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

It is currently 18 Jul 2018, 05:52

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

If k#0 and k - (3 -2k^2)/k = x/k, then x =

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

Hide Tags

Expert Post
4 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47077
If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

Show Tags

New post 24 Feb 2014, 23:50
4
9
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (00:51) correct 39% (00:58) wrong based on 712 sessions

HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

If \(k\neq{0}\) and \(k - \frac{3 -2k^2}{k} = \frac{x}{k}\), then x =

(A) -3 - k^2
(B) k^2 -3
(C) 3k^2 - 3
(D) k - 3 - 2k^2
(E) k - 3 + 2k^2

Problem Solving
Question: 111
Category: Algebra Second-degree equations
Page: 76
Difficulty: 500


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________

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

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47077
Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

Show Tags

New post 24 Feb 2014, 23:50
1
2
1 KUDOS received
Manager
Manager
User avatar
Status: GMATting
Joined: 21 Mar 2011
Posts: 106
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
GMAT ToolKit User
Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

Show Tags

New post 25 Feb 2014, 23:26
1
k - \frac{3 -2k^2}{k} = \frac{x}{k};
After simplifying and canceling k in the denominator, we get: k^2 - 3 + 2k^2 = x;
3k^2 - 3 = x;

Ans is (C).
2 KUDOS received
Manager
Manager
avatar
Joined: 20 Dec 2013
Posts: 249
Location: India
Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

Show Tags

New post 26 Feb 2014, 02:10
2
Option C.
k-(3-2k^2)/k=x/k
Multiply both sides by k
k^2-3+2k^2=x
3k^2-3=x
1 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

Show Tags

New post 08 Jul 2014, 22:17
1
Bunuel wrote:
SOLUTION

If \(k\neq{0}\) and \(k - \frac{3 -2k^2}{k} = \frac{x}{k}\), then x =

(A) -3 - k^2
(B) k^2 -3
(C) 3k^2 - 3
(D) k - 3 - 2k^2
(E) k - 3 + 2k^2

\(k - \frac{3 -2k^2}{k} = \frac{x}{k}\);

Multiply by k: \(k^2 - (3 -2k^2) = x\);

\(x=3k^2-3\).

Answer: C.


I just added a step after the highlighted one to remove -ve sign :) . Rest all did same

\(k - \frac{3 -2k^2}{k} = \frac{x}{k}\);

\(k + \frac{2k^2 - 3}{k} = \frac{x}{k}\)
_________________

Kindly press "+1 Kudos" to appreciate :)

Expert Post
GMAT Club Legend
GMAT Club Legend
User avatar
P
Joined: 16 Oct 2010
Posts: 8125
Location: Pune, India
Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

Show Tags

New post 08 Jul 2014, 23:55
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If \(k\neq{0}\) and \(k - \frac{3 -2k^2}{k} = \frac{x}{k}\), then x =

(A) -3 - k^2
(B) k^2 -3
(C) 3k^2 - 3
(D) k - 3 - 2k^2
(E) k - 3 + 2k^2





You can also put in k = 1 in \(k - \frac{3 -2k^2}{k} = \frac{x}{k}\) to get x = 0.
When you put k = 1 in options, only (C) and (E) give x = 0.

Now put k = -1 in \(k - \frac{3 -2k^2}{k} = \frac{x}{k}\) to get x = 0.
When you put k = -1 in options, only (C) gives x = 0
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Current Student
avatar
Joined: 14 Oct 2013
Posts: 45
GMAT ToolKit User
Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

Show Tags

New post 10 Mar 2015, 20:07
Why do we automatically assume there are parentheses around (3-2k^2)? I didn't assume that so then I didn't distribute the negative on the outside which of course then gave me answer A.
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6232
Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

Show Tags

New post 10 Mar 2015, 20:28
1
1
soniasawhney wrote:
Why do we automatically assume there are parentheses around (3-2k^2)? I didn't assume that so then I didn't distribute the negative on the outside which of course then gave me answer A.


