Author 
Message 
TAGS:

Hide Tags

Director
Joined: 26 Feb 2006
Posts: 899

If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
12 Jan 2007, 23:48
7
This post received KUDOS
18
This post was BOOKMARKED
Question Stats:
57% (01:45) correct
43% (00:52) wrong based on 1363 sessions
HideShow timer Statistics
If x/3 > 1, which of the following must be true? A. x > 3 B. x < 3 C. x = 3 D. x ≠ 3 E. x < 3
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 17 Sep 2014, 05:25, edited 2 times in total.
Edited the question and added the OA.



SVP
Joined: 01 May 2006
Posts: 1796

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
13 Jan 2007, 02:30
3
This post received KUDOS
(D) for me
lxl / l3l > 1
<=> x > 3
<=> x > 3 or x < 3
So, the only answer choice that we are sure of is x ≠ 3



Manager
Joined: 01 Dec 2006
Posts: 56

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
13 Jan 2007, 06:44
D
For AK :
either x<3 or x>3 => the only one that will be always true is D X != 3



Senior Manager
Joined: 24 Nov 2006
Posts: 349

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
13 Jan 2007, 07:53
One more for D.
x > 3 => x cannot be = 3.



Senior Manager
Joined: 01 Feb 2005
Posts: 271

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
13 Jan 2007, 09:50
If lxl / l3l > 1, which of the following must be true?
1. x > 3
2. x < 3
3. x = 3
4. x ≠ 3
5. x < 3
Sorry guys for asking a very dumb question. But I missed something in the explanations.
When x/3 > 1. When I see a mod question, I have 2 alternatives
x/3 > 1 and x/3> 1
if you take x/3 > 1 ==> Multiply the 2 sides by 3 you get x > 3
if you take x/3 > 1 it becomes x/3 > 1 and if you multiply the 2 sides by 3 you get x> 3.
I am sure some I may have gotten my basics wrong... Sorry for the trouble. Can you guys explain what I am doing wrong?
Thanks
axl_oz



SVP
Joined: 01 May 2006
Posts: 1796

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
13 Jan 2007, 10:12
axl_oz wrote: If lxl / l3l > 1, which of the following must be true?
1. x > 3 2. x < 3 3. x = 3 4. x ≠ 3 5. x < 3
Sorry guys for asking a very dumb question. But I missed something in the explanations.
When x/3 > 1. When I see a mod question, I have 2 alternatives
x/3 > 1 and x/3> 1
if you take x/3 > 1 ==> Multiply the 2 sides by 3 you get x > 3
if you take x/3 > 1 it becomes x/3 > 1 and if you multiply the 2 sides by 3 you get x> 3.
I am sure some I may have gotten my basics wrong... Sorry for the trouble. Can you guys explain what I am doing wrong?
Thanks axl_oz
This part is the one that is wrong
If b is constant, then b = b when b > 0 and b = b when b < 0.
So, 3 = 3. It cannot be 3 .... A constant staying fxed at right or left of zero (ok on zero it could be as well ), we just choose one of the 2 sides. .
So, we have x / 3 > 1 ... and so on



Director
Joined: 26 Feb 2006
Posts: 899

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
13 Jan 2007, 12:25
I am trapped here. If x ≠ 3, x could be 2, 1, 0, 1, 2 or any fraction. Suppose if x = 2, how the equation, lxl / l3l > 1, holds true?
Pls explain.........
What If lxl / l3l > 1, which of the following must be true?
1. x > 3 2. x < 3 3. x = 3 4. x ≠ 3 5. x > 3
Last edited by Himalayan on 13 Jan 2007, 12:29, edited 1 time in total.



SVP
Joined: 01 May 2006
Posts: 1796

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
13 Jan 2007, 12:32
Himalayan wrote: Here is I am trapped. If x ≠ 3, x could be 2, 1, 0, 1, 2 or any fraction in between integers. Suppose if x = 2, how the equation, lxl / l3l > 1, holds true?
Pls explain.........
What If lxl / l3l > 1, which of the following must be true?
1. x > 3 2. x < 3 3. x = 3 4. x ≠ 3 5. x > 3
Actually, x ≠ 3 is directly saying x is different from 3 ... But, it is not stating on the real value of it.... So, it's true .... x ≠ 3 does not say x = 2.
By the way, what is the OA ?



