If k is an integer, what is the value of k? : GMAT Data Sufficiency (DS)
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# If k is an integer, what is the value of k?

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If k is an integer, what is the value of k? [#permalink]

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23 Jan 2011, 02:13
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If k is an integer, what is the value of k?

(1) (k – 1)(k – 3) < 0
(2) (k – 5)(k – 1)(k – 3)(k – 6) < 0
[Reveal] Spoiler: OA
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Re: If k is an integer, what is the value of k? [#permalink]

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23 Jan 2011, 02:20
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MichelleSavina wrote:
Q) If k is an integer, what is the value of k?
(1) (k – 1)(k – 3) < 0
(2) (k – 5)(k – 1)(k – 3)(k – 6) < 0

If k is an integer, what is the value of k?

(1) (k – 1)(k – 3) < 0 --> 1<k<3, as given that k is an integer then k=2. Sufficient.

(2) (k – 5)(k – 1)(k – 3)(k – 6) < 0 --> 5<k<6 or 1<k<3, again as given that k is an integer then k=2 (only integer IN this ranges). Sufficient.

Check for more here: x2-4x-94661.html#p731476 or here: inequalities-trick-91482.html
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Re: If k is an integer, what is the value of k? [#permalink]

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16 Oct 2012, 22:59
Hi Bunuel,

I represented these points on a graph and drew the crests and troughs to check which ranges we need to consider the point lies.
I was confused if 3<x<5 will also be considered.
Can you please share how you quickly figured out the appropriate ranges here.

Sorry if this is a silly one
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Re: If k is an integer, what is the value of k? [#permalink]

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17 Oct 2012, 04:08
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GMATBaumgartner wrote:
Hi Bunuel,

I represented these points on a graph and drew the crests and troughs to check which ranges we need to consider the point lies.
I was confused if 3<x<5 will also be considered.
Can you please share how you quickly figured out the appropriate ranges here.

Sorry if this is a silly one

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.
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Re: If k is an integer, what is the value of k? [#permalink]

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20 Aug 2013, 14:34
Bumping for review and further discussion.
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Re: If k is an integer, what is the value of k? [#permalink]

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04 Sep 2014, 07:09
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If k is an integer, what is the value of k? [#permalink]

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04 Sep 2014, 17:46
Bunuel wrote:
MichelleSavina wrote:
Q) If k is an integer, what is the value of k?
(1) (k – 1)(k – 3) < 0
(2) (k – 5)(k – 1)(k – 3)(k – 6) < 0

If k is an integer, what is the value of k?

(1) (k – 1)(k – 3) < 0 --> 1<k<3, as given that k is an integer then k=2. Sufficient.

(2) (k – 5)(k – 1)(k – 3)(k – 6) < 0 --> 5<k<6 or 1<k<3, again as given that k is an integer then k=2 (only integer IN this ranges). Sufficient.

Check for more here: x2-4x-94661.html#p731476 or here: inequalities-trick-91482.html

I'm a little confused. How did k=1 & k=3 < 0 become 1<k<3? Is the <0 just there for me to set up the inequality? Thanks.
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Re: If k is an integer, what is the value of k? [#permalink]

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05 Sep 2014, 04:03
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xserenity114 wrote:
Bunuel wrote:
MichelleSavina wrote:
Q) If k is an integer, what is the value of k?
(1) (k – 1)(k – 3) < 0
(2) (k – 5)(k – 1)(k – 3)(k – 6) < 0

If k is an integer, what is the value of k?

(1) (k – 1)(k – 3) < 0 --> 1<k<3, as given that k is an integer then k=2. Sufficient.

(2) (k – 5)(k – 1)(k – 3)(k – 6) < 0 --> 5<k<6 or 1<k<3, again as given that k is an integer then k=2 (only integer IN this ranges). Sufficient.

Check for more here: x2-4x-94661.html#p731476 or here: inequalities-trick-91482.html

I'm a little confused. How did k=1 & k=3 < 0 become 1<k<3? Is the <0 just there for me to set up the inequality? Thanks.

