GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2018, 17:44

### 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 5 - 6/x = x, then x has how many possible values?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 177
If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

29 Dec 2012, 07:07
4
11
00:00

Difficulty:

5% (low)

Question Stats:

87% (00:54) correct 13% (01:03) wrong based on 1538 sessions

### HideShow timer Statistics

If $$5 - \frac{6}{x} = x$$, then x has how many possible values?

(A) None
(B) One
(C) Two
(D) A finite number greater than two
(E) An infinite number
Math Expert
Joined: 02 Sep 2009
Posts: 50002
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

29 Dec 2012, 07:09
2
1
If 5 - 6/x = x, then x has how many possible values?

(A) None
(B) One
(C) Two
(D) A finite number greater than two
(E) An infinite number

$$5 - \frac{6}{x} = x$$;

$$\frac{5x - 6}{x} = x$$;

$$5x -6 = x^2$$;

$$(x-3)(x-2)=0$$;

$$x=3$$ or $$x=2$$.

_________________
Intern
Joined: 17 Nov 2012
Posts: 17
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

01 Jan 2013, 11:57
Bunuel wrote:
If 5 - 6/x = x, then x has how many possible values?

(A) None
(B) One
(C) Two
(D) A finite number greater than two
(E) An infinite number

5 - 6/x = x --> (5x - 6)/x = x --> 5x -6 = x^2 --> (x-3)(x-2)=0 --> x=3 or x=2.

That's cool Bunuel.
I can approach this kind of equation with Delta method. However I'm very interested in your factoring method.
Would you please share how you quickly factor the equation x^2 - 5x + 6 = 0 into (x-3)(x-2) = 0. Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 50002
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

02 Jan 2013, 04:51
2
akhandamandala wrote:
Bunuel wrote:
If 5 - 6/x = x, then x has how many possible values?

(A) None
(B) One
(C) Two
(D) A finite number greater than two
(E) An infinite number

5 - 6/x = x --> (5x - 6)/x = x --> 5x -6 = x^2 --> (x-3)(x-2)=0 --> x=3 or x=2.

That's cool Bunuel.
I can approach this kind of equation with Delta method. However I'm very interested in your factoring method.
Would you please share how you quickly factor the equation x^2 - 5x + 6 = 0 into (x-3)(x-2) = 0. Thanks

Hope it helps.
_________________
Intern
Joined: 17 Nov 2012
Posts: 17
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

02 Jan 2013, 16:30
that's great, it helps a lot. I may save 30 seconds from this method
Intern
Joined: 10 Sep 2013
Posts: 2
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

23 Sep 2013, 14:27
2
1
Calculate b^2 and 4ac

If b^2 > 4ac then 2 solutions
If b^2 = 4ac then 1 solution
If b^2 < 4ac then undefined

I think this method will also handle cases if GMAT choose to provide equations which can't be easily factored.
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1829
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

02 Oct 2014, 03:30
2
1
If 5 - 6/x = x, then x has how many possible values?

(A) None
(B) One
(C) Two
(D) A finite number greater than two
(E) An infinite number

$$5 - \frac{6}{x} = x$$

$$x^2 - 5x + 6 = 0$$

This is a proper quadratic equation in the format $$ax^2 + bx + c = 0$$

This will provide 2 answers. No calculation required

_________________

Kindly press "+1 Kudos" to appreciate

Intern
Joined: 30 Mar 2015
Posts: 5
Location: United States
Schools: HBS '18, Stanford '18
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

05 Apr 2015, 09:47
PareshGmat wrote:
If 5 - 6/x = x, then x has how many possible values?

(A) None
(B) One
(C) Two
(D) A finite number greater than two
(E) An infinite number

$$5 - \frac{6}{x} = x$$

$$x^2 - 5x + 6 = 0$$

This is a proper quadratic equation in the format $$ax^2 + bx + c = 0$$

This will provide 2 answers. No calculation required

You could still not have exactly two answers, depending on what the discriminant gives you, right? As I understand it: get the quadratic equation, calculate the discriminant, then determine how many possible answers you have. (In this case the answer is still C, two answers, but it's not due to the quoted reasoning).

Thoughts?
Intern
Joined: 04 Mar 2014
Posts: 10
Concentration: Marketing, General Management
GMAT 1: 680 Q50 V32
GPA: 3.9
WE: Information Technology (Investment Banking)
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

24 Apr 2016, 10:46
Bunuel wrote:
If 5 - 6/x = x, then x has how many possible values?

(A) None
(B) One
(C) Two
(D) A finite number greater than two
(E) An infinite number

5 - 6/x = x --> (5x - 6)/x = x --> 5x -6 = x^2 --> (x-3)(x-2)=0 --> x=3 or x=2.

Bunnel - Can't there be non-integer values that can satisfy this equation ? I don't think the question mentions that x has to be an integer. Please advise.
Math Expert
Joined: 02 Sep 2009
Posts: 50002
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

24 Apr 2016, 11:24
Keysersoze10 wrote:
Bunuel wrote:
If 5 - 6/x = x, then x has how many possible values?

(A) None
(B) One
(C) Two
(D) A finite number greater than two
(E) An infinite number

5 - 6/x = x --> (5x - 6)/x = x --> 5x -6 = x^2 --> (x-3)(x-2)=0 --> x=3 or x=2.

Bunnel - Can't there be non-integer values that can satisfy this equation ? I don't think the question mentions that x has to be an integer. Please advise.

