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

 It is currently 18 Nov 2018, 19:05

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

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

Events & Promotions

Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
• The winning strategy for 700+ on the GMAT

November 20, 2018

November 20, 2018

06:00 PM EST

07:00 PM EST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

If x is an integer, then how many values of x will satisfy the equatio

Author Message
TAGS:

Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2203
If x is an integer, then how many values of x will satisfy the equatio  [#permalink]

Show Tags

Updated on: 13 Sep 2018, 07:18
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:18) correct 45% (01:21) wrong based on 185 sessions

HideShow timer Statistics

Different methods to solve absolute value equations and inequalities- Exercise Question #3

If x is an integer, then how many values of x will satisfy the equation |x + 2|= |3x +14|?

Options

a) 0
b) 1
c) 2
d) 3
e) 4

To read the article: Different methods to solve absolute value equations and inequalities

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

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

Originally posted by EgmatQuantExpert on 13 Sep 2018, 02:06.
Last edited by EgmatQuantExpert on 13 Sep 2018, 07:18, edited 2 times in total.
Director
Joined: 20 Feb 2015
Posts: 796
Concentration: Strategy, General Management
Re: If x is an integer, then how many values of x will satisfy the equatio  [#permalink]

Show Tags

13 Sep 2018, 07:47
4
EgmatQuantExpert wrote:
Different methods to solve absolute value equations and inequalities- Exercise Question #3

If x is an integer, then how many values of x will satisfy the equation |x + 2|= |3x +14|?

Options

a) 0
b) 1
c) 2
d) 3
e) 4

To read the article: Different methods to solve absolute value equations and inequalities

if
|x| = |y|
then
$$x^2$$ = $$y^2$$
similarly
$$(x + 2)^2$$= $$(3x +14)^2$$
upon solving ,
we get x= -6 and -4

C
General Discussion
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2203
If x is an integer, then how many values of x will satisfy the equatio  [#permalink]

Show Tags

Updated on: 17 Sep 2018, 03:25

Solution

Given:
• We are given that x is an integer, and
• We are also given an absolute value equation, |x + 2| = |3x + 14|

To find:
• We need to find the number of values of x, that satisfy the given equation

Approach and Working:
• In this question, we have modulus function on both sides of the equation.
• Let’s first apply the definition to the LHS of the equation.
• From this, we get,
o x + 2 = |3x + 14|, if x ≥ -2, and
o x + 2 = -|3x + 14|, if x < -2
• Now, let’s consider the first case, x + 2 = |3x + 14|, if x ≥ -2. And, if we remove the modulus sign on the RHS of this equation, we get,
o x + 2 = 3x + 14, if x ≥ -2 and x ≥ -14/3
 Solving this equation, we get, 2x = -12
 Implies, x = -6, which does not lie in the range
 Thus, x = -6 is not a possible value
o x + 2 = -(3x + 14), if x ≥ -2 and x < -14/3
 This case is not possible as no value of x can simultaneously be ≥ -2 and < -14/3
• Considering the second case, x + 2 = -|3x + 14|, if x < -2, and removing the modulus sign, we get,
o x + 2 = -(3x + 14), if x < -2 and x ≥ -14/3
 Solving this equation, we get, 4x = -16
 Implies, x = -4, which lies in the range [-14/3, -2)
 Thus, x = -4 is a possible value of x[/list]
o x + 2 = (3x + 14), if x < -2 and x < -14/3
 Solving this equation, we get, 2x = -12
 Implies, x = -6, which is less than both -2 and -14/3
 Thus, x = -6 is a possible value of x

Therefore, the only values of x, that satisfy the given equation, |x + 2|= |3x +14|, are -4 and -6

Hence, the correct answer is option C.

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

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

Originally posted by EgmatQuantExpert on 13 Sep 2018, 02:11.
Last edited by EgmatQuantExpert on 17 Sep 2018, 03:25, edited 1 time in total.
Intern
Joined: 17 May 2018
Posts: 3
Re: If x is an integer, then how many values of x will satisfy the equatio  [#permalink]

Show Tags

13 Sep 2018, 02:16

Solving the equation will yield two solutions , X=-6 and X=-3. Plugging these values into the equation will yield only 1 value to be valid, and that value is -6.
Intern
Joined: 10 Sep 2018
Posts: 6
GMAT 1: 700 Q45 V41
Re: If x is an integer, then how many values of x will satisfy the equatio  [#permalink]

Show Tags

13 Sep 2018, 07:26
TariqOmar wrote:

Solving the equation will yield two solutions , X=-6 and X=-3. Plugging these values into the equation will yield only 1 value to be valid, and that value is -6.

But then don't you think the answer can be both 6 as well as -6? Since the equation is the mod of x? So I think the answer should be c!
Intern
Joined: 08 Apr 2018
Posts: 16
Re: If x is an integer, then how many values of x will satisfy the equatio  [#permalink]

Show Tags

14 Sep 2018, 06:32
1
'C' it is, squaring both sides.

x^2 + 4x + 4 = 9x^2 + 84x +196

8x^2 + 80x + 192 = 0

x^2 + 10x + 24 = 0

(x+6)(x+4)=0

x = -4, -6
Intern
Joined: 14 Aug 2018
Posts: 20
Location: United States (WA)
GMAT 1: 670 Q43 V40
GMAT 2: 750 Q47 V47
GPA: 3.3
WE: Education (Education)
Re: If x is an integer, then how many values of x will satisfy the equatio  [#permalink]

Show Tags

14 Sep 2018, 08:13
2
Absolute value is the easiest / hardest concept. The GMAT uses absolute value as a proxy for logical reasoning. Students frequently get fooled by absolute value questions, so my recommendation is whenever possible rewrite the equation without absolute value. This investment of time, in my experience, greatly increases accuracy on these questions.

In this case, if we get rid of absolute value we are left with two equations:

1. x + 2 = 3x + 14
2. x + 2 = -(3x + 14)

Please note that the two other possibilities of -(x + 2) = 3x + 14 and -(x + 2) = -(3x + 14) reduce to either 1 or 2.

Checking in the with the answer choices, only B and C are now alive. Either 1 and 2 have unique values or both solve for the same value. The latter is less likely in real life but could a devious testmaker trick, so you have to check.

1. becomes -2x = 12 then x = -6
2. becomes x + 2 = -3x - 14 then 4x = -16 then x = -4

C is correct
_________________

Jayson Beatty
Indigo Prep
http://www.indigoprep.com

Intern
Joined: 25 Jan 2013
Posts: 21
Concentration: Marketing, Strategy
GPA: 3.64
If x is an integer, then how many values of x will satisfy the equatio  [#permalink]

Show Tags

14 Sep 2018, 22:55
EgmatQuantExpert wrote:
Reserving this space to post the official solution

You made me remember my old school days

_________________

pressing +1 kudos is a nice way to say thanks

If x is an integer, then how many values of x will satisfy the equatio &nbs [#permalink] 14 Sep 2018, 22:55
Display posts from previous: Sort by

If x is an integer, then how many values of x will satisfy the equatio

 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®.