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

 It is currently 23 Oct 2019, 11:46

### 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 p(x) = kx^2 - kx - 12, for all values of x, what is the value of k?

Author Message
TAGS:

### Hide Tags

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
If p(x) = kx^2 - kx - 12, for all values of x, what is the value of k?  [#permalink]

### Show Tags

Updated on: 06 Feb 2019, 06:51
00:00

Difficulty:

55% (hard)

Question Stats:

51% (01:30) correct 49% (02:38) wrong based on 41 sessions

### HideShow timer Statistics

GMATH practice exercise (Quant Class 14)

If $$\,p\left( x \right) = k{x^2} - kx - 12\,$$ for all values of $$x$$, what is the value of the constant $$k$$ ?

(1) $$p\left( 3 \right) = 0$$

(2) $$p(x)$$ is divisible by $$x+2$$

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Originally posted by fskilnik on 06 Feb 2019, 06:48.
Last edited by Bunuel on 06 Feb 2019, 06:51, edited 1 time in total.
Renamed the topic.
Math Expert
Joined: 02 Aug 2009
Posts: 8023
Re: If p(x) = kx^2 - kx - 12, for all values of x, what is the value of k?  [#permalink]

### Show Tags

06 Feb 2019, 07:46
fskilnik wrote:
GMATH practice exercise (Quant Class 14)

If $$\,p\left( x \right) = k{x^2} - kx - 12\,$$ for all values of $$x$$, what is the value of the constant $$k$$ ?

(1) $$p\left( 3 \right) = 0$$

(2) $$p(x)$$ is divisible by $$x+2$$

At the very first look, you should be tempted towards D.

(1) $$p\left( 3 \right) = 0$$
Putting x as 3, the quadratic equation would convert into a linear equation with just one variable and so should be sufficient
Put x=3 so $$p\left( 3 \right) = 0.......\,p\left( 3 \right) =0= k{3^2} - k3 - 12\.......9k-3k=12...k=2$$
Sufficient

(2) $$p(x)$$ is divisible by $$x+2$$
This should tell you to look if the equation can be converted in terms of x+2, and divisible by x+2 means substituting x as -2, we should get the equation as 0
$$k{x^2} - kx - 12\,=k(-2)^2-(-2)k-12=0........4k+2k-12=0...k=2$$
Sufficient

D
_________________
Director
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: If p(x) = kx^2 - kx - 12, for all values of x, what is the value of k?  [#permalink]

### Show Tags

06 Feb 2019, 10:44
fskilnik wrote:
GMATH practice exercise (Quant Class 14)

If $$\,p\left( x \right) = k{x^2} - kx - 12\,$$ for all values of $$x$$, what is the value of the constant $$k$$ ?

(1) $$p\left( 3 \right) = 0$$

(2) $$p(x)$$ is divisible by $$x+2$$

From 1
when we substitute the value as 3 in the expression $$\,p\left( x \right) = k{x^2} - kx - 12\,$$
We get a definite value for k

From 2
x + 2 means that x =-2, will satisfy the expression, which can be equated to 0
Again we will get a definite value for k

D
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: If p(x) = kx^2 - kx - 12, for all values of x, what is the value of k?  [#permalink]

### Show Tags

07 Feb 2019, 07:05
fskilnik wrote:
GMATH practice exercise (Quant Class 14)

If the polynomial $$p$$ in the variable $$x$$ is defined by $$\,p\left( x \right) = k{x^2} - kx - 12$$, for all values of $$x$$, what is the value of the constant $$k$$ ?

(1) $$p\left( 3 \right) = 0$$

(2) The polynomial $$p$$ is divisible by $$x+2$$

Obs.: although the above version of the question stem is a bit "wordy", we believe it´s better (mathematically speaking).

$$p\left( x \right) = k{x^2} - kx - 12\,\,\,\,\,\left( * \right)$$

$$? = k$$

$$\left( 1 \right)\,\,\,0\,\, = \,\,p\left( 3 \right)\,\,\mathop = \limits^{\left( * \right)} \,\,k{\left( 3 \right)^2} - k\left( 3 \right) - 12\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,k\,\,{\rm{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.$$

$$\left( 2 \right)\,\,\,0 = p\left( { - 2} \right)\,\,\mathop = \limits^{\left( * \right)} \,\,k{\left( { - 2} \right)^2} - k\left( { - 2} \right) - 12\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,k\,\,{\rm{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}{\rm{.}}$$

The correct answer is therefore (D).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: If p(x) = kx^2 - kx - 12, for all values of x, what is the value of k?   [#permalink] 07 Feb 2019, 07:05
Display posts from previous: Sort by