Mar 18 10:00 PM AKDT  11:00 PM AKDT Getting 700+ on the GMAT isn’t about luck. It’s about taking action and start preparing early. Start studying today with 20% off on your GMAT prep. Mar 19 08:00 AM PDT  09:00 AM PDT Beat the GMAT with a customized study plan based on your needs! Learn how to create your preparation timeline, what makes a good study plan and which tools you need to use to build the perfect plan. Register today! Mar 20 07:00 AM PDT  09:00 AM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Mar 20 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Wednesday, March 20th at 9 PM EDT Mar 23 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 174

Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
17 Dec 2012, 06:54
Question Stats:
79% (01:10) correct 21% (01:11) wrong based on 2935 sessions
HideShow timer Statistics
Attachment:
Line.png [ 3.24 KiB  Viewed 32856 times ]
Which of the following inequalities is an algebraic expression for the shaded part of the number line above? (A) x <= 3 (B) x <= 5 (C) x  2 <= 3 (D) x  1 <= 4 (E) x +1 <= 4
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 53657

Re: Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
17 Dec 2012, 06:57




Intern
Joined: 13 Sep 2012
Posts: 6

Re: Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
Updated on: 11 Jan 2014, 03:26
Walkabout wrote: Attachment: Line.png Which of the following inequalities is an algebraic expression for the shaded part of the number line above? (A) x <= 3 (B) x <= 5 (C) x  2 <= 3 (D) x  1 <= 4 (E) x +1 <= 4 Lets try to do this conceptually, The length of the line is 8. Middle point = 8/2 = 4. The point on the number line equidistant at a length of 4 from each extremeties (5 and 3) is 1. So, the equation turns out to be, x  (equidistant point) <= Middle Point i.e. x(1) <= 4 i.e. x+1 <= 4 Ans  (E)
Originally posted by adeelahmad on 11 Jan 2014, 03:18.
Last edited by adeelahmad on 11 Jan 2014, 03:26, edited 1 time in total.




Manager
Joined: 20 Dec 2013
Posts: 121

Re: Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
11 Jan 2014, 03:24
Walkabout wrote: Attachment: Line.png Which of the following inequalities is an algebraic expression for the shaded part of the number line above? (A) x <= 3 (B) x <= 5 (C) x  2 <= 3 (D) x  1 <= 4 (E) x +1 <= 4 Round 1: Eliminate the obvious, let us say x = 5 and eliminate from options (A) Eliminated (B) Okay (C) Eliminated (D) Eliminated (E) Okay Round 2: We are left between B and E. There are two things you can do. Use Algebra: x <= 5  Contains numbers from 5 to +5 which does not define the inequality as 4 and 5 are not part of the inequality Hence answer is E OR Plug in x = 4 where Option B satisfies which was not supposed to be.
_________________
76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views
Perfect Scores http://perfectscores.org http://www.youtube.com/perfectscores



Intern
Joined: 14 Jul 2013
Posts: 24

Re: Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
21 Apr 2014, 04:29
yeehaaahhh
tried with bunuel's logic. It worked within 30 sec
calculate length  8 center  from the graph = 1
only two options have r.h.s = 4 (half of length). Further, in E, LHS becomes zero when x = 1. Hence, E.



Intern
Joined: 03 Jan 2014
Posts: 2
WE: Information Technology (Computer Software)

Re: Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
16 Jun 2014, 00:48
My Approach
Looking at the number line, it can be inferred that the line would have been \(x\leq{4}\) or \(4\leq{x}\leq{4}\) if it was was centered at 0. (since length = 8 units and end points as +4)
Now since the line \(x\leq{4}\) is centered at 0 and in this case is shifted to left by 1 unit (now centered at 1), the equation of the line becomes \(x(1)\leq{4}\) or \(x+1\leq{4}\)
Hence E



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2826

Re: Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
16 Jun 2016, 06:18
Walkabout wrote: Attachment: Line.png Which of the following inequalities is an algebraic expression for the shaded part of the number line above? (A) x <= 3 (B) x <= 5 (C) x  2 <= 3 (D) x  1 <= 4 (E) x +1 <= 4 We start by expressing the interval on the number line as an inequality: 5 ≤ x ≤ 3 Looking at answer choices A and B, we see that those two equations will not produce the inequality shown above. Thus, we consider answer choices C, D, and E. When we solve an absolutevalue equation with one absolutevalue expression, we consider two cases: one with the positive version of the expression inside the absolute value bars and one with the negative (or opposite) version of the expression inside the absolute value bars. Let’s use this fact to evaluate answer choice C: Answer choice C: x  2 ≤ 3 Case 1: Expression Positive: x – 2 ≤ 3 x ≤ 5 Case 2: Expression Negative: (x  2) ≤ 3 x + 2 ≤ 3 x ≤ 1 x ≥ 1 The solution is x ≤ 5 and x ≥ 1, i.e., 1 ≤ x ≤ 5. However, this does not fit the interval represented on the number line. Answer choice D: x  1 ≤ 4 Case 1: Expression Positive: x  1 ≤ 4 x ≤ 5 Case 2: Expression Negative: (x – 1) ≤ 4 x + 1 ≤ 4 x ≤ 3 x ≥ 3 The solution is x ≤ 5 and x ≥ 3, i.e., 3 ≤ x ≤ 5. This does not fit the interval represented on the number line. Answer Choice E: x +1 ≤ 4 Case 1: Expression Positive: x + 1 ≤ 4 x ≤ 3 Case 2: Expression Negative: (x + 1) ≤ 4 x – 1 ≤ 4 x ≤ 5 x ≥ 5 The solution is x ≤ 3 and x ≥ 5, i.e., 5 ≤ x ≤ 3. This DOES describe the interval represented on the number line. Answer E
_________________
5star rated online GMAT quant self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews



