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x^2 + x - 40 = 0

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x^2 + x - 40 = 0 [#permalink] New post   15 Oct 2017, 09:13
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\(x^2 + x - 40 = 0\)

Quantity A
Quantity B
| x + 1|
5


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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A
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MyGuruStefan
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Re: x^2 + x - 40 = 0 [#permalink] New post   22 May 2019, 10:51
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\(x^2 + x - 40 = 0\)

Quantity A
Quantity B
| x + 1|
5

Always note the values in the quantities to inform your approach to any Quantitative Comparison. In this case, although we are presented a quadratic, it may actually make sense to attempt to manipulate the equation to find x + 1 since that is the value of Quantity A.

So, add 40 to each side of the equation to find that x^2 + x = 40. Then, factor the left hand side of the equation to find that x(x+1) = 40. Now, just plug 5 in as x to determine the relationship between the quantities.

If x = 5, then x(x + 1) = 5 x 6 = 30 which is < 40. Then, testing if x = 6, we discover that 6 x 7 = 42. So, therefore 5 < x < 6.

Now for the negative solution just flip the x and x - 1.

So, if x = -6, then x(x + 1) = -6 x -5 = 30 which again is < 40. Then, testing if x = -7, we discover again that -7 x - 6 = 42. So, therefore -7 < x < -6.

Now apply the ranges to test the possibilities for Quantity A. If x > 5 then |x + 1| > 5. If x < -6 then |x + 1| > 5.

In both cases Quantity A is greater, so select Choice A.
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IlCreatore
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Re: x^2 + x - 40 = 0 [#permalink] New post   15 Oct 2017, 09:30
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The solutions to the equations are \(\frac{-1\pm \sqrt161}{2}\), then given that \(sqrt161>12\), the two roots are both positive numbers. Thus, when they are summed to 1 and taken absolute value they keep being positive and greater than 5 in both the occasions.

Thus answer is A
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GREMasterBlaster
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Re: x^2 + x - 40 = 0 [#permalink] New post   28 Feb 2018, 14:18
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IlCreatore wrote:
The solutions to the equations are \(\frac{-1\pm \sqrt161}{2}\), then given that \(sqrt161>12\), the two roots are both positive numbers. Thus, when they are summed to 1 and taken absolute value they keep being positive and greater than 5 in both the occasions.

Thus answer is A

Another good explanation,
Giving you 1 more kudos.
It was a good question.
Yes, in both scenarios, Quantity A always greater.
So Choice A.
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priyanka67
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Re: x^2 + x - 40 = 0 [#permalink] New post   22 May 2019, 07:31
would youplz give anoyher solution?
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Re: x^2 + x - 40 = 0 [#permalink] New post   04 Dec 2023, 02:00
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).

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Re: x^2 + x - 40 = 0 [#permalink]
04 Dec 2023, 02:00
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