February 20, 2019 February 20, 2019 08:00 PM EST 09:00 PM EST Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST February 21, 2019 February 21, 2019 10:00 PM PST 11:00 PM PST Kick off your 2019 GMAT prep with a free 7day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
Author 
Message 
TAGS:

Hide Tags

eGMAT Representative
Joined: 04 Jan 2015
Posts: 2581

If x is an integer, then how many values of x will satisfy the equatio
[#permalink]
Show Tags
Updated on: 13 Sep 2018, 07:16
Question Stats:
52% (01:37) correct 48% (01:45) wrong based on 293 sessions
HideShow timer Statistics



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2581

If x is an integer, then how many values of x will satisfy the equatio
[#permalink]
Show Tags
Updated on: 17 Sep 2018, 02:47
Solution Given:• We are given that x is an integer, and • We are also given an absolute value equation, x  2 + 7 = 6 To find:• We need to find the number of values of x, that satisfy the given equation Approach and Working: • If we observe, we can see that there are two absolute value functions in the equation, x  2 + 7 = 6 • So, let us first solve the outer modulus by substituting x  2 as t, which gives • Now, applying the definition of x, as learnt in the article, we can write t + 7 = 6 as,
o t + 7 = 6, if t ≥ 7
Implies, t = 1 Can we consider this as a possible value of t? Obviously, No. Since, the value of t = x  2 is always greater than or equal to 0. Thus, t = 1 is not a possible value o And, t + 7 = 6, if t < 7
This is again not possible, since, t cannot be a negative number • Thus, there is no value of t, which satisfies the equation, t + 7 = 6, where t = x  2 • Therefore, the number of possible values of x is 0 Now, let’s see another approach to solve this equation. • In the equation, t + 7 = 6, the minimum value of t = 0, since t = x  2 • So, the minimum value of t + 7 = 0 + 7 = 7 • Thus, the value of t + 7 is always greater than or equal to 7 • Therefore, the number of possible values of t and x is 0
Hence, the correct answer is option A. Answer: A
_________________
Register for free sessions Number Properties: Get 5 free video lessons, 50 practice questions  Algebra:Get 4 free video lessons, 40 practice questions Quant Workshop: Get 100 practice questions  Free Strategy Weession: Key strategy to score 760
Success Stories Q38 to Q50  Q35 to Q50  More Success Stories
Ace GMAT Articles and Question to reach Q51  Question of the week  Tips From V40+ Scoreres  V27 to V42: GMAT 770  Guide to Get into ISBMBA
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2  Remainders1  Remainders2 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.egmat.com



Director
Joined: 20 Feb 2015
Posts: 795
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, 07:24
EgmatQuantExpert wrote: Different methods to solve absolute value equations and inequalities Exercise Question #1If x is an integer, then how many values of x will satisfy the equation x  2 + 7 = 6? Options Next QuestionTo read the article: Different methods to solve absolute value equations and inequalities x  2 + 7 = 6 x2 will either be 0 or a +ve integer 0+7 <> 6 (+ve integer) + 7 <> 6 so 0 A



Manager
Joined: 06 Sep 2018
Posts: 176
Location: Pakistan
Concentration: Finance, Operations
GPA: 2.87
WE: Engineering (Other)

Re: If x is an integer, then how many values of x will satisfy the equatio
[#permalink]
Show Tags
13 Sep 2018, 08:08
Left hand side to be equal to 6, x2 must be equal to either 1 or 13 which is not possible because mod of x2 always results in a positive value, so left hand side always will be equal to 7 or greater than 7 but can never be equal to 6. So there is no value of x which can satisfy this equation. Answer A Posted from my mobile device
_________________
Hitting Kudos is the best way of appreciation.
Eric Thomas, "When you want to succeed as bad as you want to breathe, then you'll be successful."



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, 05:45
'A' it is, since solving the outer modulus we are getting negative values which is not possible.



Intern
Joined: 06 Aug 2018
Posts: 3

Re: If x is an integer, then how many values of x will satisfy the equatio
[#permalink]
Show Tags
12 Oct 2018, 16:08
Can anyone explain this problem please? I dont understand the official solution.
Posted from my mobile device



Orion Director of Academics
Joined: 19 Jul 2018
Posts: 97

Re: If x is an integer, then how many values of x will satisfy the equatio
[#permalink]
Show Tags
12 Oct 2018, 16:25
Hey Jancekmichal  The trick here is the idea that once you take the absolute value of something, it must be positive. So based on that x + 2 must be positive. This is important because of what follows. Because an absolute value sign inside an absolute value sign is confusing, let's pretend that x+2 = y instead. (This is just to simplify the equation. You could leave it as is) That's going to give you  y + 7 = 6. Now solve that as an actual equation. Remember that with an absolute value sign you need to solve this twice, once as if what's inside the signs is negative and once as if it's positive. That will give you two equations: y + 7 = 6, so y = 1 and y + 7 = 6, so y =  13. BUT WAIT. We said that y = x + 2, which we said must always be positive. That means that x + 2 can't ever equal 6 or  13, which means that there are no valid values for x that would make this equation true.
_________________
Laura Academics Aficionado  ORION GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 06 Aug 2018
Posts: 3

Re: If x is an integer, then how many values of x will satisfy the equatio
[#permalink]
Show Tags
12 Oct 2018, 16:29
Thanks so much, you are a life saver!
Posted from my mobile device



Intern
Joined: 09 Apr 2018
Posts: 31
GPA: 4

Re: If x is an integer, then how many values of x will satisfy the equatio
[#permalink]
Show Tags
14 Oct 2018, 22:49
If you have 2 absolute value expressions, you just need to consider 2 cases: (1) both have the same sign (2) they have different signs Solving the equation using this approach you get 2 values for x: x=1 and x=3. Plugging them into the original equation, you see that both do not make the equation true. Thus, the answer is A (0 solutions). If you liked this approach, please hit Kudos!



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2788
Location: India
GMAT: INSIGHT
WE: Education (Education)

If x is an integer, then how many values of x will satisfy the equatio
[#permalink]
Show Tags
15 Oct 2018, 00:23
EgmatQuantExpert wrote: Different methods to solve absolute value equations and inequalities Exercise Question #1If x is an integer, then how many values of x will satisfy the equation x  2 + 7 = 6? Options Given: x  2 + 7 = 6 This is an inconsistent solution because x  2 + 7 must be 7 or greater hence can NEVER be equal to 6 i.e. There is no possible solution for the expression Answer: Option A For similar question which can be solved, please check this question and our solutions
https://gmatclub.com/forum/howmanydis ... l#p1543729
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION




If x is an integer, then how many values of x will satisfy the equatio
[#permalink]
15 Oct 2018, 00:23






