Last visit was: 05 Nov 2024, 00:30 It is currently 05 Nov 2024, 00:30

Close

GRE Prep 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 GRE 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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12176 [3]
Given Kudos: 136
Send PM
Intern
Intern
Joined: 01 May 2021
Posts: 49
Own Kudos [?]: 37 [0]
Given Kudos: 2
Send PM
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12176 [0]
Given Kudos: 136
Send PM
avatar
Intern
Intern
Joined: 11 Oct 2021
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
If b is a non-zero integer, how many different values of b [#permalink]
D?
Taking 0 not as an option as ETS considers 0^0 undefined. So, +1,-1,+2,-2 ?
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12176 [2]
Given Kudos: 136
Send PM
Re: If b is a non-zero integer, how many different values of b [#permalink]
2
GreenlightTestPrep wrote:
If \(b\) is a non-zero integer, how many different values of \(b\) satisfy the equation \(b^{(2b^2)} = b^{8}\)
A) One
B) Two
C) Three
D) Four
E) Five


I created this question to remind students that, when it comes to equations with variables in the exponents, there are three important provisos we must consider before we can conclude that two exponents are equal.
That is, if \(x^a = x^b\), then we can conclude that \(a = b\) AS LONG AS \(x \neq 0\), \(x \neq 1\), and \(x \neq -1\).
For example, if we know that \(0^x = 0^3\), we can't then conclude that \(x = 3\), since there are infinitely many values of \(x\) that satisfy the equation.


Let's begin by assuming \(b\) does not equal any of the forbidden numbers (i.e., \(x \neq 0\), \(x \neq 1\), and \(x \neq -1\))
In that case, we can conclude that \(2b^2 = 8\)
Divide both sides of the equation by \(2\) to get: \(b^2 = 4\)
So, \(b = 2\) or \(b = -2\)

Now we need to check whether each of the forbidden numbers is a possible solution to the given equation.

We already said that b is a non-zero integer, so we need not bother testing \(b = 0\).

What about \(b = 1\)?
Plug it in to get: \(1^{(2(1^2))} = 1^{8}\)
Simplify: \(1^{2} = 1^{8}\)
Works!!
So, \(b = 1\) is a solution

What about \(b = -1\)?
Plug it in to get: \((-1)^{(2(-1)^2)} = (-1)^{8}\)
Simplify: \((-1)^{2} = 1^{8}\)
Works!!
So, \(b = -1\) is a solution

So we have a total of four solutions: \(b = 2\), \(b = -2\), \(b = 1\) and \(b = -1\)

Answer: D

If you want to practice this question type, here’s a similar question:
https://gre.myprepclub.com/forum/what-is-s ... 20887.html
Intern
Intern
Joined: 01 May 2021
Posts: 49
Own Kudos [?]: 37 [0]
Given Kudos: 2
Send PM
Re: If b is a non-zero integer, how many different values of b [#permalink]
GreenlightTestPrep
You are right

Posted from my mobile device
Manager
Manager
Joined: 10 Feb 2023
Posts: 76
Own Kudos [?]: 13 [0]
Given Kudos: 172
Send PM
Re: If b is a non-zero integer, how many different values of b [#permalink]
Hi Brent GreenlightTestPrep, a bit confused that after we found out b = 2 or -2, not sure why are we start testing with 1 and -1 (forbidden numbers not allowed) instead of 2 and -2? Thanks Brent
Verbal Expert
Joined: 18 Apr 2015
Posts: 29887
Own Kudos [?]: 36118 [0]
Given Kudos: 25918
Send PM
Re: If b is a non-zero integer, how many different values of b [#permalink]
Expert Reply
You need to find out the solutions for which in the end we do have b^8

2 and -2 are one pair

Then you use 1 and -1

Seee more theory here https://gre.myprepclub.com/forum/gre-ma ... 29264.html
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5006
Own Kudos [?]: 74 [0]
Given Kudos: 0
Send PM
Re: If b is a non-zero integer, how many different values of b [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep 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.
Prep Club for GRE Bot
Re: If b is a non-zero integer, how many different values of b [#permalink]
Moderators:
GRE Instructor
77 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
228 posts

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