Find all School-related info fast with the new School-Specific MBA Forum

It is currently 24 Oct 2014, 22:51

Close

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
Your Progress

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

As x increases from 165 to 166, which of the following must

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Manager
Manager
avatar
Joined: 02 Dec 2012
Posts: 178
Followers: 2

Kudos [?]: 431 [1] , given: 0

As x increases from 165 to 166, which of the following must [#permalink] New post 26 Dec 2012, 06:13
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

68% (01:50) correct 32% (00:59) wrong based on 295 sessions
As x increases from 165 to 166, which of the following must increase?

I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x)

(A) I only
(B) III only
(C) I and II
(D) I and III
(E) II and III
[Reveal] Spoiler: OA
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23409
Followers: 3613

Kudos [?]: 28933 [0], given: 2871

Re: As x increases from 165 to 166, which of the following must [#permalink] New post 26 Dec 2012, 06:16
Expert's post
Walkabout wrote:
As x increases from 165 to 166, which of the following must increase?

I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x)

(A) I only
(B) III only
(C) I and II
(D) I and III
(E) II and III


I. 2x - 5 --> x increases from 165 to 166 --> 2x increases --> 2x - 5 increases. Correct.

II. 1 - 1/x --> x increases from 165 to 166 --> 1/x decreases --> 1 -1/x increases. Correct.

III. 1/(x^2 - x) --> x increases from 165 to 166 --> x^2-x increases --> 1/(x^2 - x) decreases.

Answer: C.
_________________

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

2 KUDOS received
Intern
Intern
avatar
Joined: 11 Aug 2013
Posts: 34
Followers: 0

Kudos [?]: 8 [2] , given: 9

Re: As x increases from 165 to 166, which of the following must [#permalink] New post 12 Aug 2013, 19:31
2
This post received
KUDOS
For the first part, I simply plugged in a positive whole number for x, then I retested with a higher number than the number I chose originally for x,

X=5

2x-5=
2*5-5
10-5=5

X=6

2*6-5
12-5=7

X increases, and so does 2x-5

For the second problem, I used the same method, third problem, decreases by theory, no need to solve.
Senior Manager
Senior Manager
avatar
Joined: 10 Jul 2013
Posts: 343
Followers: 3

Kudos [?]: 121 [0], given: 102

Re: As x increases from 165 to 166, which of the following must [#permalink] New post 13 Aug 2013, 07:12
Walkabout wrote:
As x increases from 165 to 166, which of the following must increase?

I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x)

(A) I only
(B) III only
(C) I and II
(D) I and III
(E) II and III

...
I and II can be counted easily, both increases.
And III is 1/x(x-1)
Now, 1/(165×164) > 1/(166×165) , so it decreases as 165 turns to 166 .
so I and II = C (Answer)
_________________

Asif vai.....

Intern
Intern
User avatar
Joined: 15 Aug 2011
Posts: 19
Location: United States
Concentration: Marketing, Technology
GPA: 3.6
WE: Project Management (Computer Software)
Followers: 0

Kudos [?]: 11 [0], given: 44

GMAT ToolKit User
Re: As x increases from 165 to 166, which of the following must [#permalink] New post 13 Aug 2013, 09:40
Walkabout wrote:
As x increases from 165 to 166, which of the following must increase?

I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x)

(A) I only
(B) III only
(C) I and II
(D) I and III
(E) II and III


The max difference b/w 165 and 166 is '1' and the min value can be 0.000000000000000000001 but for our convenience we shall choose 0.1
Equation 1 ==> for min value of 0.1, the value is 2(0.1) - 5 = -4.8

for max value of 1, 2(1)-5=-3
so the values are increasing from -4.8 to -3

similary submit the values 0.1 and 1 and we notice that the value increases from -9 to 0 ==> equation 2 is also increasing

for double confirmation substitute the values of 0.1 and 1 in equation 3.
for min value of x=0.1, the value is 1/(0.01-0.1)=-1/0.09
for max value of 1, the value is 'infinite' ... hence we dont count this.

So equations 1 & 2 are increasing. This is the answer
_________________

"Hit KUDOS if you like my explanation"

Intern
Intern
avatar
Joined: 22 Oct 2014
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 4

As x increases from 165 to 166, which of the following must [#permalink] New post 22 Oct 2014, 06:26
selfishmofo wrote:
For the first part, I simply plugged in a positive whole number for x, then I retested with a higher number than the number I chose originally for x,
.....
......
For the second problem, I used the same method, third problem, decreases by theory, no need to solve.


I have done the first two in the same way you did, but third one took time. Can you please connect or explain the theory that helped you?
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23409
Followers: 3613

Kudos [?]: 28933 [1] , given: 2871

Re: As x increases from 165 to 166, which of the following must [#permalink] New post 22 Oct 2014, 06:49
1
This post received
KUDOS
Expert's post
appleid wrote:
selfishmofo wrote:
For the first part, I simply plugged in a positive whole number for x, then I retested with a higher number than the number I chose originally for x,
.....
......
For the second problem, I used the same method, third problem, decreases by theory, no need to solve.


I have done the first two in the same way you did, but third one took time. Can you please connect or explain the theory that helped you?


x^2 - x is an equation of upward parabola, intercepting the x axis at 0 and 1.
Attachment:
graph.png
graph.png [ 7.08 KiB | Viewed 152 times ]
So, far away from the roots, the values of the function (x^2 - x) are increasing as x increases. Therefore 1/(x^2 - x) decreases.

Similar questions to practice:
as-x-increases-from-209-to-210-which-of-the-following-must-128561.html
as-j-increases-from-135-to-137010.html
as-y-increases-from-y-247-to-y-248-which-of-the-follow-161679.html

Hope it helps.
_________________

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 22 Oct 2014
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 4

As x increases from 165 to 166, which of the following must [#permalink] New post 24 Oct 2014, 03:11
Bunuel wrote:
appleid wrote:
selfishmofo wrote:
For the first part, I simply plugged in a positive whole number for x, then I retested with a higher number than the number I chose originally for x,
.....
......
For the second problem, I used the same method, third problem, decreases by theory, no need to solve.


I have done the first two in the same way you did, but third one took time. Can you please connect or explain the theory that helped you?


x^2 - x is an equation of upward parabola, intercepting the x axis at 0 and 1.
Attachment:
graph.png
So, far away from the roots, the values of the function (x^2 - x) are increasing as x increases. Therefore 1/(x^2 - x) decreases.

Similar questions to practice:
....
Hope it helps.


Thank you! However, I did understand the value of x^2-x will always goes up, but I am not getting the basic theory (or relevant foundation/topic) behind it. Could you please suggest me any topic which will teach me this from ground level?
As x increases from 165 to 166, which of the following must   [#permalink] 24 Oct 2014, 03:11
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic If √x = x, then which of the following must be true? emmak 3 21 Mar 2013, 23:56
Experts publish their posts in the topic As x increases from 209 to 210, which of the following must enigma123 2 04 Mar 2012, 09:33
1 Experts publish their posts in the topic If x/|x|, which of the following must be true for all praveenvino 2 15 Jan 2011, 11:44
if X ____ = X, Which of the following must be true for all arjtryarjtry 8 26 Aug 2008, 09:41
As x increase from 165 to 166, which of the following must jet1445 2 20 Feb 2007, 09:37
Display posts from previous: Sort by

As x increases from 165 to 166, which of the following must

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.