Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 01:16

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If y^(-2) + 2y^(-1) - 15 = 0, which of the following could be the valu

Author Message
TAGS:

### Hide Tags

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

### Show Tags

05 Jul 2018, 21:28
00:00

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. $$-5$$

_________________
VP
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]

### Show Tags

05 Jul 2018, 21:38
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)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
VP
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]

### Show Tags

08 Jul 2018, 05:26
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
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Intern
Status: No Progress without Struggle
Joined: 04 Aug 2017
Posts: 42
Location: Armenia
GPA: 3.4
Re: If y^(-2) + 2y^(-1) - 15 = 0, which of the following could be the valu  [#permalink]

### Show Tags

09 Jul 2018, 03:44
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?
_________________
Seryozha Sargsyan 21

Contact: sargsyanseryozha@gmail.com

What you think, you become,
What you feel, you attract,
What you imagine, you create.
VP
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]

### Show Tags

09 Jul 2018, 03:51
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
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
NUS School Moderator
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]

### Show Tags

22 Aug 2018, 06:54
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 = $$\frac{-1}{5}$$

_________________
Press +1 Kudos If my post helps!
Rice (Jones) School Moderator
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]

### Show Tags

22 Aug 2018, 08:27
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
Joined: 14 Sep 2014
Posts: 12
Re: If y^(-2) + 2y^(-1) - 15 = 0, which of the following could be the valu  [#permalink]

### Show Tags

22 Aug 2018, 08:32
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.

Posted from my mobile device
NUS School Moderator
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]

### Show Tags

22 Aug 2018, 17:55
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
_________________
Press +1 Kudos If my post helps!
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6968
Location: United States (CA)
Re: If y^(-2) + 2y^(-1) - 15 = 0, which of the following could be the valu  [#permalink]

### Show Tags

26 Aug 2018, 18:21
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

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

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
Display posts from previous: Sort by