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(a + b - 1)(a + b - 1)
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04 Mar 2022, 04:00
04 Mar 2022, 04:00
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Question Stats:
65% (01:13) correct
34% (01:29) wrong based on 26 sessions
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Note: The square brackets below are the same as the usual rounded brackets. The site's functionality doesn't permit rounded brackets in the question.
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 |
\([a + b - 1][a + b - 1]\) |
\( [a + b + 1][a + b + 1]\) |
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.
Re: (a + b - 1)(a + b - 1)
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04 Mar 2022, 20:02
04 Mar 2022, 20:02
1
Qt A
\((a + b - 1)(a + b - 1) = a^2 + ab - a + ab + b^2 - b - a - b + 1 = a^2 + b^2 + 2ab - 2a - 2b + 1\)
Qt B
\((a + b + 1)(a + b + 1) = a^2 + ab + a + ab + b^2 + b + a + b + 1 = a^2 + b^2 + 2ab + 2a + 2b + 1\)
By comparing both quantities, and removing common terms, we will have
Qt \(A = -(a + b)\)
Qt \(B = a + b\)
We don't know the signs of \(a\) & \(b\), hence we can't decide.
Answer \(D\)
\((a + b - 1)(a + b - 1) = a^2 + ab - a + ab + b^2 - b - a - b + 1 = a^2 + b^2 + 2ab - 2a - 2b + 1\)
Qt B
\((a + b + 1)(a + b + 1) = a^2 + ab + a + ab + b^2 + b + a + b + 1 = a^2 + b^2 + 2ab + 2a + 2b + 1\)
By comparing both quantities, and removing common terms, we will have
Qt \(A = -(a + b)\)
Qt \(B = a + b\)
We don't know the signs of \(a\) & \(b\), hence we can't decide.
Answer \(D\)
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Re: (a + b - 1)(a + b - 1)
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05 Mar 2022, 06:17
05 Mar 2022, 06:17
1
Carcass wrote:
Quantity A |
Quantity B |
\([a + b - 1][a + b - 1]\) |
\( [a + b + 1][a + b + 1]\) |
Given:
QUANTITY A: \((a + b - 1)(a + b - 1)\)
QUANTITY B: \((a + b + 1)(a + b + 1)\)
STRATEGY: Whenever I see a Quantitative Comparison question featuring only variables, I immediately ask myself "Are there obvious values for the variables that will make the two quantities equal?"
If so, I know that the answer will be either C or D.
More on this strategy (Looking for Equality) in the video below.
For this question, I can see that, if \(a = 0\) and \(b = 0\), we get:
QUANTITY A: \((a + b - 1)(a + b - 1) = (0 + 0 - 1)(0 + 0 - 1) = (-1)(-1) = 1\)
QUANTITY B: \((a + b + 1)(a + b + 1) = (0 + 0 + 1)(0 + 0 + 1) = (1)(1) = 1 \)
In this case, the two quantities are equal.
Conversely, if \(a = 1\) and \(b = 1\), we can immediately see that the two quantities are NOT equal
Answer: D
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