We solved 5 - 6/x = x and got two solutions: 3 and 2. So, the answer to your question is no, this equation does not have any other solution, integer or non-integer.
_________________
Intern
Joined: 04 Mar 2014
Posts: 10
Concentration: Marketing, General Management
GMAT 1: 680 Q50 V32
GPA: 3.9
WE: Information Technology (Investment Banking)
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

24 Apr 2016, 11:39
Bunuel wrote:
Keysersoze10 wrote:
Bunuel wrote:
If 5 - 6/x = x, then x has how many possible values?

(A) None
(B) One
(C) Two
(D) A finite number greater than two
(E) An infinite number

5 - 6/x = x --> (5x - 6)/x = x --> 5x -6 = x^2 --> (x-3)(x-2)=0 --> x=3 or x=2.

Bunnel - Can't there be non-integer values that can satisfy this equation ? I don't think the question mentions that x has to be an integer. Please advise.

We solved 5 - 6/x = x and got two solutions: 3 and 2. So, the answer to your question is no, this equation does not have any other solution, integer or non-integer.

Thanks Bunnel. I might be overthinking, but if we draw a parabola for the above equation wont there be infinite number of points on that parabola which would satisfy the above equation ?
Math Expert
Joined: 02 Sep 2009
Posts: 50002
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

24 Apr 2016, 11:50
1
Keysersoze10 wrote:
Thanks Bunnel. I might be overthinking, but if we draw a parabola for the above equation wont there be infinite number of points on that parabola which would satisfy the above equation ?

No. There will be only TWO. There is a clear solution given above, which gives TWO values of x satisfying the equation.
_________________
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4094
Location: India
GPA: 3.5
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

24 Apr 2016, 11:56
1
Keysersoze10 wrote:

We solved 5 - 6/x = x and got two solutions: 3 and 2. So, the answer to your question is no, this equation does not have any other solution, integer or non-integer.

Thanks Bunnel. I might be overthinking, but if we draw a parabola for the above equation wont there be infinite number of points on that parabola which would satisfy the above equation ?

GMAT Quants is simple, keep it simple !!

For scoring 700+ and a good score in QA knowledge of Quadratic equation is more than sufficient, don't go into such depths , GMAT will seldom go into such depths....

Regards

AbhisheK
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Current Student
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

Updated on: 24 Apr 2016, 12:48
1
Keysersoze10 wrote:

Thanks Bunnel. I might be overthinking, but if we draw a parabola for the above equation wont there be infinite number of points on that parabola which would satisfy the above equation ?

If you rearrange the given equation, 5-6/x = x --> (5-x) = 6/x means that you have to find points of intersection for the line y=5-x and the hyperbola y=6/x (do note that hyperbolas are asymptotic to the coordinate axes). Clearly, the line y=5-x can only intersect the hyperbola at 2 and only 2 points (refer to the image below):

Attachment:

2016-04-24_15-45-43.jpg [ 43.11 KiB | Viewed 11127 times ]

Thus you get 2 solutions.

FYI, knowledge of hyperbolas is not in GMAT's scope.

Originally posted by ENGRTOMBA2018 on 24 Apr 2016, 12:26.
Last edited by ENGRTOMBA2018 on 24 Apr 2016, 12:48, edited 2 times in total.
Edited the solution.
Current Student
Joined: 23 Mar 2016
Posts: 31
Schools: Tulane '18 (M)
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

28 Apr 2016, 19:31
1
5 - (6/x) = x
5=x + (6/x)
5 = (x^2+6)/x
5x = x^2+6 <<<<< you can really stop here if you recognize this is a factorization problem and not a perfect square
0 = x^2 - 5x + 6
0 = (x-3)(x-2)
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

15 Jul 2016, 04:51
If 5 - 6/x = x, then x has how many possible values?

(A) None
(B) One
(C) Two
(D) A finite number greater than two
(E) An infinite number

We need to simplify the equation 5 – 6/x = x. We start by multiplying the entire equation by x and we obtain:

5x – 6 = x^2

x^2 – 5x + 6 = 0

(x – 3)(x – 2) = 0

x = 3 or x = 2.

We see that x has 2 possible values.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 29 Aug 2015
Posts: 16
GMAT 1: 550 Q44 V22
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

14 May 2017, 03:09
As its a quadric equation, there can be 2 values of x. So do you really to calculate or can select answer 2 without calculating what is the value of x?
Math Expert
Joined: 02 Sep 2009
Posts: 50002
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

14 May 2017, 03:18
sisirkant wrote:
As its a quadric equation, there can be 2 values of x. So do you really to calculate or can select answer 2 without calculating what is the value of x?

Quadratic equation can have 0, 1 or two roots, so you should do some additional math here.
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12676
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

17 Mar 2018, 12:03
1
Hi All,

You'll have to do a bit of algebra to deduce the number of solutions to this equation…

5 - (6/x) = x

First, multiply everything by x…

5x - 6 = x^2

Now, move everything "to the right"….

0 = x^2 - 5x + 6

You can now factor this into two terms…

0 = (x -2)(x - 3)

And answer the question… There are 2 solutions

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

# 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/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Intern
Joined: 13 Sep 2016
Posts: 21
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

### Show Tags

28 Mar 2018, 10:43
Bunuel wrote:
If 5 - 6/x = x, then x has how many possible values?

(A) None
(B) One
(C) Two
(D) A finite number greater than two
(E) An infinite number

$$5 - \frac{6}{x} = x$$;

$$\frac{5x - 6}{x} = x$$;

$$5x -6 = x^2$$;

$$(x-3)(x-2)=0$$;

$$x=3$$ or $$x=2$$.

Well i wanted to reconfirm , we eliminated the possibility of x=0 , because equating x=0 in the equation doesn't solve it , Right ??
Re: If 5 - 6/x = x, then x has how many possible values? &nbs [#permalink] 28 Mar 2018, 10:43

Go to page    1   2    Next  [ 21 posts ]

Display posts from previous: Sort by