It is currently 12 Dec 2017, 14:00

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

As x increases from 209 to 210, which of the following must

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Director
Director
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 531

Kudos [?]: 4312 [1], given: 217

Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
As x increases from 209 to 210, which of the following must [#permalink]

Show Tags

New post 04 Mar 2012, 09:33
1
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

67% (00:59) correct 33% (00:56) wrong based on 279 sessions

HideShow timer Statistics

As x increases from 209 to 210, which of the following must increase?

I. \(3x - 4\)
II. \(\frac{x - 1}{x}\)
III. \(x - x^2\)

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

How come the answer is C guys?
[Reveal] Spoiler: OA

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730


Last edited by enigma123 on 04 Mar 2012, 13:25, edited 1 time in total.

Kudos [?]: 4312 [1], given: 217

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42571

Kudos [?]: 135384 [0], given: 12691

Re: Must increase [#permalink]

Show Tags

New post 04 Mar 2012, 15:30
Expert's post
1
This post was
BOOKMARKED
enigma123 wrote:
As x increases from 209 to 210, which of the following must increase?

I. \(3x - 4\)
II. \(\frac{x - 1}{x}\)
III. \(x - x^2\)

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

How come the answer is C guys?


I. \(3x - 4\) --> \(x\) increases from 209 to 210 --> \(3x\) increases --> \(3x-4\) increases. Correct.

II. \(\frac{x - 1}{x}\) --> \(\frac{209-1}{209}=\frac{208}{209}\) which is less than \(\frac{210-1}{210}=\frac{209}{210}\), (the same way as 1/2 is less than 2/3). Correct.

III. \(x - x^2\) --> \(x\) increases from 209 to 210 --> \(x^2\) increases more than \(x\) --> \(x - x^2\) decreases.

Answer: C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135384 [0], given: 12691

Intern
Intern
User avatar
B
Joined: 12 Jun 2016
Posts: 27

Kudos [?]: 10 [0], given: 18

Location: India
Concentration: Entrepreneurship, Finance
GPA: 3.76
WE: Information Technology (Computer Software)
Re: As x increases from 209 to 210, which of the following must [#permalink]

Show Tags

New post 25 Jul 2016, 21:18
1
This post was
BOOKMARKED
When x increases from 209 to 210.

I. 3x-4 will also increase as x is increasing.
II.((x-1)/x) can be written as 1-1/x.
As x increases, 1/x will decrease. That means, lesser value will be subtracted from 1 now. Hence, Increases.
III. As x increases, x^2 increase faster than x. Hence, x-x^2 will decrease.

So, Answer should be C.

Kudos [?]: 10 [0], given: 18

Manager
Manager
avatar
B
Joined: 28 Apr 2016
Posts: 100

Kudos [?]: 7 [0], given: 79

Re: As x increases from 209 to 210, which of the following must [#permalink]

Show Tags

New post 18 Aug 2016, 01:39
What's the best way to compare such large fractions?

Bunuel wrote:
enigma123 wrote:
As x increases from 209 to 210, which of the following must increase?



II. \(\frac{x - 1}{x}\) --> \(\frac{209-1}{209}=\frac{208}{209}\) which is less than \(\frac{210-1}{210}=\frac{209}{210}\), (the same way as 1/2 is less than 2/3). Correct.

Answer: C.

Kudos [?]: 7 [0], given: 79

Expert Post
3 KUDOS received
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 755

Kudos [?]: 2237 [3], given: 123

Re: As x increases from 209 to 210, which of the following must [#permalink]

Show Tags

New post 18 Aug 2016, 02:05
3
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
ameyaprabhu wrote:
What's the best way to compare such large fractions?

Bunuel wrote:
enigma123 wrote:
As x increases from 209 to 210, which of the following must increase?



II. \(\frac{x - 1}{x}\) --> \(\frac{209-1}{209}=\frac{208}{209}\) which is less than \(\frac{210-1}{210}=\frac{209}{210}\), (the same way as 1/2 is less than 2/3). Correct.

Answer: C.



Hey ameyaprabhu,

To understand the nature of a fraction, you should first simplify the fraction as far as possible.

