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

Question

What is the value of x? (1) (x^2 + 3)^2 - 11(x^2 + 3) + 28 = 0 (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/simplifyi ... -the-gmat/ Mike

Anamika2014 · Answer

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.

seabhi · Answer

Can't find the options.

mikemcgarry · Answer

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: DS Statements, algebra.JPG 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 :-)

rashminuligonda · Answer

Hello,

In general in questions like these, if the stem of the question asks, if outcome can be found out? 
statement A gives certain outcome 
Statement B gives different outcome.

Now, both statements are giving outcomes but they are different. Just like in above questions. X is obtaining different values. How to proceed in such instances.

And, specific to this question, on combining 2 statements, if x yields 2 values, why cant we consider that?

SilverFire · Answer

The key point is that this is a Data Sufficiency question. Even after combining both statements, (x) can be either (-2) or (1). Since we don't get a unique value for (x), the statements are still insufficient.
So the answer is  E .

Bunuel · Answer

When a DS question asks for the value of an expression (or a variable), a statement is sufficient only if it gives a  single  numerical value for that expression.

Here, even after combining the statements, x could still be either -2 or 1. Since the value of x is not uniquely determined, the correct answer is E.

P.S. Pure algebraic questions are no longer a part of the  DS syllabus  of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

Word Problems 
 Work Problems 
 Distance Problems 
 Mixture Problems 
 Percent and Interest Problems 
 Overlapping Sets Problems 
 Statistics Problems 
 Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check  GMAT Syllabus for Focus Edition

You can also visit the  Data Sufficiency forum  and filter questions by  OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources  to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.

rashminuligonda · Answer

Yes. Thankyouuu very muchhh

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

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

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