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

It is currently 21 Aug 2018, 20:26

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 x is an integer and |x|+(x/3)<5, what is the value of x?

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

Hide Tags

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6046
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
If x is an integer and |x|+(x/3)<5, what is the value of x?  [#permalink]

Show Tags

New post 18 Dec 2017, 00:24
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

46% (01:33) correct 54% (01:36) wrong based on 35 sessions

HideShow timer Statistics

[GMAT math practice question]

If \(x\) is an integer and \(|x|+(\frac{x}{3})<5\), what is the value of \(x\)?

1) \(x>-12\)
2) \(x<-6\)

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6562
If x is an integer and |x|+(x/3)<5, what is the value of x?  [#permalink]

Show Tags

New post 18 Dec 2017, 00:54
MathRevolution wrote:
[GMAT math practice question]

If \(x\) is an integer and \(|x|+(\frac{x}{3})<5\), what is the value of \(x\)?

1) \(x>-12\)
2) \(x<-6\)




Let's solve the equation..
\(|x|+(\frac{x}{3})<5......3|x|+x<5\),
So ..
A) 3x+x<15.....4x<15.....x<15/4
B) -3x+x<15.....-2x<15.....2x>-15....x> -15/2....x>-7.5
So the question basically gives the value of x between -7.5 and 15/4

Let's see what each statement tells us
1) x>-12
x could be -7,-6,....0,1,2,3
Insufficient
2) x<-6
x=-7..YES
So ans -7
Sufficient

B

Edited.. mixed two Qs
_________________

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

Senior Manager
Senior Manager
User avatar
S
Joined: 05 Dec 2016
Posts: 259
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
GMAT ToolKit User
Re: If x is an integer and |x|+(x/3)<5, what is the value of x?  [#permalink]

Show Tags

New post 18 Dec 2017, 01:42
Solving the inequality we get the following possible values for x:
-7,5<x<3,75
Taken that x is an integer we get
-7<=x<=3
(1) x>-12
x can be -7;-6.....3
(2) x<-6
Taken that limit, only one integer conforms to it, x=-7

Answer B
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6046
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If x is an integer and |x|+(x/3)<5, what is the value of x?  [#permalink]

Show Tags

New post 20 Dec 2017, 01:50
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.

Modifying the original condition:
There are two cases to consider.
Case 1) \(x ≥ 0\)
\(|x|+(\frac{x}{3})<5\)
\(⇔ x + \frac{x}{3} < 5\)
\(⇔ (\frac{4}{3})x < 5\)
\(⇔ x < \frac{15}{4}\)
\(⇔ x = 0, 1, 2, 3\)

Case 2) \(x < 0\)
\(|x|+(\frac{x}{3})<5\)
\(⇔ -x + \frac{x}{3} < 5\)
\(⇔ -(\frac{2}{3})x <5\)
\(⇔ x > \frac{-15}{2}\)
\(⇔ x > -7.5\)
\(⇔ x = -7, -6, -5, -4, -3, -2 or -1\)

The question asks for the value of \(x\) if \(x\) is one of \(-7, -6, -5, …, 0, 1, 2, 3\). Since we have 1 variable (x), D is most likely to be the answer.

Condition 1)
All of the possible values of \(x\) are greater than \(-12\). Therefore, we do not have a unique solution, and this condition is not sufficient.

Condition 2)
The only possible value of \(x\) is \(-7\). Since we have a unique solution, condition 2) is sufficient.

Therefore, B is the answer.

Answer: B
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: If x is an integer and |x|+(x/3)<5, what is the value of x? &nbs [#permalink] 20 Dec 2017, 01:50
Display posts from previous: Sort by

If x is an integer and |x|+(x/3)<5, what is the value of x?

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

Events & Promotions

PREV
NEXT


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®.