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# What is the value of x?

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Intern
Joined: 30 Jun 2014
Posts: 32
What is the value of x?  [#permalink]

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01 May 2015, 06:32
1
7
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Difficulty:

55% (hard)

Question Stats:

58% (01:45) correct 42% (01:44) wrong based on 130 sessions

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What is the value of x?

(1) $$x^2+x+10=16$$
(2) $$x=4y^4+2y^2+2$$

Could an Expert please help with the difficulty level as well? I'm not sure if this falls in 600-700.
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Joined: 02 Sep 2009
Posts: 50058
Re: What is the value of x?  [#permalink]

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01 May 2015, 07:23
3
1
Shalabh09 wrote:
What is the value of x?

(1) $$x^2+x+10=16$$
(2) $$x=4y^4+2y^2+2$$

Could an Expert please help with the difficulty level as well? I'm not sure if this falls in 600-700.

What is the value of x?

(1) $$x^2+x+10=16$$ --> $$x^2+x-6=0$$ --> x=-3 or x=2. Not sufficient.

(2) $$x=4y^4+2y^2+2$$. Without knowing the value of y we cannot get the value of x. Not sufficient.
Notice that from this statement it follows that x must be positive: $$x=4y^4+2y^2+2=(nonnegative)+(nonnegative)+(positive)=positive$$.

(1)+(2) Since from (2) x is positive, then from (1) we are left with x=2. Sufficient.

P.S. As for the difficulty level, I'd say it's ~550-600 level question.
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Re: What is the value of x?  [#permalink]

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01 May 2015, 15:09
1
Hi Shalabh09,

The GMAT often finds ways to test you on concepts that you know, but in ways that you're not used to thinking about. This question isn't too difficult (I'd rank it in the low-600s), but it does test you on Quadratics in ways that you're probably not used to thinking about.

Bunuel's explanation showcases the necessary "math" involved, so I won't rehash any of that here. Instead, I'll talk about the 'patterns' that you're supposed to spot in the construction of this question.

First, we're asked for the value of X. This is a standard question to ask in DS.

Second, Fact 1 gives us what appears to be a Quadratic equation with some extra "math" thrown in. You're probably used to solving Quadratic equations when they are set equal to 0..... so do the necessary math to set THIS equation equal to 0 and solve. You'll find that there are 2 solutions: X = -3 and X = 2. Fact 1 is INSUFFICIENT

Third, Fact 2 shows us that X is based on the value of Y. Since Y could be ANY value, there are multiple values for X. Fact 2 is INSUFFICIENT. There IS another thing worth noting about Fact 2 though...Notice the "even powers".....no matter what value you plug in for Y, the value of X will ALWAYS be POSITIVE.....

