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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] New post 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] New post 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.

Answer: D.

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] New post 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] New post 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
xy-plane-71492.html?hilit=solving%20quadratic#p841486

Hope it helps.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If k is an integer, what is the value of k? [#permalink] New post 20 Aug 2013, 14:34
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Re: If k is an integer, what is the value of k? [#permalink] New post 04 Sep 2014, 07:09
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Re: If k is an integer, what is the value of k? [#permalink] New post 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.

Answer: D.

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] New post 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.

Answer: D.

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:
Solving Quadratic Inequalities - Graphic Approach: solving-quadratic-inequalities-graphic-approach-170528.html
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
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: If k is an integer, what is the value of k?   [#permalink] 05 Sep 2014, 04:03
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