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# x < 0

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x < 0 [#permalink]  26 Aug 2017, 01:59
Expert's post
00:00

Question Stats:

80% (00:45) correct 20% (01:15) wrong based on 50 sessions

$$x < 0$$

 Quantity A Quantity B $$x^2$$ $$- 5x + 6$$ $$x^2$$ $$- 9x + 20$$

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.
[Reveal] Spoiler: OA

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Re: x < 0 [#permalink]  27 Aug 2017, 04:53
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Expert's post
Carcass wrote:
x < 0

 Quantity A Quantity B $$x^2$$ – 5x + 6 $$x^2$$ – 9x + 20

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.

Let's use matching operations

Given:
Quantity A: x² - 5x + 6
Quantity B: x² - 9x + 20

Subtract x² from both quantities to get:
Quantity A: -5x + 6
Quantity B: -9x + 20

Add 9x to both quantities to get:
Quantity A: 4x + 6
Quantity B: 20

Subtract 6 from both quantities to get:
Quantity A: 4x
Quantity B: 14

Divide both quantities by 4 to get:
Quantity A: x
Quantity B: 3.5

Since we're told that x is NEGATIVE, it must be the case that Quantity B is greater.

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Re: x < 0 [#permalink]  13 Nov 2018, 17:50
Is there any other approach?
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Re: x < 0 [#permalink]  13 Nov 2018, 18:09
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Expert's post
AE wrote:
Is there any other approach?

You could try testing numbers.

More here:

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Re: x < 0 [#permalink]  19 Nov 2018, 16:53
AE wrote:
Is there any other approach?

An easier way would be to notice that x^2 will always give a positive value. So on both sides that part is equal.

Moving on to -5x vs -9x for whatever negative value of x the -9x will be larger because (-ve) * (-ve) yields positive.

For example let x be -1 it will be (-1)*(-5) vs (-1)*(-9)

Finally 20 is larger than 6 so on that basis we could tell that B is larger.
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Re: x < 0 [#permalink]  22 Nov 2018, 23:44
AE wrote:
Is there any other approach?

x<0
We want to compare x^2 - 5x +6 and x^2 -9x +20, as x^2 is the same amount in both of them, we can omit it and compare - 5x +6 and -9x +20

- 5x +6 and -9x +20
We subtract 6 from both sides, then we will have:
-5x and -9x + 14
As x is something negative, if it’s multiplied by a negative number (-5 in A and -9 in B) it will be positive, So -9x is bigger than -5x. Assume -9x as 9*(-x) and as x is negative, (-x) will be positive, same for -5x)
So B is bigger than A.
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Re: x < 0 [#permalink]  23 Nov 2018, 02:26
Think plugging in with x= -1 and x=-20, the extreme case will be better
Re: x < 0   [#permalink] 23 Nov 2018, 02:26
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