Author 
Message 
TAGS:

Hide Tags

Current Student
Joined: 12 Aug 2015
Posts: 2552

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
10 Mar 2016, 10:59
[quote="mn2010"]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 Hey Everyone I am facing majo issues with this one .. the second statement specifies X>1 or X<5 now x can be 100 too hence it will make the inequality insufficient... I am rooting for B only Someone i the thread mentioned X<5 is given right... but what if X is 100 .. i have every statement in this thread and still believe the answer is B .. Can anyone tell me where am i doing wrong P.S => DON'T tell me X<5 IS GIVEN
_________________



Intern
Joined: 10 Feb 2016
Posts: 6
Location: Finland
Concentration: General Management, Strategy
WE: Information Technology (Computer Software)

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
20 Mar 2016, 14:54
try to plug in any number less than 5 and check because that's the condition given in question.
x < 5 means x can be 6,7,8 .... x+3>2 when x= 6 => 6+3>2 true when x=100 => 100+3>2 true



Intern
Joined: 13 Mar 2011
Posts: 21

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
01 Apr 2016, 02:17
Bunuel 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. Yes. Basically we are given that x<5 and then asked whether x+3>2 is true. We know that if x < 5, then x+3>2 must be true. Chiragjordan 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
Hey Everyone I am facing majo issues with this one .. the second statement specifies X>1 or X<5 now x can be 100 too hence it will make the inequality insufficient... I am rooting for B only
Someone i the thread mentioned X<5 is given right... but what if X is 100 .. i have every statement in this thread and still believe the answer is B ..
Can anyone tell me where am i doing wrong
P.S => DON'T tell me X<5 IS GIVEN Bunuel, Sorry that bother you but, in my humble opinion, it seems that Chiragjordan is correct. II is not true. A simple check can prove it : From II we have that Case A: x > 1 OR Case B: x < 5 From Case A let's take x = 0 4<[(7x)/3] => 4<[(70)/3]  is not true => Case A => is not working Because problem's type is MUST BE not COULD BE => the answer is B ( only III MUST BE true ) . Bunuel, please, could you confirm ?



Math Expert
Joined: 02 Sep 2009
Posts: 59730

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
01 Apr 2016, 02:26
leeto wrote: Bunuel, Sorry that bother you but, in my humble opinion, it seems that Chiragjordan is correct. II is not true. A simple check can prove it :
From II we have that Case A: x > 1 OR Case B: x < 5 From Case A let's take x = 0 4<[(7x)/3] => 4<[(70)/3]  is not true => Case A => is not working Because problem's type is MUST BE not COULD BE => the answer is B ( only III MUST BE true ) .
Bunuel, please, could you confirm ?
This is an OG question and the answer is D. There are several solutions given on previous pages. Sorry but I don't have anything much to add...
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 59730

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
01 Apr 2016, 02:33
Bunuel wrote: leeto wrote: Bunuel, Sorry that bother you but, in my humble opinion, it seems that Chiragjordan is correct. II is not true. A simple check can prove it :
From II we have that Case A: x > 1 OR Case B: x < 5 From Case A let's take x = 0 4<[(7x)/3] => 4<[(70)/3]  is not true => Case A => is not working Because problem's type is MUST BE not COULD BE => the answer is B ( only III MUST BE true ) .
Bunuel, please, could you confirm ?
This is an OG question and the answer is D. There are several solutions given on previous pages. Sorry but I don't have anything much to add... The 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.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 59730

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
01 Apr 2016, 02:36
Bunuel wrote: Bunuel wrote: leeto wrote: Bunuel, Sorry that bother you but, in my humble opinion, it seems that Chiragjordan is correct. II is not true. A simple check can prove it :
From II we have that Case A: x > 1 OR Case B: x < 5 From Case A let's take x = 0 4<[(7x)/3] => 4<[(70)/3]  is not true => Case A => is not working Because problem's type is MUST BE not COULD BE => the answer is B ( only III MUST BE true ) .
Bunuel, please, could you confirm ?
This is an OG question and the answer is D. There are several solutions given on previous pages. Sorry but I don't have anything much to add... The 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. Similar questions to practice: if4x12x9whichofthefollowingmustbetrue101732.htmlifitistruethatx2andx7whichofthefollowingm129093.html
_________________



Retired Moderator
Joined: 22 Jun 2014
Posts: 1090
Location: India
Concentration: General Management, Technology
GPA: 2.49
WE: Information Technology (Computer Software)

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
12 Apr 2016, 00:31
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 ???? Simplify 4<(7x)/3 and you get x < 5. Any of the statement says it would be true. (I) 5 < X i.e. X > 5 NOT true. (II) x+3>2  range for this is 5 < X < 5. True. (III) (x+5) i.e. x5 as x is less than 5 the values it would take will be 6, 7 and so on. in all these cases (x+5) will be positive. True Hence D is the correct answer.
_________________



Intern
Joined: 21 Jun 2014
Posts: 28

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
01 Nov 2016, 21:11
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. In II. x+3>2 If we have two cases where x>1 and x<5, then how can it MUST BE TRUE? Not 100% clear on this. Thanks for Looking into this. Sandeep



Intern
Joined: 29 Jul 2015
Posts: 12
Location: India
Concentration: Marketing, Strategy
WE: Information Technology (Retail Banking)

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
02 Jan 2017, 22:31
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. Regarding the option II shouldn't the condition x>1 be satisfied ?



Math Expert
Joined: 02 Sep 2009
Posts: 59730

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
03 Jan 2017, 02:02
Animatzer 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. Regarding the option II shouldn't the condition x>1 be satisfied ? Check here: if47x3whichofthefollowingmustbetrue99015.html#p853541
_________________



Manager
Joined: 03 Jan 2017
Posts: 134

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
23 Mar 2017, 08:02
let's simpify from the beginning: 12<7x x<5 let's test 1: doesn't work C,E out let's test 2: 6+3>2 works fine let's test 3: (6+5)= 1, hence, positive
Answer is D



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9876
Location: Pune, India

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
05 Apr 2017, 10:24
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 ???? Responding to a pm: Quote: In this question, I found that option two has two ranges. x >  or x < 5. So why this becomes sufficient? Don't we need only one clear answer to prove the sufficiency? If I have three ranges and one of them is good to prove the sufficiency, then also can we discard the other two?
You are given that x < 5. You obtain this because you are given that 4<(7x)/3. So x can take values such as 5.4, 6, 100, 54637 etc Which of the following MUST BE TRUE? II. x+3>2 Gives x < 5 OR x > 1 For every value that x can take, is this statement true? Yes. For every value that x can take it is "'less than 5" or "more than 1". All our values are actually "less than 5". We need x to satisfy either "x < 5" or "x > 1".
_________________
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 >



Math Expert
Joined: 02 Sep 2009
Posts: 59730

Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
Show Tags
29 May 2017, 22:50
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 ???? OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if47x3w ... 68681.html OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if47x3w ... 68681.html
_________________




Re: If 4<(7x)/3, which of the following must be true?
[#permalink]
29 May 2017, 22:50



Go to page
Previous
1 2
[ 33 posts ]