Current Student
Joined: 12 Jan 2017
Posts: 5
Location: United States
GPA: 3.26
WE: Marketing (Consumer Products)

Re: Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
10 Apr 2017, 23:07
Got this quickly using the Kaplan trick, start at the bottom for "which of the following" type questions. Didn't waste time evaluating the first four wrong ones.



Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 278

Re: Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
06 Aug 2017, 12:01
adeelahmad wrote: Walkabout wrote: Attachment: Line.png Which of the following inequalities is an algebraic expression for the shaded part of the number line above? (A) x <= 3 (B) x <= 5 (C) x  2 <= 3 (D) x  1 <= 4 (E) x +1 <= 4 Lets try to do this conceptually, The length of the line is 8. Middle point = 8/2 = 4. The point on the number line equidistant at a length of 4 from each extremeties (5 and 3) is 1. So, the equation turns out to be, x  (equidistant point) <= Middle Point i.e. x(1) <= 4 i.e. x+1 <= 4 Ans  (E) beautiful approach I will say ... can you please, however, say to me what you will do when you cannot find out the midpoint, specifically , in the cases when the length of the line is an odd number, for instance, suppose, 9....? thanks in advance ..



Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1304
Location: India
WE: Engineering (Other)

Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
Updated on: 27 Aug 2017, 03:39
Bunuel mikemcgarry IanStewart shashankism Engr2012 Can someone please explain statement (C) in Bunuel's approach in detail. I got through OA by opening modulus, but took more steps and time. WR, Arpit
Attachments
OG16 Q168.jpeg [ 85.35 KiB  Viewed 11085 times ]
_________________
It's the journey that brings us happiness not the destination.
Feeling stressed, you are not alone!!
Originally posted by adkikani on 27 Aug 2017, 03:01.
Last edited by adkikani on 27 Aug 2017, 03:39, edited 1 time in total.



Math Expert
Joined: 02 Sep 2009
Posts: 53657

Re: Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
27 Aug 2017, 03:15



Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1304
Location: India
WE: Engineering (Other)

Re: Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
27 Aug 2017, 03:28
hi BunuelThanks a lot for pointing out my mistake. What I meant earlier was explanation of point (C) in your approach since it was too concise particularly this step: (C) x  2 <= 3 > −3≤x−2≤3−3≤x−2≤3 > add 2 to all parts: −1≤x≤5−1≤x≤5. Discard.. Discard.WR, Arpit
_________________
It's the journey that brings us happiness not the destination.
Feeling stressed, you are not alone!!



Math Expert
Joined: 02 Sep 2009
Posts: 53657

Re: Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
27 Aug 2017, 03:42



VP
Joined: 09 Mar 2016
Posts: 1277

Re: Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
27 Dec 2017, 13:03
Bunuel wrote: Which of the following inequalities is an algebraic expression for the shaded part of the number line above? (A) x <= 3 (B) x <= 5 (C) x  2 <= 3 (D) x  1 <= 4 (E) x +1 <= 4 From the number line it follows that \(5\leq{x}\leq{3}\) (A) x <= 3 > \(3\leq{x}\leq{3}\). Discard. (B) x <= 5 > \(5\leq{x}\leq{5}\). Discard. (C) x  2 <= 3 > \(3\leq{x2}\leq{3}\) > add 2 to all parts: \(1\leq{x}\leq{5}\). Discard.. Discard. (D) x  1 <= 4 > \(4\leq{x1}\leq{4}\) > add 1 to all parts: \(3\leq{x}\leq{5}\). Discard.. Discard. (E) x +1 <= 4 > \(4\leq{x+1}\leq{4}\) > subtract 1 from all parts: \(5\leq{x}\leq{3}\). OK. Answer: E. Hello Bunuel, I have two questions: Why in options C and D you add 1 to all parts, whereas in option E you subtract 1 from all parts ? And another question: if you subtract +1 from 4 and +4 how do you get 5 and 3 ?



Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1304
Location: India
WE: Engineering (Other)

Re: Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
27 Dec 2017, 17:57
dave13, niks18 Quote: I have two questions: Why in options C and D you add 1 to all parts, whereas in option E you subtract 1 from all parts ? While dealing with inequality we always compare a variable x wrt numbers, not x1 or x+1 Note that in C and D we have added +2 and +1 resp, but in E we have added 1 on both sides. Quote: And another question: if you subtract +1 from 4 and +4 how do you get 5 and 3 ? Adding or subtracting same no from inequality does not change the inequality. Multiplying 1 on both sides changes inequality. Hope this helps!
_________________
It's the journey that brings us happiness not the destination.
Feeling stressed, you are not alone!!



Math Expert
Joined: 02 Sep 2009
Posts: 53657

Re: Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
27 Dec 2017, 20:39
dave13 wrote: Bunuel wrote: Which of the following inequalities is an algebraic expression for the shaded part of the number line above? (A) x <= 3 (B) x <= 5 (C) x  2 <= 3 (D) x  1 <= 4 (E) x +1 <= 4 From the number line it follows that \(5\leq{x}\leq{3}\) (A) x <= 3 > \(3\leq{x}\leq{3}\). Discard. (B) x <= 5 > \(5\leq{x}\leq{5}\). Discard. (C) x  2 <= 3 > \(3\leq{x2}\leq{3}\) > add 2 to all parts: \(1\leq{x}\leq{5}\). Discard.. Discard. (D) x  1 <= 4 > \(4\leq{x1}\leq{4}\) > add 1 to all parts: \(3\leq{x}\leq{5}\). Discard.. Discard. (E) x +1 <= 4 > \(4\leq{x+1}\leq{4}\) > subtract 1 from all parts: \(5\leq{x}\leq{3}\). OK. Answer: E. Hello Bunuel, I have two questions: Why in options C and D you add 1 to all parts, whereas in option E you subtract 1 from all parts ? And another question: if you subtract +1 from 4 and +4 how do you get 5 and 3 ? 1. We add or subtract to get only x in the middle. 2. 4  1 = 5 and 4  1 = 3.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 278

Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
04 Jan 2018, 10:42
adeelahmad wrote: Walkabout wrote: Attachment: Line.png Which of the following inequalities is an algebraic expression for the shaded part of the number line above? (A) x <= 3 (B) x <= 5 (C) x  2 <= 3 (D) x  1 <= 4 (E) x +1 <= 4 Lets try to do this conceptually, The length of the line is 8. Middle point = 8/2 = 4. The point on the number line equidistant at a length of 4 from each extremeties (5 and 3) is 1. So, the equation turns out to be, x  (equidistant point) <= Middle Point i.e. x(1) <= 4 i.e. x+1 <= 4 Ans  (E) OR as can be seen, and it is very important to notice that "3" and "5" both numbers are exactly "1" distance away from the middle point "4" to forming an algebraic expression so the actual expression should be 5 + 1 <= x + 1 <= 3 + 1 thus, 4 <= x + 1 <= 4 thanks



Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1218
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Re: Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
27 Sep 2018, 10:19
Steps to convert inequality graph to algebraic expression: 1) Plot the midpoint (a) of the solution set on the number line: here the midpoint, a = (5+3)/2 = 1 2) Find the distance (b unit) of either end points from the mid point : here the distance, b = 3(1) = 4 3) Insert the appropriate sign of inequality between xa and b: Here , putting a and b, we get x+1<=4 hence, the Required inequality is x+1<=4Answer = E
_________________
Win GMAT CLUB Test Weekly Quant Quiz Contest Weekly Quant Quiz Questions Direct Download SC: Confusable words All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory Error log/Key Concepts Combination Concept: Division into groups Question of the Day (QOTD) Free GMAT CATS



Senior Manager
Joined: 17 Mar 2014
Posts: 434

Re: Which of the following inequalities is an algebraic expressi
[#permalink]
Show Tags
29 Dec 2018, 17:14
adeelahmad wrote: Walkabout wrote: Attachment: Line.png Which of the following inequalities is an algebraic expression for the shaded part of the number line above? (A) x <= 3 (B) x <= 5 (C) x  2 <= 3 (D) x  1 <= 4 (E) x +1 <= 4 Lets try to do this conceptually, The length of the line is 8. Middle point = 8/2 = 4. The point on the number line equidistant at a length of 4 from each extremeties (5 and 3) is 1. So, the equation turns out to be, x  (equidistant point) <= Middle Point i.e. x(1) <= 4 i.e. x+1 <= 4 Ans  (E) Bunuel, Will above method be Valid of all questions of this type




Re: Which of the following inequalities is an algebraic expressi
[#permalink]
29 Dec 2018, 17:14






