Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50005

If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
12 Mar 2014, 00:07
Question Stats:
46% (01:56) correct 54% (02:03) wrong based on 1537 sessions
HideShow timer Statistics
The Official Guide For GMAT® Quantitative Review, 2ND EditionIf 4<(7x)/3, which of the following must be true? I. 5<x II. x+3>2 III. (x+5) is positive (A) II only (B) III only (C) I and II only (D) II and III only (E) I, II and III Problem Solving Question: 156 Category: Algebra Inequalities Page: 82 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a solution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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




Math Expert
Joined: 02 Sep 2009
Posts: 50005

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
12 Mar 2014, 00:10
SOLUTIONIf 4<(7x)/3, which of the following must be true?
I. 5<x II. x+3>2 III. (x+5) is positive(A) II only (B) III only (C) I and II only (D) II and III only (E) I, II and III Note that we are asked to determine which MUST be true, not could be true. \(4<\frac{7x}{3}\) > \(12<7x\) > \(x<5\). So we know that \(x<5\), it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range \(x<5\). Basically the question asks: if \(x<5\) which of the following is true? I. \(5<x\) > not true as \(x<5\). II. \(x+3>2\), this inequality holds true for 2 cases, (for 2 ranges): 1. when \(x+3>2\), so when \(x>1\) or 2. when \(x3>2\), so when \(x<5\). We are given that second range is true (\(x<5\)), so this inequality holds true. Or another way: ANY \(x\) from the range \(x<5\) (5.1, 6, 7, ...) will make \(x+3>2\) true, so as \(x<5\), then \(x+3>2\) is always true. III. \((x+5)>0\) > \(x<5\) > true. Answer: D.
_________________
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




Director
Joined: 25 Apr 2012
Posts: 692
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
12 Mar 2014, 00:56
If 4<(7x)/3, which of the following must be true?
I. 5<x II. x+3>2 III. (x+5) is positive
(A) II only (B) III only (C) I and II only (D) II and III only (E) I, II and III
Sol:The given expression can be 4<(7x)/3 (multiply by 3) we get 12<7x or x<5 St 1 can be ruled out St 3 must be true So Option A,C and E can be ruled out Consider st 2 x+3>2 When x+3 >/ 0 then x+3= x+3 and also x>/3 or x+3> 2 or x>1 but our condition is x>/3 so x> 1 (because if x>1 then x surely is greater than 3) When x+3 <0 then x+3= (x+3) and the st2 equation becomes x+3<2 or x<5 and thus x<5 (because of x<5 then x <3 as well) So we have x >1 or x<5 > In this range the St 2 will hold good. But we are given that x<5 thus St 2 is true Ans is D....
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Current Student
Joined: 25 Sep 2012
Posts: 250
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31 GMAT 2: 680 Q48 V34

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
12 Mar 2014, 07:12
Solved the equation to get x < 5 As the question says must be true, it means that for any below 5 the statements have to hold true. So just assumed it to be 6 in every statement
Answer D Time Taken 1:25 Difficulty level 550



Intern
Joined: 16 Jan 2014
Posts: 12
Concentration: Operations, Sustainability
GPA: 3.12
WE: Supply Chain Management (Manufacturing)

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
12 Mar 2014, 08:42
Answer is D As statement 1 can be ruled out as from question statementx<5 statement 2 holds ok as modulus of lx+3l>2 : as from question statementx<5 staement 3 is also correct as from question statementx<5 therefore multiplication of 2 negative term is positive



Manager
Joined: 14 Jan 2013
Posts: 145
Concentration: Strategy, Technology
GMAT Date: 08012013
GPA: 3.7
WE: Consulting (Consulting)

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
21 Mar 2014, 05:10
Bunuel wrote: SOLUTION
If 4<(7x)/3, which of the following must be true?
I. 5<x II. x+3>2 III. (x+5) is positive
(A) II only (B) III only (C) I and II only (D) II and III only (E) I, II and III
Note that we are asked to determine which MUST be true, not could be true.
\(4<\frac{7x}{3}\) > \(12<7x\) > \(x<5\). So we know that \(x<5\), it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range \(x<5\).
Basically the question asks: if \(x<5\) which of the following is true?
I. \(5<x\) > not true as \(x<5\).
II. \(x+3>2\), this inequality holds true for 2 cases, (for 2 ranges): 1. when \(x+3>2\), so when \(x>1\) or 2. when \(x3>2\), so when \(x<5\). We are given that second range is true (\(x<5\)), so this inequality holds true.
Or another way: ANY \(x\) from the range \(x<5\) (5.1, 6, 7, ...) will make \(x+3>2\) true, so as \(x<5\), then \(x+3>2\) is always true.
III. \((x+5)>0\) > \(x<5\) > true.
Answer: D. Bunuel, For Statement 2, the red part does not hold true as X>1 but green part holds true. So in such situation when one part of inequality is true, does it qualify for " Must be true"?
_________________
"Where are my Kudos" ............ Good Question = kudos
"Start enjoying all phases" & all Sections
__________________________________________________________________ http://gmatclub.com/forum/collectionofarticlesoncriticalreasoning159959.html
http://gmatclub.com/forum/percentages700800levelquestions130588.html
http://gmatclub.com/forum/700to800levelquantquestionwithdetailsoluition143321.html