hi soniasawhney..
it does not require any parenthesis as any sign in front of a fraction modifies the entire fraction irrespective of the term..
just an example..
let the fraction be - \(\frac{7-9}{2}\)..
two ways to do it ..
first change signs first and then find answer...
\(\frac{-7+9}{2}\)=\(\frac{2}{2}\)=1...

second simplify and then change the signs...
- \(\frac{7-9}{2}\)=- \(\frac{-2}{2}\)=-(-1)=1..

so both ways answer is same, which means parentheses is not required and a sign in front of a fraction automatically means that the entire fraction is inside bracket....
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Expert Post
2 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
P
Joined: 16 Oct 2010
Posts: 8125
Location: Pune, India
Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

Show Tags

New post 10 Mar 2015, 21:24
2
soniasawhney wrote:
Why do we automatically assume there are parentheses around (3-2k^2)? I didn't assume that so then I didn't distribute the negative on the outside which of course then gave me answer A.


To clarify further:
There are 3 ways in which you can make a fraction negative
\(\frac{-3}{5}\)

\(-\frac{3}{5}\) Take this to mean \(\frac{-3}{5}\)

and \(\frac{3}{-5}\)

Each one of these fractions is the same as \(\frac{-3}{5}\)

Now what happens in case you have multiple terms in numerator:

\(\frac{-x + 2}{4}\) The negative is only in front of x.

\(-\frac{x+2}{4}\) The negative is in effect, in front of the entire numerator. So this is the same as \(\frac{-(x+2)}{4}\)
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Expert Post
SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1888
Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

Show Tags

New post 12 Mar 2015, 23:12
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If \(k\neq{0}\) and \(k - \frac{3 -2k^2}{k} = \frac{x}{k}\), then x =

(A) -3 - k^2
(B) k^2 -3
(C) 3k^2 - 3
(D) k - 3 - 2k^2
(E) k - 3 + 2k^2

Problem Solving
Question: 111
Category: Algebra Second-degree equations
Page: 76
Difficulty: 500


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!


Given that,
k - (3 - 2k^2)/k = x/k
Take LCM of denominators,
So, [k^2 - (3 - 2k^2)]/k = x/k
So, [k^2 - 3 + 2k^2]/k = x/k
Canceling out k from the denominators of both sides,
So, [k^2 - 3 + 2k^2] = x
So, 3k^2 - 3 = x
Hence option C.

--
Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course
Intern
Intern
avatar
Joined: 31 Oct 2013
Posts: 3
Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

Show Tags

New post 07 Apr 2016, 16:29
I'm not sure whats wrong here:

1. k - [3-2k^2][/k] = [x][/k]

2. k - 3 + 2k^2 = x

I am assuming I can't move the denominator to the right side because of the first term (k), just not sure why.
Expert Post
2 KUDOS received
SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1888
Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

Show Tags

New post 10 Apr 2016, 20:06
2
Apollon wrote:
I'm not sure whats wrong here:

1. k - [3-2k^2][/k] = [x][/k]

2. k - 3 + 2k^2 = x

I am assuming I can't move the denominator to the right side because of the first term (k), just not sure why.


1. k - [3-2k^2][/k] = [x][/k]

2. k - 3 + 2k^2 = x

Hi Apollon,

If you see, only two of the three terms have the denominator k.
In order to cancel out the denominator from all the terms, you need to have the same denominator in each term.

In the given case,

1. k - (3-2k^2)/ k = x / k
We need to make sure that the denominator of the first term is also the same.

Hence
k^2/k - (3-2k^2)/ k = x / k
From here on, we can cancel the terms.
k^2 - 3 + 2k^2 = x
Or x = 3k^2 - 3
Option C

Does this help?
Expert Post
1 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
P
Joined: 16 Oct 2010
Posts: 8125
Location: Pune, India
Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

Show Tags

New post 10 Apr 2016, 23:10
1
Apollon wrote:
I'm not sure whats wrong here:

1. k - [3-2k^2][/k] = [x][/k]

2. k - 3 + 2k^2 = x

I am assuming I can't move the denominator to the right side because of the first term (k), just not sure why.


