Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 21 Jun 2010
Posts: 111
Schools: Tuck, Duke, Cambridge, Said

If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
12 Aug 2010, 15:05
11
This post received KUDOS
52
This post was BOOKMARKED
Question Stats:
45% (02:37) correct
55% (01:29) wrong based on 1836 sessions
HideShow timer Statistics
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 I am confused about statement II ???? OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if47x3w ... 68681.html
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 29 May 2017, 22:50, edited 3 times in total.
Hided spoiler



Math Expert
Joined: 02 Sep 2009
Posts: 40326

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
12 Aug 2010, 15:39
15
This post received KUDOS
Expert's post
17
This post was BOOKMARKED
mn2010 wrote: 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
I am not confused about statement II ???? Good question, +1. 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. Hope it's clear.
_________________
New to the Math Forum? Please read this: 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: 21 Jun 2010
Posts: 111
Schools: Tuck, Duke, Cambridge, Said

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
12 Aug 2010, 15:50
1
This post received KUDOS
thanks Bunuel... Inequality still rattles me .... more practice I guess ....



Manager
Joined: 27 May 2010
Posts: 102

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
14 Aug 2010, 08:50
thanks for the explanation bunuel.



Manager
Joined: 03 Jun 2010
Posts: 181
Location: United States (MI)
Concentration: Marketing, General Management
WE: Business Development (Consumer Products)

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
20 Dec 2010, 05:29
Great question. I thought we should eliminate II.



Senior Manager
Joined: 12 Dec 2010
Posts: 278
Concentration: Strategy, General Management
GMAT 1: 680 Q49 V34 GMAT 2: 730 Q49 V41
GPA: 4
WE: Consulting (Other)

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
16 Jan 2011, 20:15
Bunuel wrote: mn2010 wrote: 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
I am not confused about statement II ???? Good question, +1. 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. Hope it's clear. here for the x+3 >2 we have 2cases x> 1 or x <5 (while second one satisfies the condn as asked but is not it we should be looking at all the possibilities and if all satisfies then only we can say that this option also holds as for as GMAT is concerned ) so I am not clear about the explanation for II to be true.
_________________
My GMAT Journey 540>680>730!
~ When the going gets tough, the Tough gets going!



Math Expert
Joined: 02 Sep 2009
Posts: 40326

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
17 Jan 2011, 03:29
yogesh1984 wrote: Bunuel wrote: mn2010 wrote: 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
I am not confused about statement II ???? Good question, +1. 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. Hope it's clear. here for the x+3 >2 we have 2cases x> 1 or x <5 (while second one satisfies the condn as asked but is not it we should be looking at all the possibilities and if all satisfies then only we can say that this option also holds as for as GMAT is concerned ) so I am not clear about the explanation for II to be true. Is \(x+3>2\) true? > this inequality is true if \(x>1\) OR \(x<5\). Now, it's given that \(x<5\), so it must hold true. Or: 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. Hope it's clear.
_________________
New to the Math Forum? Please read this: 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
Joined: 12 Dec 2010
Posts: 278
Concentration: Strategy, General Management
GMAT 1: 680 Q49 V34 GMAT 2: 730 Q49 V41
GPA: 4
WE: Consulting (Other)

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
17 Jan 2011, 10:22
Quote: Is \(x+3>2\) true? > this inequality is true if \(x>1\) OR \(x<5\). Now, it's given that \(x<5\), so it must hold true.
Or: 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.
Hope it's clear. Hmm... It was so obvious thanks for your patience & reply
_________________
My GMAT Journey 540>680>730!
~ When the going gets tough, the Tough gets going!



