Author 
Message 
TAGS:

Hide Tags

GMAT Forum Moderator
Joined: 27 May 2014
Posts: 433

How many integer values of x satisfy the inequality x  5 ≤ 2.5? [#permalink]
Show Tags
22 Mar 2017, 23:02
6
This post was BOOKMARKED
Question Stats:
73% (00:44) correct 27% (00:50) wrong based on 371 sessions
HideShow timer Statistics
How many integer values of x satisfy the inequality x  5 ≤ 2.5? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 43898

Re: How many integer values of x satisfy the inequality x  5 ≤ 2.5? [#permalink]
Show Tags
22 Mar 2017, 23:11



Director
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 518
Location: India

Re: How many integer values of x satisfy the inequality x  5 ≤ 2.5? [#permalink]
Show Tags
23 Mar 2017, 02:05
Hi saswata4s, We can solve this question using number line too, because modulus (or absolute value) is nothing but the length, Here the question says, x5 ≤ 2.5 That is distance between x and 5 has to be less than or equal to 2.5, So, let’s draw this in the number line, we can see that from the below diagram, that x has to be between 2.5 and 7.5, Since question ask about integer values, The values are 3,4,5,6 and 7. So there are 5 values, Answer has to be C. Hope this helps.
Attachments
number lineGC.png [ 12.15 KiB  Viewed 2881 times ]
_________________
Join Free 4 part MBA Through GMAT Video Training Series here  https://gmat.crackverbal.com/mbathroughgmatvideo2018
Enroll for our GMAT Trial Course here  http://gmatonline.crackverbal.com/
For more info on GMAT and MBA, follow us on @AskCrackVerbal



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7960
Location: Pune, India

Re: How many integer values of x satisfy the inequality x  5 ≤ 2.5? [#permalink]
Show Tags
23 Mar 2017, 02:31
saswata4s wrote: How many integer values of x satisfy the inequality x  5 ≤ 2.5?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 This post discusses this concept in detail: https://www.veritasprep.com/blog/2011/0 ... edoredid/
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Joined: 22 Oct 2016
Posts: 22

Re: How many integer values of x satisfy the inequality x  5 ≤ 2.5? [#permalink]
Show Tags
23 Mar 2017, 05:54
Please correct me if i'm wrong. For the inequality x5 <= 2.5 to be +ve, x>5 For the inequality x5 <= 2.5 to be ve, x<5 By removing the modulus, (x5) = 2.5; x = 7.5 (x5) = 2.5; x = 2.5 Hence the inequality lies between 2.5 < (x5) < 7.5 Since the question asks for integers within this range, we have 3,4,5,6 and 7. Hence answer is C.
Is there any possibility this question be asked for noninteger values.? Just trying to understand the concept better.
TIA
_________________
Regards, Sarugiri



Manager
Joined: 02 Aug 2015
Posts: 70

Re: How many integer values of x satisfy the inequality x  5 ≤ 2.5? [#permalink]
Show Tags
23 Mar 2017, 08:14
sarugiri wrote: Please correct me if i'm wrong. For the inequality x5 <= 2.5 to be +ve, x>5 For the inequality x5 <= 2.5 to be ve, x<5 By removing the modulus, (x5) = 2.5; x = 7.5 (x5) = 2.5; x = 2.5 Hence the inequality lies between 2.5 < (x5) < 7.5 Since the question asks for integers within this range, we have 3,4,5,6 and 7. Hence answer is C.
Is there any possibility this question be asked for noninteger values.? Just trying to understand the concept better.
TIA Hello there, For the given set of options, the question cannot ask for noninteger values as there are infinite non integral values between any two integers. However, had the options were limits, then there's a possibility to ask for nonintegeral values. Cheers!



GMAT Forum Moderator
Joined: 27 May 2014
Posts: 433

How many integer values of x satisfy the inequality x  5 ≤ 2.5? [#permalink]
Show Tags
23 Mar 2017, 23:43
Diwakar003 wrote: Hello there,
For the given set of options, the question cannot ask for noninteger values as there are infinite non integral values between any two integers. However, had the options were limits, then there's a possibility to ask for nonintegeral values.
Cheers!
Hi, Could you please explain this in little more details. Cheers.