Yes, you re right. To move the denominator to the other side, it must be the denominator of the entire expression.

Look at it from a very basic viewpoint:

1/2 = x
1 = 2x
Since x is 1/2, twice of x will be 1.

1 + 1/2 = x
1 + 1 = 2x ????
x is actually 3/2 or (1.5). If you double it, will you get 2? No.

On the other hand,
(1 + 3+ 5)/2 = x
Then (1 + 3 + 5) = 2x is correct.
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Manager
Manager
User avatar
S
Status: On a 600-long battle
Joined: 22 Apr 2016
Posts: 138
Location: Hungary
Concentration: Accounting, Leadership
Schools: Erasmus '19
GMAT 1: 410 Q18 V27
GMAT 2: 490 Q35 V23
GMAT ToolKit User
Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

Show Tags

New post 30 Apr 2017, 01:33
VeritasPrepKarishma wrote:
soniasawhney wrote:
Why do we automatically assume there are parentheses around (3-2k^2)? I didn't assume that so then I didn't distribute the negative on the outside which of course then gave me answer A.


To clarify further:
There are 3 ways in which you can make a fraction negative
\(\frac{-3}{5}\)

\(-\frac{3}{5}\) Take this to mean \(\frac{-3}{5}\)

and \(\frac{3}{-5}\)

Each one of these fractions is the same as \(\frac{-3}{5}\)

Now what happens in case you have multiple terms in numerator:

\(\frac{-x + 2}{4}\) The negative is only in front of x.

\(-\frac{x+2}{4}\) The negative is in effect, in front of the entire numerator. So this is the same as \(\frac{-(x+2)}{4}\)


Thank you, VeritasPrepKarishma

I too fell for this rule.

So basically in this exercise.

\(-\cfrac { 3-2{ k }^{ 2 } }{ k } \neq \cfrac { -3-2{ k }^{ 2 } }{ k } \\ \\ -\cfrac { 3-2{ k }^{ 2 } }{ k } \rightarrow \cfrac { -\left( 3-2{ k }^{ 2 } \right) }{ k }\)
_________________

"When the going gets tough, the tough gets going!"

|Welcoming tips/suggestions/advices (you name it) to help me achieve a 600|

Director
Director
User avatar
G
Joined: 09 Mar 2016
Posts: 653
Re: If k#0 and k - (3 -2k^2)/k = x/k, then x = [#permalink]

Show Tags

New post 14 Apr 2018, 03:41
chetan2u wrote:
soniasawhney wrote:
Why do we automatically assume there are parentheses around (3-2k^2)? I didn't assume that so then I didn't distribute the negative on the outside which of course then gave me answer A.


hi soniasawhney..
it does not require any parenthesis as any sign in front of a fraction modifies the entire fraction irrespective of the term..
just an example..
let the fraction be - \(\frac{7-9}{2}\)..
two ways to do it ..
first change signs first and then find answer...
\(\frac{-7+9}{2}\)=\(\frac{2}{2}\)=1...

second simplify and then change the signs...
- \(\frac{7-9}{2}\)=- \(\frac{-2}{2}\)=-(-1)=1..

so both ways answer is same, which means parentheses is not required and a sign in front of a fraction automatically means that the entire fraction is inside bracket....


Hello chetan2u

if fraction is - \(\frac{7-9}{2}\)

then why didnt you rewrite is as \(\frac{-(7-9)}{2}\) ----> \(\frac{-7+9}{2}\) :?

have a great weekend :)
Re: If k#0 and k - (3 -2k^2)/k = x/k, then x =   [#permalink] 14 Apr 2018, 03:41
Display posts from previous: Sort by

If k#0 and k - (3 -2k^2)/k = x/k, then x =

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

Events & Promotions

PREV
NEXT


cron

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.