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Math Expert V
Joined: 02 Sep 2009
Posts: 56300
If y^(-2) + 2y^(-1) - 15 = 0, which of the following could be the valu  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 69% (01:50) correct 31% (01:58) wrong based on 170 sessions

### HideShow timer Statistics If $$y^{-2} + 2y^{-1} -15 = 0$$, which of the following could be the value of y?

A. $$3$$

B. $$\frac{1}{5}$$

C. $$\frac{-1}{5}$$

D. $$\frac{-1}{3}$$

E. $$-5$$

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VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
If y^(-2) + 2y^(-1) - 15 = 0, which of the following could be the valu  [#permalink]

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3
Bunuel wrote:
If $$y^{-2} + 2y^{-1} -15 = 0$$, which of the following could be the value of y?

A. $$3$$

B. $$\frac{1}{5}$$

C. $$\frac{-1}{5}$$

D. $$\frac{-1}{3}$$

E. $$-5$$

Let $$y^{-1}=x$$

So, $$y^{-2} + 2y^{-1} -15 = 0$$
Or, $$x^2+2x-15=0$$
Or, x=-5 or x=3

1. x=-5, or, $$y^{-1}=-5$$ or, $$y=\frac{-1}{5}$$
2. x=3,or, $$y^{-1}=3$$ or, $$y=\frac{1}{3}$$

Among given options, correct answer is (C)
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PKN

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VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
Re: If y^(-2) + 2y^(-1) -15 = 0, which of the following could be the value  [#permalink]

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Bunuel wrote:
If $$y^{-2} + 2y^{-1} -15 = 0$$, which of the following could be the value of y?

A. $$3$$

B. $$\frac{1}{5}$$

C $$\frac{-1}{5}$$

D. $$\frac{-1}{3}$$

E. $$-5$$

Let $$y^{-1}=x$$

So, $$y^{-2} + 2y^{-1} -15 = 0$$
Or, $$x^2+2x-15=0$$
Or, x=-5 or x=3

1. x=-5, or, $$y^{-1}=-5$$ or, $$y=\frac{-1}{5}$$
2. x=3,or, $$y^{-1}=3$$ or, $$y=\frac{1}{3}$$

Among given options, correct answer is (C)[/quote]
https://gmatclub.com/forum/if-y-2-2y-1- ... 69804.html
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PKN

Rise above the storm, you will find the sunshine
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Status: No Progress without Struggle
Joined: 04 Aug 2017
Posts: 42
Location: Armenia
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Re: If y^(-2) + 2y^(-1) - 15 = 0, which of the following could be the valu  [#permalink]

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PKN wrote:
Bunuel wrote:
If $$y^{-2} + 2y^{-1} -15 = 0$$, which of the following could be the value of y?

A. $$3$$

B. $$\frac{1}{5}$$

C. $$\frac{-1}{5}$$

D. $$\frac{-1}{3}$$

E. $$-5$$

Let $$y^{-1}=x$$

So, $$y^{-2} + 2y^{-1} -15 = 0$$
Or, $$x^2+2x-15=0$$
Or, x=-5 or x=3

1. x=-5, or, $$y^{-1}=-5$$ or, $$y=\frac{-1}{5}$$
2. x=3,or, $$y^{-1}=3$$ or, $$y=\frac{1}{3}$$

Among given options, correct answer is (C)

Is there an alternative way to solve this problem?
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Seryozha Sargsyan 21

Contact: sargsyanseryozha@gmail.com

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What you feel, you attract,
What you imagine, you create.
VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
Re: If y^(-2) + 2y^(-1) - 15 = 0, which of the following could be the valu  [#permalink]

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Plugin answer choices and put in LHS of the given equation.The value of y for which the LHS becomes zero is the correct answer choice.

Posted from my mobile device
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PKN

Rise above the storm, you will find the sunshine
NUS School Moderator D
Joined: 18 Jul 2018
Posts: 985
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If y^(-2) + 2y^(-1) - 15 = 0, which of the following could be the valu  [#permalink]

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1
$$y^{-2}$$ can be written as $$\frac{1}{y^2}$$
Similarly $$y^{-1}$$ can be written as $$\frac{1}{y}$$

Then the equation becomes $$\frac{1}{y^2}$$ + 2$$\frac{1}{y}$$ - 15 = 0.