Intern
Joined: 12 Aug 2014
Posts: 17

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
04 Jan 2015, 05:49
Bunuel wrote: SOLUTION
If 4<(7x)/3, which of the following must be true?
I. 5<x II. x+3>2 III. (x+5) is positive
(A) II only (B) III only (C) I and II only (D) II and III only (E) I, II and III
Note that we are asked to determine which MUST be true, not could be true.
\(4<\frac{7x}{3}\) > \(12<7x\) > \(x<5\). So we know that \(x<5\), it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range \(x<5\).
Basically the question asks: if \(x<5\) which of the following is true?
I. \(5<x\) > not true as \(x<5\).
II. \(x+3>2\), this inequality holds true for 2 cases, (for 2 ranges): 1. when \(x+3>2\), so when \(x>1\) or 2. when \(x3>2\), so when \(x<5\). We are given that second range is true (\(x<5\)), so this inequality holds true.
Or another way: ANY \(x\) from the range \(x<5\) (5.1, 6, 7, ...) will make \(x+3>2\) true, so as \(x<5\), then \(x+3>2\) is always true.
III. \((x+5)>0\) > \(x<5\) > true.
Answer: D. For (2): X could be a positive number or a negative number, if x is a negative number than solving inequality would result into X < 5 which is true because it is the exact same inequality which has been given in the question. But if x would be positive that solving inequality would result into x >1 which would make the option (2) not true. So in other words when x is negative than statement (2) is true but when x is positive than statement (2) is not true. So statement (2) is not ALWAYS true. Can you please tell me why im unable to get the right answer? what is flaw in my reasoning?



Math Expert
Joined: 02 Sep 2009
Posts: 50005

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
05 Jan 2015, 03:28
mulhinmjavid wrote: Bunuel wrote: SOLUTION
If 4<(7x)/3, which of the following must be true?
I. 5<x II. x+3>2 III. (x+5) is positive
(A) II only (B) III only (C) I and II only (D) II and III only (E) I, II and III
Note that we are asked to determine which MUST be true, not could be true.
\(4<\frac{7x}{3}\) > \(12<7x\) > \(x<5\). So we know that \(x<5\), it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range \(x<5\).
Basically the question asks: if \(x<5\) which of the following is true?
I. \(5<x\) > not true as \(x<5\).
II. \(x+3>2\), this inequality holds true for 2 cases, (for 2 ranges): 1. when \(x+3>2\), so when \(x>1\) or 2. when \(x3>2\), so when \(x<5\). We are given that second range is true (\(x<5\)), so this inequality holds true.
Or another way: ANY \(x\) from the range \(x<5\) (5.1, 6, 7, ...) will make \(x+3>2\) true, so as \(x<5\), then \(x+3>2\) is always true.
III. \((x+5)>0\) > \(x<5\) > true.
Answer: D. For (2): X could be a positive number or a negative number, if x is a negative number than solving inequality would result into X < 5 which is true because it is the exact same inequality which has been given in the question. But if x would be positive that solving inequality would result into x >1 which would make the option (2) not true. So in other words when x is negative than statement (2) is true but when x is positive than statement (2) is not true. So statement (2) is not ALWAYS true. Can you please tell me why im unable to get the right answer? what is flaw in my reasoning? It should be other way around. To elaborate more. Question uses the same logic as in the examples below:If \(x=5\), then which of the following must be true about \(x\):A. x=3 B. x^2=10 C. x<4 D. x=1 E. x>10 Answer is E (x>10), because as x=5 then it's more than 10. Or: If \(1<x<10\), then which of the following must be true about \(x\):A. x=3 B. x^2=10 C. x<4 D. x=1 E. x<120 Again answer is E, because ANY \(x\) from \(1<x<10\) will be less than 120 so it's always true about the number from this range to say that it's less than 120. Or: If \(1<x<0\) or \(x>1\), then which of the following must be true about \(x\):A. x>1 B. x>1 C. x<1 D. x=1 E. x^2>1 As \(1<x<0\) or \(x>1\) then ANY \(x\) from these ranges would satisfy \(x>1\). So B is always true. \(x\) could be for example 1/2, 3/4, or 10 but no matter what \(x\) actually is it's IN ANY CASE more than 1. So we can say about \(x\) that it's more than 1. On the other hand for example A is not always true as it says that \(x>1\), which is not always true as \(x\) could be 1/2 and 1/2 is not more than 1. Hope it's clear.
_________________
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



