It is currently 17 Jun 2019, 21:19

### 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

# GRE Math Challenge #3-Which of the following values of x

Author Message
TAGS:
Director
Joined: 16 May 2014
Posts: 595
GRE 1: Q165 V161
Followers: 97

Kudos [?]: 475 [0], given: 64

GRE Math Challenge #3-Which of the following values of x [#permalink]  09 Aug 2014, 02:35
Expert's post
00:00

Question Stats:

70% (00:30) correct 30% (02:23) wrong based on 10 sessions
Attachment:

q2.png [ 11.35 KiB | Viewed 4285 times ]

Which of the following values of x satisfy the equation?
Indicate all possible values.

A) -6
B) -4.5
C) -3
D) 0
E) 3
F) 4.5
G) 6
[Reveal] Spoiler: OA

_________________

My GRE Resources
Free GRE resources | GRE Prep Club Quant Tests
If you find this post helpful, please press the kudos button to let me know !

Director
Joined: 16 May 2014
Posts: 595
GRE 1: Q165 V161
Followers: 97

Kudos [?]: 475 [1] , given: 64

Re: GRE Math Challenge #3 [#permalink]  09 Aug 2014, 02:38
1
KUDOS
Expert's post
_________________

My GRE Resources
Free GRE resources | GRE Prep Club Quant Tests
If you find this post helpful, please press the kudos button to let me know !

Intern
Joined: 03 Sep 2014
Posts: 3
Followers: 0

Kudos [?]: 1 [0], given: 2

Re: GRE Math Challenge #3 [#permalink]  04 Sep 2014, 07:13
B,E
GRE Instructor
Joined: 10 Apr 2015
Posts: 1968
Followers: 60

Kudos [?]: 1797 [2] , given: 9

Re: GRE Math Challenge #3 [#permalink]  16 May 2015, 13:29
2
KUDOS
Expert's post
soumya1989 wrote:
Attachment:
q2.png

Which of the following values of x satisfy the equation?
Indicate all possible values.

A) -6
B) -4.5
C) -3
D) 0
E) 3
F) 4.5
G) 6

For our first step, let's eliminate the fraction by multiplying both sides by 2x to get:
8x^21 + 12x^20 - 108x^19 + √(36x^4) = 6x^2
Now simplify √(36x^4) to get: 8x^21 + 12x^20 - 108x^19 + 6x^2 = 6x^2
Subtract 6x^2 from both sides to get: 8x^11 + 12x^20 - 108x^19 = 0
Factor out 4x^19 to get: 4x^19(2x^2 + 3x - 27) = 0
Factor to get: 4x^19(2x + 9)(x - 3) = 0
So, it's possible that 4x^19 = 0, in which case x = 0*
Or 2x + 9 = 0, in which case x = -4.5
Or x - 3 = 0, in which case x = 3

IMPORTANT: Early in our approach, we multiplied both sides by 2x. We need to be careful here, because if we inadvertently multiplied both sides by zero, then our solution may be incorrect.
Notice that x = 0 IS NOT a solution to the original equation.
If plug in x = 0 we get: 0/0 = 0, which is not true.
So, x = 0 is NOT a valid solution.

So, our two valid solutions are x = -4.5 and x = 3

[Reveal] Spoiler:
B and E

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Intern
Joined: 20 Aug 2017
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: GRE Math Challenge #3-Which of the following values of x [#permalink]  21 Aug 2017, 08:57
I quite didn't get how the expression 2x^2+3x-27 =0 was factorised
GRE Instructor
Joined: 10 Apr 2015
Posts: 1968
Followers: 60

Kudos [?]: 1797 [2] , given: 9

Re: GRE Math Challenge #3-Which of the following values of x [#permalink]  21 Aug 2017, 09:20
2
KUDOS
Expert's post
abbasiime wrote:
I quite didn't get how the expression 2x^2 + 3x - 27 = 0 was factorised

There's a formal technique for factoring quadratics that do NOT have a 1 as the coefficient of the x^2 term.
However, the GRE will never give us a super complicated expression to factor.
So, we can just play around with some numbers.

First, we know that the two x-terms must multiply together to give us 2x^2.
So, one term must be 2x and the other term must be x

So far, we have: 2x^2 + 3x - 27 = (2x +/- ??)(x +/- ??)

For the two missing terms, we know that they multiply to get -27
So, let's try some options.

We get: 2x^2 + 3x - 27 = (2x + 27)(x - 1)
To see if this works, we'll EXPAND (2x + 27)(x - 1) using the FOIL Method
(2x + 27)(x - 1) = 2x^2 - 2x + 27x - 27
= 2x^2 + 25x - 27
This doesn't equal 2x^2 + 3x - 27. So, our missing numbers are NOT 27 and -1

We get: 2x^2 + 3x - 27 = (2x + 9)(x - 3)
To see if this works, we'll EXPAND (2x + 9)(x - 3) using the FOIL Method
(2x + 9)(x - 3) = 2x^2 - 6x + 9x - 27
= 2x^2 + 3x - 27
Perfect - this equals the original expression!
So, our missing numbers are NOT 27 and -1

Go, given: 2x^2 + 3x - 27 = 0
Factor to get: (2x + 9)(x - 3) = 0
This means EITHER 2x + 9 = 0 OR x - 3 = 0

If 2x + 9 = 0, then x = -4.5
If x - 3 = 0, then x = 3

Our solutions are x = -4.5 and x = 3
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: GRE Math Challenge #3-Which of the following values of x   [#permalink] 21 Aug 2017, 09:20
Display posts from previous: Sort by