So, in this case you can rewrite \(\frac{(x-1)}{x} = \frac{x}{x} – \frac{1}{x} = 1 – \frac{1}{x}.\)

Now, from this simplified version, you can see that x is in the denominator. So, as x increases, the value of \(\frac{1}{x}\) would decrease. Since \(\frac{1}{x}\) is being subtracted from 1, the decrease in the value of \(\frac{1}{x}\) would result in increase in value of the overall fraction.

For example: consider x = 2. So, we have \(1 - \frac{1}{x} = 1 - \frac{1}{2} = \frac{1}{2}\). Now, when x = 3, we have \(1 - \frac{1}{x} = 1 - \frac{1}{3} = \frac{2}{3}\). So, as x increases from 2 to 3, the value of the fraction \(1 - \frac{1}{x}\) also increases from \(\frac{1}{2}\) to \(\frac{2}{3}\).


So, you can now confidently say that as x increases from 209 to 210, the value of \(\frac{(x-1)}{x}\) would increase as well.

Hope this helps. :)

Regards,
Harsh
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Kudos [?]: 2237 [3], given: 123

1 KUDOS received
Manager
Manager
User avatar
B
Joined: 15 Mar 2015
Posts: 113

Kudos [?]: 29 [1], given: 7

Re: As x increases from 209 to 210, which of the following must [#permalink]

Show Tags

New post 18 Aug 2016, 05:44
1
This post received
KUDOS
I. The answer clearly will increase as a negative constant stays the same (-4) whereas the variable with a positive constant(3x) increases.

II.
Any proper and improper fraction that gets a number added to both the numerator and the denominator gets closer to 1.
100/101 is closer to 1 than 99/100.
100/99 is further away from 1 than 101/100.
As the fraction (x-1)/x is less than 1 it will increase. (note how the question would change if II. stated (x+1)/x In that case the fraction would decrease(towards 1).

III.
The positive part (x) gets +1 whereas the negative part -(x^2) receives an exponential increase larger than 1.

I and II must increase. Answer choice: C.
_________________

I love being wrong. An incorrect answer offers an extraordinary opportunity to improve.

Kudos [?]: 29 [1], given: 7

Manager
Manager
avatar
B
Joined: 03 May 2014
Posts: 166

Kudos [?]: 17 [0], given: 126

Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: As x increases from 209 to 210, which of the following must [#permalink]

Show Tags

New post 11 Oct 2017, 22:06
ameyaprabhu wrote:
What's the best way to compare such large fractions?

Bunuel wrote:
enigma123 wrote:
As x increases from 209 to 210, which of the following must increase?



II. \(\frac{x - 1}{x}\) --> \(\frac{209-1}{209}=\frac{208}{209}\) which is less than \(\frac{210-1}{210}=\frac{209}{210}\), (the same way as 1/2 is less than 2/3). Correct.

Answer: C.


One way could be we replace the large number with a smaller one
say X will increase from 3 to 4.
let us first check the extremes.

1- 3x-4=9-4=5 and 12-4=8
8>5-Increase
2. x-1/x=(3-1)/3=2/3=2/3 and (4-1)/4=3/4
2/3>3/4 or 0.6>0.7
3. x-\(x^2\)=3-9=(-6) and 4-16=(-12)
(-6)>(-12)-decrease
hence C

Kudos [?]: 17 [0], given: 126

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1793

Kudos [?]: 980 [0], given: 5

Re: As x increases from 209 to 210, which of the following must [#permalink]

Show Tags

New post 16 Oct 2017, 15:54
enigma123 wrote:
As x increases from 209 to 210, which of the following must increase?

I. \(3x - 4\)
II. \(\frac{x - 1}{x}\)
III. \(x - x^2\)

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


We are being tested on the result when an integer is increased. So, rather than using 209 to 210, let’s use 2 to 3 (since the relationship won’t change).

I.

3(2) - 4 = 2

3(3) - 4 = 5

We see that an increase occurs.

II.

(2 - 1)/2 = 1/2

(3 - 1)/3 = 2/3

We see that an increase occurs.

III.

2 - 2^2 = -2

3 - 3^2 = -6

We see that an increase DOES NOT occur.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 980 [0], given: 5

Re: As x increases from 209 to 210, which of the following must   [#permalink] 16 Oct 2017, 15:54
Display posts from previous: Sort by

As x increases from 209 to 210, which of the following must

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.