Math Expert
Joined: 02 Sep 2009
Posts: 43898

Re: How many integer values of x satisfy the inequality x  5 ≤ 2.5? [#permalink]
Show Tags
24 Mar 2017, 00:03
saswata4s wrote: Diwakar003 wrote: Hello there,
For the given set of options, the question cannot ask for noninteger values as there are infinite non integral values between any two integers. However, had the options were limits, then there's a possibility to ask for nonintegeral values.
Cheers!
Hi, Could you please explain this in little more details. Cheers. The point is that there are infinitely many numbers in any interval. For example, if we don't limit the values of x to integers only, then infinitely many values of x satisfy 2.5 ≤ x ≤ 7.5. Does this make sense?
_________________
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



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2016

Re: How many integer values of x satisfy the inequality x  5 ≤ 2.5? [#permalink]
Show Tags
27 Mar 2017, 10:54
saswata4s wrote: How many integer values of x satisfy the inequality x  5 ≤ 2.5?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 Let’s solve for when (x  5) is positive and when (x  5) is negative. When (x  5) is positive: x  5 ≤ 2.5 x ≤ 7.5 When (x  5) is negative: (x  5) ≤ 2.5 x + 5 ≤ 2.5 x ≤ 2.5 x ≥ 2.5 Thus, 2.5 ≤ x ≤ 7.5. We see that there are 5 integer values that satisfy the inequality: 3, 4, 5, 6, and 7. Answer: C
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11074
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: How many integer values of x satisfy the inequality x  5 ≤ 2.5? [#permalink]
Show Tags
28 Mar 2017, 19:41
Hi saswata4s, A certain number of questions in the Quant section of the GMAT can be solved rather easily with 'brute force' arithmetic. You don't need to know/complete any complex math  you just have to put the pen on the pad and work your way through the possibilities. The answer choices to this question show that there are at least 3, but no more than 7, integer values that 'fit' this inequality. I bet that you can find them all in under a minute if you try. X  5 < 2.5 Let's start with an obvious value: X = 5 5  5 = 0, which is clearly less than 2.5 X = 6 > 1 is less than 2.5 X = 7 > 7 is less than 2.5 X = 8 > 3 is NOT less than 2.5.... Increasing the value of X will just increase the value of the inequality, so there's no reason to check any higher integers. Let's stop here and try going in the other direction.... X = 4 > 1 = 1 is less than 2.5 X = 3 > 2 = 2 is less than 2.5 X = 2 > 3 = 3 is NOT less than 2.5....Decreasing the value of X will just increase the value of the inequality, so there's no reason to check any lower integers. Thus, we're done  and there are 5 integer values that fit the inequality. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Manager
Status: Gmat lover
Joined: 27 Mar 2017
Posts: 88
Location: India
GPA: 3.91

Re: How many integer values of x satisfy the inequality x  5 ≤ 2.5? [#permalink]
Show Tags
15 May 2017, 04:35
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7
2.5<=x<=7.5
As x is integer so x can be 3,4,5,6,7
Hence 5 values can x take
_________________
_________________ Rules for posting in verbal Gmat forum, read it before posting anything in verbal forum Giving me + 1 kudos if my post is valuable with you
The more you like my post, the more you share to other's need.
“The great secret of true success, of true happiness, is this: the man or woman who asks for no return, the perfectly unselfish person, is the most successful.” Swami Vivekananda



Senior Manager
Joined: 09 Mar 2016
Posts: 253

How many integer values of x satisfy the inequality x  5 ≤ 2.5? [#permalink]
Show Tags
10 Feb 2018, 06:05
Bunuel wrote: saswata4s wrote: How many integer values of x satisfy the inequality x  5 ≤ 2.5?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 x  5 ≤ 2.5; Get rid of modulus: 2.5 ≤ x  5 ≤ 2.5; Add 5 to all three parts: 2.5 ≤ x ≤ 7.5 Integer values of x that satisfy the inequality are 3, 4, 5, 6, and 7. So, 5 values. Answer: C. Hello Bunuel, Zeus of all real numbers and unreal numbers please show your kindness to mortal GMAT student by explaining what i did wrong in my solution below:) I approached this question by opening the modulus  modulus always is associated with opening modulus no ? x  5 ≤ 2.5 Case 1: x is positive x  5≤ 2.5 > x = 7.5 Case 2: x is negative x  5≤ 2.5 > x = 2.5 (Not valid, our initial condition was that x is negative but we got positive. So whats wrong with my approach ?



