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

 It is currently 12 Dec 2019, 01:26 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # By what factor should the smaller root of the equation 6x^2 -13x + 6 =

Author Message
TAGS:

### Hide Tags

Director  V
Joined: 18 Feb 2019
Posts: 607
Location: India
GMAT 1: 460 Q42 V13 GPA: 3.6
By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

### Show Tags 00:00

Difficulty:   55% (hard)

Question Stats: 58% (01:49) correct 42% (01:51) wrong based on 67 sessions

### HideShow timer Statistics

By what factor should the smaller root of the equation 6x^2 -13x + 6 = 0 increase so that it equals larger root of the equation.

A. 4/9
B. 5/6
C. 6/5
D. 2
E. 9/4
Manager  S
Joined: 23 Apr 2018
Posts: 162
By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

### Show Tags

2
1
quote="Luca1111111111111"]
nick1816 wrote:
6x^2 -13x + 6 = 0
(3x-2)(2x-3)=0
Smaller root=2/3
Larger root=3/2
2/3*k=3/2
k=9/4

I find it difficult to transfrom 6x^2 -13x + 6 = 0 into (3x-2)(2x-3)=0
Is there a trick?[/quote]

Luca1111111111111
Hi there, no trick at all
I used to find it challenging at once

its like normal quadratic only, the 6 with X^2 leads to confusion for some

here is how you can do it-
In the equation
aX^2 + bX + c = 0
a= 6 and c = 6 as you can see
we have to multiply these roots
AC multiplied is what the product of the equation is, and b is the sum of roots (which is -13 here)
for AC = 36,
there is 9 and 4 which multiplied gives 36, and will give us the sum of 9+4=13, but we don't need +13 here

also -9 and -4 will give the same result, 36, and will give us -13 too, the sum we need. voila!

Therefore the equation can be written as
6x^2-13x+6 = 0
6x^2 - 9x - 4x +6 = 0
now take common factors out
3x(2x-3) -2 (2x-3) = 0
(3x-2) = 0 and (2x-3) = 0
x = 3/2 and 2/3
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4834
Location: India
GPA: 3.5
Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

### Show Tags

1
Luca1111111111111 wrote:
nick1816 wrote:
6x^2 -13x + 6 = 0
(3x-2)(2x-3)=0
Smaller root=2/3
Larger root=3/2
2/3*k=3/2
k=9/4

I find it difficult to transfrom 6x^2 -13x + 6 = 0 into (3x-2)(2x-3)=0
Is there a trick?

Yes there certainly is a formula for solving this , $$x$$ = $$\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$ if $$b^2>4ac$$
_________________
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 )
VP  V
Joined: 19 Oct 2018
Posts: 1172
Location: India
Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

### Show Tags

6x^2 -13x + 6 = 0
(3x-2)(2x-3)=0
Smaller root=2/3
Larger root=3/2
2/3*k=3/2
k=9/4
Manager  S
Joined: 20 Apr 2019
Posts: 113
Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

### Show Tags

nick1816 wrote:
6x^2 -13x + 6 = 0
(3x-2)(2x-3)=0
Smaller root=2/3
Larger root=3/2
2/3*k=3/2
k=9/4

I find it difficult to transfrom 6x^2 -13x + 6 = 0 into (3x-2)(2x-3)=0
Is there a trick?
Manager  S
Joined: 23 Apr 2018
Posts: 162
Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

### Show Tags

nick1816 wrote:
6x^2 -13x + 6 = 0
(3x-2)(2x-3)=0
Smaller root=2/3
Larger root=3/2
2/3*k=3/2
k=9/4

if I do it this way
2/3+x = 3/2
x gives 5/6 (b) in that case

Why don't we add in order to increase it ? and multiply instead ?
What part of language I missed ?
ISB School Moderator G
Joined: 08 Dec 2013
Posts: 619
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '21
GMAT 1: 630 Q47 V30 WE: Operations (Non-Profit and Government)
Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

### Show Tags

kiran120680 wrote:
By what factor should the smaller root of the equation 6x^2 -13x + 6 = 0 increase so that it equals larger root of the equation.

A. 4/9
B. 5/6
C. 6/5
D. 2
E. 9/4

Solve the quadratic equation to find:

x= 3/2 and 2/3
Larger root = k * Smaller root, to find k
3/2 = k* (2/3)
9/4 = k
ISB School Moderator G
Joined: 08 Dec 2013
Posts: 619
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '21
GMAT 1: 630 Q47 V30 WE: Operations (Non-Profit and Government)
Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

### Show Tags

1
Shrey9 wrote:
nick1816 wrote:
6x^2 -13x + 6 = 0
(3x-2)(2x-3)=0
Smaller root=2/3
Larger root=3/2
2/3*k=3/2
k=9/4

if I do it this way
2/3+x = 3/2
x gives 5/6 (b) in that case

Why don't we add in order to increase it ? and multiply instead ?
What part of language I missed ?

Shrey9
Increase/reduce by a factor means multiplied/divided.

GMAT also plays with words like increase to and increase by...
Manager  S
Joined: 20 Apr 2019
Posts: 113
Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

### Show Tags

Shrey9 wrote:
quote="Luca1111111111111"]
nick1816 wrote:
6x^2 -13x + 6 = 0
(3x-2)(2x-3)=0
Smaller root=2/3
Larger root=3/2
2/3*k=3/2
k=9/4

I find it difficult to transfrom 6x^2 -13x + 6 = 0 into (3x-2)(2x-3)=0
Is there a trick?

Luca1111111111111
Hi there, no trick at all
I used to find it challenging at once

its like normal quadratic only, the 6 with X^2 leads to confusion for some

here is how you can do it-
In the equation
aX^2 + bX + c = 0
a= 6 and c = 6 as you can see
we have to multiply these roots
AC multiplied is what the product of the equation is, and b is the sum of roots (which is -13 here)
for AC = 36,
there is 9 and 4 which multiplied gives 36, and will give us the sum of 9+4=13, but we don't need +13 here

also -9 and -4 will give the same result, 36, and will give us -13 too, the sum we need. voila!

Therefore the equation can be written as
6x^2-13x+6 = 0
6x^2 - 9x - 4x +6 = 0
now take common factors out
3x(2x-3) -2 (2x-3) = 0
(3x-2) = 0 and (2x-3) = 0
x = 3/2 and 2/3[/quote]

Thank you so much!!
Manager  S
Joined: 23 Apr 2018
Posts: 162
Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

### Show Tags

Abhishek009 wrote:
Luca1111111111111 wrote:
nick1816 wrote:
6x^2 -13x + 6 = 0
(3x-2)(2x-3)=0
Smaller root=2/3
Larger root=3/2
2/3*k=3/2
k=9/4

I find it difficult to transfrom 6x^2 -13x + 6 = 0 into (3x-2)(2x-3)=0
Is there a trick?

Yes there certainly is a formula for solving this , $$x$$ = $$\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$ if $$b^2>4ac$$

Can you solve using this formula as an example ? Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =   [#permalink] 02 Jun 2019, 13:28
Display posts from previous: Sort by

# By what factor should the smaller root of the equation 6x^2 -13x + 6 =  