
Given Kudos: 291
Send PM
Reviews Badge
Re: The equation [m]((5-3-A)^2+3-6)^B=1[/m] can be made true for certain v [#permalink] New post   31 Mar 2024, 21:16
Expert Reply
Aditya8624 wrote:
any number raised to the power of zero always equals 1
so why can't we take B=0 while A can have any value?


You are correct and that is what the answer is.

Posted from my mobile device
GMAT Club Bot
gmatclubot
Re: The equation [m]((5-3-A)^2+3-6)^B=1[/m] can be made true for certain v [#permalink]
31 Mar 2024, 21:16
Moderators:
Bunuel
Math Expert
92955 posts
BottomJee
DI Forum Moderator
1030 posts
chetan2u
RC & DI Moderator
11182 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions