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What is the value of x? (x^2 + 3)^2 - 11(x^2 + 3) + 28 = 0

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mikemcgarry
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What is the value of x? (x^2 + 3)^2 - 11(x^2 + 3) + 28 = 0 [#permalink] New post   11 Sep 2014, 13:57
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35% (medium)

Question Stats:

68% (01:50) correct 32% (01:57) wrong based on 221 sessions
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What is the value of x?
Statement #1: \((x^2 + 3)^2 - 11(x^2 + 3) + 28 = 0\)
Statement #2: \(x^2 + x - 2 = 0\)

For the more mathematically adept, it may be perfectly obvious how to simply that monstrosity in Statement #1. If that is not perfectly clear, see this blog for more details:
https://magoosh.com/gmat/2013/simplifyin ... -the-gmat/

Mike :-)
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E
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Anamika2014
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Re: What is the value of x? (x^2 + 3)^2 - 11(x^2 + 3) + 28 = 0 [#permalink] New post   13 Sep 2014, 07:24
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mikemcgarry wrote:
What is the value of x?
Statement #1: \((x^2 + 3)^2 - 11(x^2 + 3) + 28 = 0\)
Statement #2: \(x^2 + x - 2 = 0\)

1) \((x^2 + 3)^2 - 11(x^2 + 3) + 28 = 0\)
The simplest way to do this is to assume \((x^2 + 3)^2\) to be another variable \(y\). The equation now reduces to

\(y^2 - 11y + 28 = 0\) => \(y^2 - 7y - 4y + 28 = 0\) => \((y - 7) * (y -4) = 0\)

So, \(y = 7\) or \(y = 4\). Substituting the value of \(y\) back, we get

\(x^2 + 3 = 7\) or \(x^2 + 3 = 4\)

=> \(x^2 = 4\) or \(x^2 = 1\)

=> \(x = -2, 2, -1 or 1\) -------> Insufficient

2) \(x^2 + x - 2 = 0\)

=> \(x^2 +2x - x - 2 = 0\)

=> \((x + 2) * (x - 1) = 0\)

=> \(x = -2 or 1\) -------> Insufficient

Combining, we still have \(x = -2 or 1\) -------> Insufficient

So, the answer is E.

Hope that helps.
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seabhi
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Re: What is the value of x? (x^2 + 3)^2 - 11(x^2 + 3) + 28 = 0 [#permalink] New post   12 May 2015, 06:48
Can't find the options.
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mikemcgarry
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Re: What is the value of x? (x^2 + 3)^2 - 11(x^2 + 3) + 28 = 0 [#permalink] New post   12 May 2015, 10:47
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seabhi wrote:
Can't find the options.

Dear seabhi,
I'm happy to respond. :-) Both my problem and Anamika2014's good solution use GMAT Club's system for writing math formulas. I believe they are converted to some kind of picture file. Many math problems on this site have formulas written the same way, so I think it would be worthwhile to check the settings on your computer and figure out why you are unable to view them.

In the meantime, I took a picture of the question as it shows up on my screen. Here it is:
Attachment:
DS Statements, algebra.JPG
DS Statements, algebra.JPG [ 18.35 KiB | Viewed 3675 times ]

I don't know whether you will be able to see that. That is what you should see in my post at the top as well, and if you don't, there's some kind of problem. It may be that it is simply taking the images time to load, and you have to wait a bit for them. It may be that your browser is not supporting this image format. If your connection speed is slow, that might create a problem. If you are viewing this post at work, some companies have software that blocks images. There are many things that might contributed to this problem. I would suggest looking at GMAT Club outside of work, on the newest possible computer connected at to a high speed internet, if all that is possible.

Let me know if you can't see the picture in this post either. You might also try to see the problem here:
https://magoosh.com/gmat/2013/simplifyin ... -the-gmat/

Mike :-)
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Re: What is the value of x? (x^2 + 3)^2 - 11(x^2 + 3) + 28 = 0 [#permalink]
12 May 2015, 10:47
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