Manager
Joined: 26 Feb 2015
Posts: 115

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
14 May 2015, 01:03
Bunuel wrote: mulhinmjavid wrote: Bunuel wrote: SOLUTION
If 4<(7x)/3, which of the following must be true?
I. 5<x II. x+3>2 III. (x+5) is positive
(A) II only (B) III only (C) I and II only (D) II and III only (E) I, II and III
Note that we are asked to determine which MUST be true, not could be true.
\(4<\frac{7x}{3}\) > \(12<7x\) > \(x<5\). So we know that \(x<5\), it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range \(x<5\).
Basically the question asks: if \(x<5\) which of the following is true?
I. \(5<x\) > not true as \(x<5\).
II. \(x+3>2\), this inequality holds true for 2 cases, (for 2 ranges): 1. when \(x+3>2\), so when \(x>1\) or 2. when \(x3>2\), so when \(x<5\). We are given that second range is true (\(x<5\)), so this inequality holds true.
Or another way: ANY \(x\) from the range \(x<5\) (5.1, 6, 7, ...) will make \(x+3>2\) true, so as \(x<5\), then \(x+3>2\) is always true.
III. \((x+5)>0\) > \(x<5\) > true.
Answer: D. For (2): X could be a positive number or a negative number, if x is a negative number than solving inequality would result into X < 5 which is true because it is the exact same inequality which has been given in the question. But if x would be positive that solving inequality would result into x >1 which would make the option (2) not true. So in other words when x is negative than statement (2) is true but when x is positive than statement (2) is not true. So statement (2) is not ALWAYS true. Can you please tell me why im unable to get the right answer? what is flaw in my reasoning? It should be other way around. To elaborate more. Question uses the same logic as in the examples below:If \(x=5\), then which of the following must be true about \(x\):A. x=3 B. x^2=10 C. x<4 D. x=1 E. x>10 Answer is E (x>10), because as x=5 then it's more than 10. Or: If \(1<x<10\), then which of the following must be true about \(x\):A. x=3 B. x^2=10 C. x<4 D. x=1 E. x<120 Again answer is E, because ANY \(x\) from \(1<x<10\) will be less than 120 so it's always true about the number from this range to say that it's less than 120. Or: If \(1<x<0\) or \(x>1\), then which of the following must be true about \(x\):A. x>1 B. x>1 C. x<1 D. x=1 E. x^2>1 As \(1<x<0\) or \(x>1\) then ANY \(x\) from these ranges would satisfy \(x>1\). So B is always true. \(x\) could be for example 1/2, 3/4, or 10 but no matter what \(x\) actually is it's IN ANY CASE more than 1. So we can say about \(x\) that it's more than 1. On the other hand for example A is not always true as it says that \(x>1\), which is not always true as \(x\) could be 1/2 and 1/2 is not more than 1. Hope it's clear. I still don't understand the application of this, to the question. Sure, I understand that if x = 5 its > 10. But, here, we get two different cases. Solving the question stem we get x < 5. In "II" we have that x is either x < 5 or x > 1. If I plug in a value where x > 1. Say x = 3. The equation doesn't hold? We get 4 < (73)/3 > 12 < 4. Not true? How can this be a valid answer choice then Edit: Don't know if this is how you should go about doing it, correct me if I'm wrong:
If we have \(x < 5.\)
Plugging in a value < 5, say 6 into II: \(6+3 > 2\). This holds true, aka sufficient



