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x^2 + x - 40 = 0
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15 Oct 2017, 09:13
15 Oct 2017, 09:13
Expert Reply
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Question Stats:
58% (01:52) correct
41% (01:42) wrong based on 235 sessions
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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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Posts: 186
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Location: United States
GMAT 1: 770 Q51 V44
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WE:Education (Education)
Re: x^2 + x - 40 = 0
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22 May 2019, 10:51
22 May 2019, 10:51
4
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Quote:
\(x^2 + x - 40 = 0\)
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.
Re: x^2 + x - 40 = 0
[#permalink]
15 Oct 2017, 09:30
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
Thus answer is A