Combined, we know.....
X = -3 or X = 2
X will ALWAYS be positive

Combined, SUFFICIENT

GMAT assassins aren't born, they're made,
Rich
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# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Director Joined: 07 Aug 2011 Posts: 540 Concentration: International Business, Technology GMAT 1: 630 Q49 V27 What is the value of x? [#permalink] ### Show Tags 03 May 2015, 07:27 Bunuel wrote: Shalabh09 wrote: What is the value of x? (1) $$x^2+x+10=16$$ (2) $$x=4y^4+2y^2+2$$ Could an Expert please help with the difficulty level as well? I'm not sure if this falls in 600-700. What is the value of x? (1) $$x^2+x+10=16$$ --> $$x^2+x-6=0$$ --> x=-3 or x=2. Not sufficient. (2) $$x=4y^4+2y^2+2$$. Without knowing the value of y we cannot get the value of x. Not sufficient. Notice that from this statement it follows that x must be positive: $$x=4y^4+2y^2+2=(nonnegative)+(nonnegative)+(positive)=positive$$. (1)+(2) Since from (2) x is positive, then from (1) we are left with x=2. Sufficient. Answer: C. P.S. As for the difficulty level, I'd say it's ~550-600 level question. Hi Bunuel There is no information given about Y , Y can be a complex number too, so shouldn't i choose answer E ? The roots of the polynomial $$4y^4+2y^2+5=0$$ are: $$Y_1=0.6588+0.82705∗i$$ $$Y_2=0.6588−0.82705∗i$$ $$Y_3=−0.6588+0.82705∗i$$ $$Y_4=−0.6588−0.82705∗i$$ Generally i have seen that GMAT questions always give hints about the numbers, in this question nothing has been told about Y,Strange. noticed that there are a few questions floating in gmatclub , testing knowledge on complex numbers... eg : if-the-square-of-the-sum-of-the-roots-of-a-quadratic-equation-197205.html _________________ Thanks, Lucky _______________________________________________________ Kindly press the to appreciate my post !! Intern Joined: 30 Jun 2014 Posts: 32 Re: What is the value of x? [#permalink] ### Show Tags 03 May 2015, 08:08 Hi Bunuel & EMPOWERgmatRichC, Thank you very much for your detailed explanations. I guess it was just a new type of question so startled me a bit. Once the catch, which you both have shown, is seen it becomes quite simple. Moreover, I guess due to these gaps I'm still stuck at Q41/42. I need some resources to practice such concepts. Could you guide me in this direction too? Lucky : I read in one other forum, GMAT always deals with real numbers. So, there is no concept of complex numbers here. Hope this helps as well. Thank you again. Best Regards, Shalabh. Director Joined: 07 Aug 2011 Posts: 540 Concentration: International Business, Technology GMAT 1: 630 Q49 V27 What is the value of x? [#permalink] ### Show Tags 03 May 2015, 08:28 Shalabh09 wrote: Hi Bunuel & EMPOWERgmatRichC, Thank you very much for your detailed explanations. I guess it was just a new type of question so startled me a bit. Once the catch, which you both have shown, is seen it becomes quite simple. Moreover, I guess due to these gaps I'm still stuck at Q41/42. I need some resources to practice such concepts. Could you guide me in this direction too? Lucky : I read in one other forum, GMAT always deals with real numbers. So, there is no concept of complex numbers here. Hope this helps as well. Thank you again. Best Regards, Shalabh. i am aware . what i am trying to say is that GMAT questions always are always unambiguous such that even you do not read the official disclaimers (eg: GMAT always tests real numbers ) , you will be able to arrive a definitive conclusion. _________________ Thanks, Lucky _______________________________________________________ Kindly press the to appreciate my post !! Math Expert Joined: 02 Sep 2009 Posts: 50058 Re: What is the value of x? [#permalink] ### Show Tags 03 May 2015, 11:52 Lucky2783 wrote: Bunuel wrote: Shalabh09 wrote: What is the value of x? (1) $$x^2+x+10=16$$ (2) $$x=4y^4+2y^2+2$$ Could an Expert please help with the difficulty level as well? I'm not sure if this falls in 600-700. What is the value of x? (1) $$x^2+x+10=16$$ --> $$x^2+x-6=0$$ --> x=-3 or x=2. Not sufficient. (2) $$x=4y^4+2y^2+2$$. Without knowing the value of y we cannot get the value of x. Not sufficient. Notice that from this statement it follows that x must be positive: $$x=4y^4+2y^2+2=(nonnegative)+(nonnegative)+(positive)=positive$$. (1)+(2) Since from (2) x is positive, then from (1) we are left with x=2. Sufficient. Answer: C. P.S. As for the difficulty level, I'd say it's ~550-600 level question. Hi Bunuel There is no information given about Y , Y can be a complex number too, so shouldn't i choose answer E ? The roots of the polynomial $$4y^4+2y^2+5=0$$ are: $$Y_1=0.6588+0.82705∗i$$ $$Y_2=0.6588−0.82705∗i$$ $$Y_3=−0.6588+0.82705∗i$$ $$Y_4=−0.6588−0.82705∗i$$ Generally i have seen that GMAT questions always give hints about the numbers, in this question nothing has been told about Y,Strange. noticed that there are a few questions floating in gmatclub , testing knowledge on complex numbers... eg : if-the-square-of-the-sum-of-the-roots-of-a-quadratic-equation-197205.html All numbers used on the GMAT are real numbers by default. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12702 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: What is the value of x? [#permalink] ### Show Tags 04 May 2015, 13:53 Hi Shalabh09, With a Q41 or Q42, your "issue(s)" might not be with content knowledge but in how you "see" (and respond to) the GMAT. It might be that you actually need to focus more on tactics, pattern-matching, etc. and less on doing more of the same things that you've already done. 1) How long have you studied? 2) What practice resources have you used so far? 3) What is your goal score? GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

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Re: What is the value of x?  [#permalink]

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29 Oct 2017, 09:58
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