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505-555 (Easy)|   Algebra|      
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AbdurRakib
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If (z^2 + 6z + 9)/(z^2 - 9) = 2 , what is the value of z ? Updated on: 15 Nov 2018, 03:46
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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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

82% (01:16) correct 18% (01:37) wrong based on 145 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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A
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KarishmaB
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If (z^2 + 6z + 9)/(z^2 - 9) = 2 , what is the value of z ? 01 Sep 2015, 22:33
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AbdurRakib
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


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

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

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

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

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

Answer (A)
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If (z^2 + 6z + 9)/(z^2 - 9) = 2 , what is the value of z ? 01 Sep 2015, 23:26
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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).

So let's start with Answer A....
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.

Final Answer:
Show Spoiler
A

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If (z^2 + 6z + 9)/(z^2 - 9) = 2 , what is the value of z ? 08 Mar 2016, 07:28
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VeritasPrepKarishma
AbdurRakib
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 :cry: :)


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

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

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

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

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

Answer (A)
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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)
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EMPOWERgmatRichC
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If (z^2 + 6z + 9)/(z^2 - 9) = 2 , what is the value of z ? 08 Mar 2016, 12:59
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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
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If (z^2 + 6z + 9)/(z^2 - 9) = 2 , what is the value of z ? 08 Jun 2024, 17:40
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