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2069

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
14 May 2015, 02:17
Quote: I still don't understand the application of this, to the question. Sure, I understand that if x = 5 its > 10.
But, here, we get two different cases. Solving the question stem we get x < 5.
In "II" we have that x is either x < 5 or x > 1. If I plug in a value where x > 1. Say x = 3. The equation doesn't hold?
We get 4 < (73)/3 > 12 < 4. Not true?
How can this be a valid answer choice then
Edit: Don't know if this is how you should go about doing it, correct me if I'm wrong:
If we have \(x < 5.\)
Plugging in a value < 5, say 6 into II: \(6+3 > 2\). This holds true, aka sufficient Hi erikvm, Let me explain the solution to you using the representation on number line. We need to evaluate if for every value in the range of the question statement i.e. x < 5, do the statements hold true. Refer the below diagram for the range given to us in the question & the other statements: Question Statement: The question statement gives us the range as x < 5. We need to see for every value of x < 5, are the inequality in the statements true. StatementI: StI gives us the range as x > 5. We see that this range does not hold true for any value of x. Hence, it can't be true. StatementII: StII gives us the range as x > 1 or x < 5. We see that for every value of x < 5 (i.e. the inequality in the question statement), we can write x +3 > 2 holds. Hence this is a must be true statement. StatementIII: StIII gives us the range as x < 5 which is nothing but the range in question statement. Hence this is a must be true statement. Therefore, stII & III are true for every value of x < 5 and hence must be true statements. Hope its clear Regards Harsh
_________________
Register for free sessions 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
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2 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



Manager
Joined: 26 Feb 2015
Posts: 115

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
19 May 2015, 06:12
Thanks, I'm just abit confused about the whole "must be true". I know how absolute values work, but \(x+3 > 2\) provides me with 2 different values for x, so I just assumed that this statement was not true because we have two different possibilities for X



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8399
Location: Pune, India

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
19 May 2015, 22:47
erikvm wrote: Thanks, I'm just abit confused about the whole "must be true". I know how absolute values work, but \(x+3 > 2\) provides me with 2 different values for x, so I just assumed that this statement was not true because we have two different possibilities for X Actually, \(x+3 > 2\) provides you infinite values of x. It gives you two ranges: x < 5 OR x > 1. The inequality implies that distance of x from 3 is more than 2. So x can lie to the right of 1 or to the left of 5. (Draw it on a number line to see). Hence you get two ranges: x < 5 OR x > 1 The question gives you that x < 5. So x will take any value less than 5. When it does, for all such values \(x+3 > 2\) will always be true because it holds for all values such that x < 5. It holds for some more values too (x > 1) but we don't care about those. All values that x can take in our question, for those \(x+3 > 2\) will always work. So \(x+3 > 2\) must be true.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Manager
Joined: 09 Jun 2015
Posts: 94

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
16 Mar 2016, 23:40
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf 4<(7x)/3, which of the following must be true? I. 5<x II. x+3>2 III. (x+5) is positive (A) II only (B) III only (C) I and II only (D) II and III only (E) I, II and III Problem Solving Question: 156 Category: Algebra Inequalities Page: 82 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you! The answer is B. Statement II is not always true. The question is about 'must be' true. What is given is x<5. There are not two answers. Statement II should produce a unique answer that satisfies x<5.



Manager
Joined: 09 Jun 2015
Posts: 94

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
16 Mar 2016, 23:56
VeritasPrepKarishma wrote: erikvm wrote: Thanks, I'm just abit confused about the whole "must be true". I know how absolute values work, but \(x+3 > 2\) provides me with 2 different values for x, so I just assumed that this statement was not true because we have two different possibilities for X Actually, \(x+3 > 2\) provides you infinite values of x. It gives you two ranges: x < 5 OR x > 1. The inequality implies that distance of x from 3 is more than 2. So x can lie to the right of 1 or to the left of 5. (Draw it on a number line to see). Hence you get two ranges: x < 5 OR x > 1 The question gives you that x < 5. So x will take any value less than 5. When it does, for all such values \(x+3 > 2\) will always be true because it holds for all values such that x < 5. It holds for some more values too (x > 1) but we don't care about those. All values that x can take in our question, for those \(x+3 > 2\) will always work. So \(x+3 > 2\) must be true. It is true, you need not care if the question is framed like 'which of the following is true for all values of x?'. Otherwise, you need to care. The problem is confirmation bias. Fallacy 1: Framing Fallacy 2: Appeal to Authority



Manager
Joined: 23 Jan 2016
Posts: 199
Location: India
GPA: 3.2

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
04 May 2016, 06:26
Why can statement 1 not be true? if we consider x to be negative, the question stem gives us x>5 as a possible result of x.
Thank you.