We don't have that k=1 or k=3, we have an inequality which says that (k – 1)(k – 3) < 0. This inequality means that 1 < k < 3. I think that you should brush-up fundamentals on inequalities. Please go through the following topics:

Theory on Inequalities:
Inequality tips: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1379270

inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html
everything-is-less-than-zero-108884.html
graphic-approach-to-problems-with-inequalities-68037.html
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Re: If k is an integer, what is the value of k? [#permalink]

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30 Jul 2015, 03:07
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I N T E G E R ! ! ! ! !

when the question state it clearly - i a real number
when it doesnt, i consider integers.

hope this little steam release will help me notice that in the future.
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Re: If k is an integer, what is the value of k? [#permalink]

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03 Jul 2016, 00:58
can somebody help with why 4 is not considered in the range 3<k<5??
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03 Jul 2016, 01:01
Sorry I got it.Need to check the value for the inequality after identify the Critical keypoints:)
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Re: If k is an integer, what is the value of k? [#permalink]

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23 Aug 2016, 01:00
If k is an integer, what is the value of k?

(1) (k – 1)(k – 3) < 0
(2) (k – 5)(k – 1)(k – 3)(k – 6) < 0

K is between 1& 3 only integer is 2.

(k – 5)(k – 1)(k – 3)(k – 6) < 0
so K = between 1 &3 or 5&6

Only integer 2. so D
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Re: If k is an integer, what is the value of k? [#permalink]

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29 Sep 2016, 07:49
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MichelleSavina wrote:
If k is an integer, what is the value of k?

(1) (k – 1)(k – 3) < 0
(2) (k – 5)(k – 1)(k – 3)(k – 6) < 0

Statement 1: (k – 1)(k – 3) < 0
Let's make a few observations.

First, k is an integer.
Notice that k=1 is not a solution to the given inequality, because if we replace k with 1, we get 0<0, which isn't true.
For the same reason, k=3 is not a solution to the given inequality,

What about k=2? We'll plug it in to get:
(k – 1)(k – 3) =(2 – 1)(2 – 3)
Important: We need not evaluate this. All we need to do is determine whether each piece is positive or negative
So, (2 – 1)(2 – 3) = (positive)(negative) = (negative) < 0
So, k=2 is one possible value for k.

Now notice what happens when we try ANY number greater than 3 for a possible value of k. To do this, we'll use the following notation: biggerthan3
We get: (k – 1)(k – 3) = (biggerthan3 – 1)(biggerthan3 – 3) = (positive)(positive) = positive
However, the given inequality says: (k – 1)(k – 3) < 0
So, k cannot be greater than 3.

Is it possible for k to be less than 1?
Let's try it.
(k – 1)(k – 3) = (lessthan1 – 1)(lessthan1 – 3) = (negative)(negative) = positive
However, the given inequality says: (k – 1)(k – 3) < 0
So, k cannot be less than 1.

We've now ruled out every possible integer value of k EXCEPT k=2
So, k must equal 2, which means statement 1 IS SUFFICIENT

Statement 2: (k – 5)(k – 1)(k – 3)(k – 6) < 0
In other words, (k – 5)(k – 1)(k – 3)(k – 6) is negative.
We can see that k = 5, 1, 3 and 6 are NOT possible solutions.
Plug it in to get: (k – 5)(k – 1)(k – 3)(k – 6) = (2 – 5)(2 – 1)(2 – 3)(2 – 6) = (negative)(positive)(negative)(negative) = negative
Great, k=2 is one possible value of k

Plug it in to get: (k – 5)(k – 1)(k – 3)(k – 6) = (4 – 5)(4 – 1)(4 – 3)(4 – 6) = (negative)(positive)(positive)(negative) = positive
No, k=4 is not a possible value of k

Plug it in to get: (lessthan1 – 5)(lessthan1 – 1)(lessthan1 – 3)(lessthan1 – 6) = (negative)(negative)(negative)(negative) = positive
No, k=lessthan1 is not a possible value of k

Plug it in to get: (greaterthan6 – 5)(greaterthan6 – 1)(greaterthan6 – 3)(greaterthan6 – 6) = (positive)(positive)(positive)(positive) = positive
No, k=greaterthan6 is not a possible value of k

We've now ruled out every possible integer value of k EXCEPT k=2
So, k must equal 2, which means statement 2 IS SUFFICIENT

[Reveal] Spoiler:
D

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Re: If k is an integer, what is the value of k? [#permalink]

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29 Sep 2016, 10:26
Statement 1 k cannot equal 1 or 3 since it make the equation =0 and we know its <0 and cannot be "-" or else the equation>0 so the only number that works here is sufficient
Statement 2 k cannot be 5,3,6, or 1. and cannot be negative. only works with k=2

D
Re: If k is an integer, what is the value of k?   [#permalink] 29 Sep 2016, 10:26
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