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a^2 = b^2 - 1, b is not equal to 0
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04 Oct 2020, 21:48
04 Oct 2020, 21:48
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71% (01:02) correct
28% (01:08) wrong based on 39 sessions
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\(a^2\) = \(b^2- 1\), 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.
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Re: a^2 = b^2 - 1, b is not equal to 0
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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
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06 Jan 2023, 16:12
06 Jan 2023, 16:12
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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.