Math Expert
Joined: 02 Aug 2009
Posts: 6966

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
04 May 2016, 06:31
BobbyAssassinCross wrote: Why can statement 1 not be true? if we consider x to be negative, the question stem gives us x>5 as a possible result of x.
Thank you. Hi BobbyAssassinCross, look at the highlighted portion.. initially you start with x as ive and then get a +ive value for x as x>5.. so contradictory solution.. hence NOT possible
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Current Student
Joined: 18 Oct 2014
Posts: 856
Location: United States
GPA: 3.98

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
02 Jun 2016, 08:42
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf 4<(7x)/3, which of the following must be true? I. 5<x II. x+3>2 III. (x+5) is positive (A) II only (B) III only (C) I and II only (D) II and III only (E) I, II and III Problem Solving Question: 156 Category: Algebra Inequalities Page: 82 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you! 4<(7x)/3 12<(7x) 5<x x<5 That means x is ve and less than 5 Now lets look at the options I. 5<x not possible. we know that x<5 II. x+3>2 putting any ve value for x <5 will yield +ve value >2. True III. (x+5) is positive. Since X <5, expression (x5) will be ve and because it is multiplied by ve, it will give +ve result. True (D) II and III only is the answer
_________________
I welcome critical analysis of my post!! That will help me reach 700+



Manager
Joined: 21 Mar 2017
Posts: 141
Location: India
WE: Other (Computer Software)

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
03 Jan 2018, 23:46
Hi Bunuel can we think of 2nd statement as a Big set of ( 0,1,2,3,4,5 and also 6,7,8...) and what we need for must be true is a subset (6, 7, 8...) ? Is this correct?
_________________
 When nothing seem to help, I would go and look at a Stonecutter hammering away at his rock perhaps a hundred time without as much as a crack showing in it. Yet at the hundred and first blow it would split in two. And I knew it was not that blow that did it, But all that had gone Before.



Math Expert
Joined: 02 Sep 2009
Posts: 50005

If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
04 Jan 2018, 01:09
Prashant10692 wrote: Hi Bunuel can we think of 2nd statement as a Big set of ( 0,1,2,3,4,5 and also 6,7,8...) and what we need for must be true is a subset (6, 7, 8...) ? Is this correct? We are not given that x is necessarily an integer. For x + 3 > 2 to hold true, x < 5 or x > 1 must be true. We know that x < 5, so x + 3 > 2, will be true. Check other similar questions from Trickiest Inequality Questions Type: Confusing Ranges (part of our Special Questions Directory).
_________________
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



CEO
Joined: 12 Sep 2015
Posts: 3020
Location: Canada

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
06 Feb 2018, 15:48
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf 4<(7x)/3, which of the following must be true? I. 5<x II. x+3>2 III. (x+5) is positive (A) II only (B) III only (C) I and II only (D) II and III only (E) I, II and III First, let's deal with the given inequality. 4 < (7x)/3 Multiply both sides by 3 to get: 12 < 7  x Add x to both sides: x + 12 < 7 Subtract 12 from both sides to get: x < 5So, if x < 5, which of the following statements MUST be true? Aside: When dealing with "MUST be true" questions, we can eliminate a statement if we can find an instance where it is not true.I. 5 < x (MUST this be true?) No! If x < 5, then it could be the case that x = 7, and 7 is NOT greater than 5 So, statement I need NOT be true. II. x+3 > 2 (MUST this be true?) The answer is Yes. Here's why: IMPORTANT CONCEPT: x  k represents the DISTANCE between x and k on the number line. So, for example, we can think of 4  7 as the distance between 4 and 7 on the number line. Notice that 4  7 = 3 = 3, and 3 is indeed the distance between 4 and 7 on the number line. Now let's examine x+3 We can rewrite this as x  (3) This represents the DISTANCE between x and 3 on the number line. So, the inequality x(3) > 2 is stating that the DISTANCE between x and 3 on the number line is GREATER THAN 2 Well, since we're told that x < 5, we can be certain that the DISTANCE between x and 3 on the number line is definitely GREATER THAN 2 [If you're not convinced, sketch a number line, and place a big dot at 3. Then choose ANY value for x such that x < 5. You'll see that the distance between x and 3 is greater than 2] So, statement II MUST be true. III. (x+5) is positive This is the same as saying (x+5) > 0 (MUST this be true?) The answer is Yes. Here's why: We're told that x < 5If we add 5 to both sides we get x+5 < 0 Now, if we multiply both sides by 1, we get (x+5) > 0[aside: notice that, since I multiplied both sides by a negative value, I reversed the direction of the inequality] As we can see, statement III MUST be true. Answer: D Cheers, Brent
_________________
Brent Hanneson – GMATPrepNow.com
Sign up for our free Question of the Day emails




Re: If 4<(7x)/3, which of the following must be true? &nbs
[#permalink]
06 Feb 2018, 15:48



Go to page
1 2
Next
[ 24 posts ]



