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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
a^2 = b^2 - 1, b is not equal to 0
[#permalink]
04 Oct 2020, 21:48
04 Oct 2020, 21:48
2
Bookmarks
00:00
Question Stats:
75% (01:02) correct
24% (01:03) wrong based on 37 sessions
Hide Show timer Statistics
\(a^2\) = \(b^2- 1\), and \(b\) is not equal to \(0\)
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(a^4\) |
\(b^4+1\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: a^2 = b^2 - 1, b is not equal to 0
[#permalink]
05 Oct 2020, 05:49
05 Oct 2020, 05:49
3
Farina wrote:
\(a^2\) = \(b^2- 1\), and \(b\) is not equal to \(0\)
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(a^4\) |
\(b^4+1\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Since \(a^4 = (a^2)^2\), we can rewrite Quantity A as follows:
Quantity A: \((a^2)^2\)
Quantity B: \(b^4+1\)
Substitute:
Quantity A: \((b^2- 1)^2\)
Quantity B: \(b^4+1\)
Expand and simplify Quantity A
Quantity A: \(b^4-2b^2+1\)
Quantity B: \(b^4+1\)
Subtract \(b^4\) and subtract \(1\) from both quantities to get:
Quantity A: \(-2b^2\)
Quantity B: \(0\)
Since \(b^2\) must be positive, we can be certain that \(-2b^2\) is NEGATIVE, which means Quantity B must be greater
Answer: B
Re: a^2 = b^2 - 1, b is not equal to 0
[#permalink]
06 Jan 2023, 16:12
06 Jan 2023, 16:12
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.
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.