Taking LCM, the equation becomes 1+2y-15$$y^2$$ = 0.

Re-arranging gives 15$$y^2$$-2y-1 = 0.

15$$y^2$$-5y+3y-1 = 0.

5y(3y-1)+1(3y-1) = 0

Either y = $$\frac{-1}{3}$$ or y = $$\frac{-1}{5}$$.

y = $$\frac{-1}{5}$$

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Rice (Jones) School Moderator G
Joined: 18 Jun 2018
Posts: 238
Location: United States (AZ)
Concentration: Finance, Healthcare
GMAT 1: 600 Q44 V28 GPA: 3.36
If y^(-2) + 2y^(-1) - 15 = 0, which of the following could be the valu  [#permalink]

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Afc0892

Sure it is a typo (since you got the answer) but -1/3 is not a root, otherwise option D will be correct too. The roots are 1/3 and -1/5 (option C). I am also an arsenal fan. Up gunners!!!

Afc0892 wrote:
$$y^{-2}$$ can be written as $$\frac{1}{y^2}$$
Similarly $$y^{-1}$$ can be written as $$\frac{1}{y}$$

Then the equation becomes $$\frac{1}{y^2}$$ + 2$$\frac{1}{y}$$ - 15 = 0.

Taking LCM, the equation becomes 1+2y-15$$y^2$$ = 0.

Re-arranging gives 15$$y^2$$-2y-1 = 0.

15$$y^2$$-5y+3y-1 = 0.

5y(3y-1)+1(3y-1) = 0

Either y = $$\frac{-1}{3}$$ or y = $$\frac{-1}{5}$$.

y = $$\frac{-1}{5}$$

Intern  B
Joined: 14 Sep 2014
Posts: 12
Re: If y^(-2) + 2y^(-1) - 15 = 0, which of the following could be the valu  [#permalink]

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The best way to go here is to put the options.
And only select options that is any option more than 1 will not satisfy.
Only options less than 1 will satisfy since the power is negative.

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NUS School Moderator D
Joined: 18 Jul 2018
Posts: 985
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If y^(-2) + 2y^(-1) - 15 = 0, which of the following could be the valu  [#permalink]

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funsogu wrote:
Afc0892

Sure it is a typo (since you got the answer) but -1/3 is not a root, otherwise option D will be correct too. The roots are 1/3 and -1/5 (option C). I am also an arsenal fan. Up gunners!!!

Afc0892 wrote:
$$y^{-2}$$ can be written as $$\frac{1}{y^2}$$
Similarly $$y^{-1}$$ can be written as $$\frac{1}{y}$$

Then the equation becomes $$\frac{1}{y^2}$$ + 2$$\frac{1}{y}$$ - 15 = 0.

Taking LCM, the equation becomes 1+2y-15$$y^2$$ = 0.

Re-arranging gives 15$$y^2$$-2y-1 = 0.

15$$y^2$$-5y+3y-1 = 0.

5y(3y-1)+1(3y-1) = 0

Either y = $$\frac{-1}{3}$$ or y = $$\frac{-1}{5}$$.

y = $$\frac{-1}{5}$$

Yes its typo. Thanks for mentioning. COYG ?

Posted from my mobile device
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Re: If y^(-2) + 2y^(-1) - 15 = 0, which of the following could be the valu  [#permalink]

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Bunuel wrote:
If $$y^{-2} + 2y^{-1} -15 = 0$$, which of the following could be the value of y?

A. $$3$$

B. $$\frac{1}{5}$$

C. $$\frac{-1}{5}$$

D. $$\frac{-1}{3}$$

E. $$-5$$

Simplifying we have:

1/y^2 + 2/y - 15 = 0

Multiplying by y^2 we have:

1 + 2y - 15y^2 = 0

15y^2 - 2y - 1 = 0

(3y - 1)(5y + 1) = 0

3y - 1 = 0 → 3y = 1 → y = 1/3

Or

5y + 1 = 0 → 5y = -1 → y = -⅕

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If y^(-2) + 2y^(-1) - 15 = 0, which of the following could be the valu   [#permalink] 26 Aug 2018, 18:21
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