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11074
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: How many integer values of x satisfy the inequality x  5 ≤ 2.5? [#permalink]
Show Tags
10 Feb 2018, 22:13
Hi dave13, Your approach to solving this problem isn't "wrong", but it appears "incomplete." You've determined the "upper limit" and lower limit" for what X could be (meaning that 2.5 <= X <= 7.5), but you did not factor in ALL of the given information. We're told that X MUST be an INTEGER, so given the range that you've determined... how many INTEGER values could X be? X could be 3, 4, 5, 6 or 7... meaning that there are 5 potential INTEGER solutions to this question. GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Senior Manager
Joined: 09 Mar 2016
Posts: 253

Re: How many integer values of x satisfy the inequality x  5 ≤ 2.5? [#permalink]
Show Tags
11 Feb 2018, 06:52
EMPOWERgmatRichC wrote: Hi dave13,
Your approach to solving this problem isn't "wrong", but it appears "incomplete."
You've determined the "upper limit" and lower limit" for what X could be (meaning that 2.5 <= X <= 7.5), but you did not factor in ALL of the given information. We're told that X MUST be an INTEGER, so given the range that you've determined... how many INTEGER values could X be?
X could be 3, 4, 5, 6 or 7... meaning that there are 5 potential INTEGER solutions to this question.
GMAT assassins aren't born, they're made, Rich Hello EMPOWERgmatRichC, Many thanks for your reply :) you know what confused? :? CASE 2 Case 2: x is negative x  5≤ 2.5 > x = 2.5 (Not valid, our initial condition was that x is negative but we got positivecase two was not valid so that's why I thought I again did something wrong, case two was invalid... could you explain the logic behind case TWO? what does "INVALID" mean ? thanks!



Math Expert
Joined: 02 Sep 2009
Posts: 43898

Re: How many integer values of x satisfy the inequality x  5 ≤ 2.5? [#permalink]
Show Tags
11 Feb 2018, 07:08
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
dave13 wrote: Bunuel wrote: saswata4s wrote: How many integer values of x satisfy the inequality x  5 ≤ 2.5?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 x  5 ≤ 2.5; Get rid of modulus: 2.5 ≤ x  5 ≤ 2.5; Add 5 to all three parts: 2.5 ≤ x ≤ 7.5 Integer values of x that satisfy the inequality are 3, 4, 5, 6, and 7. So, 5 values. Answer: C. Hello Bunuel, Zeus of all real numbers and unreal numbers please show your kindness to mortal GMAT student by explaining what i did wrong in my solution below:) I approached this question by opening the modulus  modulus always is associated with opening modulus no ? x  5 ≤ 2.5 Case 1: x is positive x  5≤ 2.5 > x = 7.5 Case 2: x is negative x  5≤ 2.5 > x = 2.5 (Not valid, our initial condition was that x is negative but we got positive. So whats wrong with my approach ? When opening the modulus you should consider the EXPRESSION being positive or negative, not x. The simplest approach is given in my post but if we solve the way you are going then we'd have the following. x  5 ≤ 2.5 When x  5 < 0 (NOT x), so when x < 5, we'd have (x  5) ≤ 2.5 > \(x \geq 2.5\). Since we consider the range when x < 5, then for this range we'd have \(2.5 \leq x < 5\) When x  5 >= 0 (NOT x), so when x >= 5, we'd have x  5 ≤ 2.5 > \(x \leq 7.5\). Since we consider the range when x >= 5, then for this range we'd have \(5 \leq x \leq 7.5\) Combining both: \(2.5 \leq x \leq 7.5\) You should study articles below carefully: 10. Absolute Value [/list] For more check Ultimate GMAT Quantitative Megathread Hope it helps.
_________________
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




Re: How many integer values of x satisfy the inequality x  5 ≤ 2.5?
[#permalink]
11 Feb 2018, 07:08






