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# If (z^2 + 6z + 9)/(z^2 - 9) = 2 , what is the value of z ?

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If (z^2 + 6z + 9)/(z^2 - 9) = 2 , what is the value of z ?  [#permalink]

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Updated on: 15 Nov 2018, 03:46
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Difficulty:

15% (low)

Question Stats:

78% (01:14) correct 22% (01:41) wrong based on 79 sessions

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If $$\frac{z^2+6z+9}{z^2-9}=2$$, what is the value of z ?

A. 9

B. 6

C. 3

D. -3

E. -9

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Md. Abdur Rakib

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

Originally posted by AbdurRakib on 01 Sep 2015, 22:24.
Last edited by Bunuel on 15 Nov 2018, 03:46, edited 3 times in total.
Renamed the topic and edited the question.
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Re: If (z^2 + 6z + 9)/(z^2 - 9) = 2 , what is the value of z ?  [#permalink]

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01 Sep 2015, 22:33
3
1
AbdurRakib wrote:
If $$z^2$$+6z+9/$$z^2$$-9=2 , what is the value of z ?

A. 9

B. 6

C. 3

D. -3

E. -9

$$\frac{z^2 + 6z + 9}{z^2 - 9} = 2$$

$$\frac{(z + 3)^2}{z^2 - 3^2} = 2$$

$$\frac{(z + 3)*(z + 3)}{(z + 3)(z - 3)} = 2$$

$$\frac{(z + 3)}{(z-3)} = 2$$

Now plug in values from the options. When x = 9, you get (9 + 3)/(9 - 3) = 12/6 = 2
It satisfies.

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Re: If (z^2 + 6z + 9)/(z^2 - 9) = 2 , what is the value of z ?  [#permalink]

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01 Sep 2015, 23:26
2
Hi AbdurRakib,

This question can be solved rather easily by TESTing THE ANSWERS. You can actually AVOID 2 of the answer choices - since the GMAT does NOT test the concept of 'dividing by zero', and the denominator of the fraction is (Z^2 - 9), we know that Z cannot be 3 or -3. From there, whether you simplify the given equation or not, you have only three potential answers to TEST (although from the work that Karishma did, you can see that simplifying the fraction will help make the math go a bit faster).

IF Z = 9....
(81+54+9)/(81-9) =
144/72 =
2

This is an exact match for what we were told, so this MUST be the answer.

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/ Current Student Joined: 12 Aug 2015 Posts: 2603 Schools: Boston U '20 (M) GRE 1: Q169 V154 Re: If (z^2 + 6z + 9)/(z^2 - 9) = 2 , what is the value of z ? [#permalink] ### Show Tags 08 Mar 2016, 07:28 VeritasPrepKarishma wrote: AbdurRakib wrote: If $$z^2$$+6z+9/$$z^2$$-9=2 , what is the value of z ? A. 9 B. 6 C. 3 D. -3 E. -9 Kudos Please $$\frac{z^2 + 6z + 9}{z^2 - 9} = 2$$ $$\frac{(z + 3)^2}{z^2 - 3^2} = 2$$ $$\frac{(z + 3)*(z + 3)}{(z + 3)(z - 3)} = 2$$ $$\frac{(z + 3)}{(z-3)} = 2$$ Now plug in values from the options. When x = 9, you get (9 + 3)/(9 - 3) = 12/6 = 2 It satisfies. Answer (A) Personal Opinion => Plugging in values in these types of questions makes it more tedious . Shouldn't i be doing this with the basic identity => (a+b) (a-b) _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14868 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If (z^2 + 6z + 9)/(z^2 - 9) = 2 , what is the value of z ? [#permalink] ### Show Tags 08 Mar 2016, 12:59 Hi Chiragjordan, You bring up a question that impacts all Test Takers - what really is the fastest/easiest way for you to answer a given Quant question AND score at the highest level possible on Test Day? The Quant section of the GMAT is NOT, strictly-speaking, a 'math test.' As such, if you try to treat it as if it were a math test (and just do lots of traditional math to answer the questions you face), then it's likely that you'll miss out on some points. In addition, you might actually run into a pacing issue, since 'math approaches' can sometimes take far longer to implement than Tactical approaches. If you're already scoring at a high level in Quant (Q49+), then you likely have nothing to worry about - you should tackle the Quant section any way that you choose. Since you're asking the question though, that makes me think that you're currently facing some challenges in your studies. 1) How long have you been studying? 2) How have you scored on your CATs (including the Quant and Verbal Scaled Scores)? 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 *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: If (z^2 + 6z + 9)/(z^2 - 9) = 2 , what is the value of z ?  [#permalink]

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25 Nov 2018, 06:03
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Re: If (z^2 + 6z + 9)/(z^2 - 9) = 2 , what is the value of z ?   [#permalink] 25 Nov 2018, 06:03
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