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Which is greater: 2x^2-7x-3 5x^2+x-3

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Which is greater: 2x^2-7x-3 5x^2+x-3 [#permalink] New post 19 Oct 2017, 22:57
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Question Stats:

81% (01:01) correct 18% (00:00) wrong based on 11 sessions
Quantity A
Quantity B
2x^2-7x-3
5x^2+x-3


A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

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Re: Which is greater: 2x^2-7x-3 5x^2+x-3 [#permalink] New post 20 Oct 2017, 02:52
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Summing 3, subtracting 2x^2 and summing 7x on both quantities, we get a comparison between 0 and 3x^2+8x = x(3x+8). Then, this expression has two possible solutions, 0 and -8/3. Thus, in one case the two quantities are equal and in the other A is greater.

Answer D
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Re: Which is greater: 2x^2-7x-3 5x^2+x-3 [#permalink] New post 03 Mar 2018, 12:18
IlCreatore wrote:
Summing 3, subtracting 2x^2 and summing 7x on both quantities, we get a comparison between 0 and 3x^2+8x = x(3x+8). Then, this expression has two possible solutions, 0 and -8/3. Thus, in one case the two quantities are equal and in the other A is greater.

Answer D

thanks for good explaination, I harried to get the roots of the both quantities without thinking
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Re: Which is greater: 2x^2-7x-3 5x^2+x-3 [#permalink] New post 09 Mar 2018, 07:46
In such questions of quantitative comparison, always first simplify the two quantities as below:

Quantity A: \(2x^2\) - 7x - 3
Quantity B: \(5x^2\) + x - 3

First, you can add 3 on both quantities, because it will not change the answer. i.e if a quantity is greater, after addition or subtraction by same number to both quantities, the greater quantity will remain greater. Also if both quantities are equals, the addition and subtraction has no effect, and both will remain equal after adding or subtracting same number to both quantities.

Thus, after adding 3 and 7x to both quantities,

Quantity A: \(2x^2\)
Quantity B: \(5x^2\) + 8x

Now, similarly, we can subtract \(2x^2\) from both quantities and get,

Quantity A: 0
Quantity B: \(3x^2\) + 8x

Now, at this point, again you don't need to plugin. Just you need to think and use common sense here:

\(3x^2\) is either 0 or positive. If x is 0, which can be possible, then the two quantities becomes equal. Otherwise, if x positive, then Quantity B is greater. And if x is negative, then Quantity A become greater.

Thus, Choice D is correct.
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Re: Which is greater: 2x^2-7x-3 5x^2+x-3   [#permalink] 09 Mar 2018, 07:46
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