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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If x/4 = 5x-2/x+8, then x^2 - 12x + 40 =
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30 Sep 2019, 09:29
30 Sep 2019, 09:29
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If \(\frac{x}{4}=\frac{5x-2}{x+8}\), then \(x^2 - 12x + 40 =\) ?
A) 0
B) 4
C) 8
D) 12
E) 32
A) 0
B) 4
C) 8
D) 12
E) 32
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x/4 = 5x-2/x+8, then x^2 - 12x + 40 =
[#permalink]
30 Sep 2019, 09:52
30 Sep 2019, 09:52
2
GreenlightTestPrep wrote:
If \(\frac{x}{4}=\frac{5x-2}{x+8}\), then \(x^2 - 12x + 40 =\) ?
A) 0
B) 4
C) 8
D) 12
E) 32
A) 0
B) 4
C) 8
D) 12
E) 32
Given: \(\frac{x}{4}=\frac{5x-2}{x+8}\)
Cross multiply to get: \((x)(x+8)=4(5x-2)\)
Expand to get: \(x^2+8x=20x-8\)
Subtract \(20x\) from both sides: \(x^2-12x=-8\)
Add \(8\) to both sides: \(x^2-12x+8=0\)
STOP! Do NOT try to solve this quadratic equation for x
Instead, notice that we now know that \(x^2-12x+8=0\).
Our goal is to find the value of the expression \(x^2 - 12x + 40\)
Since \(x^2-12x+8\) and \(x^2-12x+40\) are similar, we can do the following...
Take: \(x^2-12x+8=0\)
Add \(32\) to both sides to get: \(x^2-12x+40=32\)
Perfect! We now know the value of \(x^2-12x+40\)
Answer: E
Cheers,
Brent
Re: If x/4 = 5x-2/x+8, then x^2 - 12x + 40 =
[#permalink]
30 Sep 2019, 13:48
30 Sep 2019, 13:48
2
One of the keys here is to see that there is a quadratic that cannot be factored out (or in other words, broken down) "nicely".
This should raise a red flag, and alert the test taker that something "clever" can be done. For example, the second equation of x^2−12x+40 = ? can not be broken down into integers, like what we may be use to. When you hit this point, stop and look at the other equation and then be on the look out for something clever to do.
With equation x/4=(5x−2)/(x+8), I cross multiply to remove the denominators. The result is x^2 -12x +40 = 32.
Here I notice that now both equations have x^2 -12x, and this is the big clue. So I rearrange this equation to be x^2 -12 = -8, and now I see replace x^2 -12 in the equation x^2−12x+40 = ? with -8, so it become (-8)
+40 = ?. Completing -8 + 40 = ?, results in 32.
Choice E is the answer.
This should raise a red flag, and alert the test taker that something "clever" can be done. For example, the second equation of x^2−12x+40 = ? can not be broken down into integers, like what we may be use to. When you hit this point, stop and look at the other equation and then be on the look out for something clever to do.
With equation x/4=(5x−2)/(x+8), I cross multiply to remove the denominators. The result is x^2 -12x +40 = 32.
Here I notice that now both equations have x^2 -12x, and this is the big clue. So I rearrange this equation to be x^2 -12 = -8, and now I see replace x^2 -12 in the equation x^2−12x+40 = ? with -8, so it become (-8)
+40 = ?. Completing -8 + 40 = ?, results in 32.
Choice E is the answer.