Intern
Joined: 17 Jan 2011
Posts: 4

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
17 Jan 2011, 18:52
Nice one, got it myself as D



Math Expert
Joined: 02 Sep 2009
Posts: 40326

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
19 Jun 2013, 04:52



Intern
Joined: 13 May 2013
Posts: 2

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
21 Aug 2013, 08:41



Math Expert
Joined: 02 Sep 2009
Posts: 40326

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
21 Aug 2013, 08:44



Senior Manager
Joined: 19 Oct 2012
Posts: 296
Location: India
Concentration: General Management, Operations
GPA: 3.81
WE: Information Technology (Computer Software)

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
23 Aug 2013, 23:38
Good one! I got stumped with II, but now it makes more sense.
_________________
Citius, Altius, Fortius



Current Student
Joined: 03 Feb 2013
Posts: 941
Location: India
Concentration: Operations, Strategy
GPA: 3.88
WE: Engineering (Computer Software)

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
08 Jan 2014, 07:35
mn2010 wrote: 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
I am confused about statement II ???? 12 < 7x => x < 5 I. 5 < x not possible. II. x+3 > 2 . now x < 5 or lets say x = 5.1 so x+3 = 2.1 = 2.1 > 2 So any case, it will always be more than 2. Definitely. III. (x+5) as x < 5 so x can be 5.1 so (.1) so +ve hence III is also possible. hence D)
_________________
Thanks, Kinjal My Debrief : http://gmatclub.com/forum/hardworknevergetsunrewardedforever189267.html#p1449379 My Application Experience : http://gmatclub.com/forum/hardworknevergetsunrewardedforever18926740.html#p1516961 Linkedin : https://www.linkedin.com/in/kinjaldas/
Please click on Kudos, if you think the post is helpful



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16529

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
07 Mar 2015, 04:35
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Booth Thread Master
Affiliations: Scrum Alliance
Joined: 09 Feb 2010
Posts: 84
Location: United States (MI)
Concentration: Strategy, General Management
GMAT 1: 600 Q48 V25 GMAT 2: 710 Q48 V38
WE: Information Technology (Retail)

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
26 Aug 2015, 13:23
1
This post received KUDOS
1
This post was BOOKMARKED
I tried an alternate solution by plugging numbers Given that \(x < 5\), we could pick a number that satisfies this condition, lets say \(x = 7\) I. \(5 < x\), is \(5 < 7\), Not true, Eliminate II. \(x + 3 > 2\), plug in 7 in place of x, we get \( 7 + 3  > 2, 4 > 2\), True III. \( (x + 5) > 0,  ( 7 + 5) =  (2) = 2 > 0\), True Answer is D. II & III only
_________________
kudos please
Last edited by hideyoshi on 17 Feb 2016, 21:25, edited 1 time in total.



Intern
Joined: 23 Mar 2014
Posts: 2

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
04 Sep 2015, 22:06
mn2010 wrote: 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 I am confused about statement II ???? Correct answer is only III. According to II, x can be 2 or 10. But according to the given question x<5. Hence II can not be true always.



Math Expert
Joined: 02 Sep 2009
Posts: 40326

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
05 Sep 2015, 04:03



Manager
Joined: 06 Jun 2013
Posts: 151
Location: India
Concentration: Finance, Economics
GPA: 3.6
WE: Engineering (Computer Software)

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
23 Sep 2015, 09:27
got this question correct, but selected wrong option as statement D is partially correct .



Manager
Joined: 10 May 2014
Posts: 142

Re: If 4<(7x)/3, which of the following must be true? [#permalink]
Show Tags
02 Jan 2016, 15:15
Bunuel wrote: mn2010 wrote: 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
I am not confused about statement II ???? Good question, +1. 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. Hope it's clear. Hi Bunuel, Statements I and III are perfectly clear. But let me ask you a question about statement II to clear all my doubts, if you don´t mind. Question stem states that x < 5 and then asks "if this is true, then what else must be true?" Statement II gives us 2 options. Case A: x > 1 OR Case B: x < 5. Since the question stem already stated that x < 5, then Case A cannot be true (since x cannot be less than 5 and bigger than 1 at the same time) and Case B must be true. Therefore, Statement II must be true. Is this reasoning correct? Thank you so much!
_________________
Consider giving me Kudos if I helped, but don´t take them away if I didn´t!
What would you do if you weren´t afraid?




Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
02 Jan 2016, 15:15



Go to page
1 2
Next
[ 34 posts ]