Senior Manager
Joined: 12 Mar 2006
Posts: 365
Schools: Kellogg School of Management

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
14 Jan 2007, 17:37
i'm not sure what 3 means its just 3 right ?
If so x/3 > 1 => x > 3
so x < 3 or x > 3
so either way x <> 3
so D ?



Intern
Joined: 16 Feb 2007
Posts: 8

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
25 Feb 2007, 17:55
Himalayan wrote: If lxl / l3l > 1, which of the following must be true?
1. x > 3 2. x < 3 3. x = 3 4. x ≠ 3 5. x <3> 3.
In response to the comments above:
It is D, however the way the ACs are put is really crappy. x ≠ 3 means all numbers non 3.



Intern
Joined: 23 Feb 2013
Posts: 8

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
08 Mar 2013, 00:08
I dont know why I am not convinced with the answer. I eliminated B,C and D. D eliminated for the same reasons as mentioned above by few GMAT friends. Can someone please tell me why is A or B wrong ? A says that any value of X is above 3, which actually makes the LHS greater than 1. Example, I take the value of X as 10 (greater than 3),> 10/3 > 1 Same is the case with B. B states that any value of X is below 3, which again makes the LHS greater than 1 Example, I take the value of X as 10 (smaller than 3),> 10/3 > 1 Can someone please explain me, why these two answer choices does not come under MUST category ? Thanks
_________________
A Ship in port is safe but that is not what Ships are built for !



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 629

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
08 Mar 2013, 00:34
3
This post received KUDOS
Backbencher wrote: I dont know why I am not convinced with the answer. I eliminated B,C and D. D eliminated for the same reasons as mentioned above by few GMAT friends. Can someone please tell me why is A or B wrong ? A says that any value of X is above 3, which actually makes the LHS greater than 1. Example, I take the value of X as 10 (greater than 3),> 10/3 > 1 Same is the case with B. B states that any value of X is below 3, which again makes the LHS greater than 1 Example, I take the value of X as 10 (smaller than 3),> 10/3 > 1 Can someone please explain me, why these two answer choices does not come under MUST category ? Thanks The question asks "which of the following must be true". Thus, the answer choice must be valid and satisfy the given condition ALL the times. We can't choose A as because a value of x<3 also satisfies the given condition. Take x = 5, we still have the condition satisfied. Thus, it is not absolutely necessary that x has to be greater than 3. If the question would have asked which of the following choices COULD BE TRUE, then you could have selected A. The same goes for E as well. Any value of x, greater than 3, say x = 6 also satisfies the given condition. But for x =3, we can never get the given inequality, as then it equals one. Thus, x can never be equal to 3.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Math Expert
Joined: 02 Sep 2009
Posts: 39658

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
08 Mar 2013, 03:20
1
This post received KUDOS
Expert's post
5
This post was BOOKMARKED
Backbencher wrote: I dont know why I am not convinced with the answer. I eliminated B,C and D. D eliminated for the same reasons as mentioned above by few GMAT friends. Can someone please tell me why is A or B wrong ? A says that any value of X is above 3, which actually makes the LHS greater than 1. Example, I take the value of X as 10 (greater than 3),> 10/3 > 1 Same is the case with B. B states that any value of X is below 3, which again makes the LHS greater than 1 Example, I take the value of X as 10 (smaller than 3),> 10/3 > 1 Can someone please explain me, why these two answer choices does not come under MUST category ? Thanks If x / 3 > 1, which of the following must be true?A. x > 3 B. x < 3 C. x = 3 D. x ≠ 3 E. x < 3 Notice that if x = 3, then x / 3 = 3 / 3 = 1, so x / 3 is NOT more than 1, it's equal to 1. Thus if x = 3, the given inequality does NOT hold true. As for the other options. First, simplify the given inequity: x / 3 > 1 > x / 3 > 1 > x > 3 > x < 3 or x > 3. This is given as a fact. Now, if x < 3 or x > 3, then which of the options MUST be true? A. x > 3 > this option is not necessarily true since x could be less than 3, for example 4, which will make this options not true. B. x < 3 > this option is not necessarily true since x could be more than 3, for example 4, which will make this options not true. C. x = 3 > this option is NEVER true since we know that x < 3 or x > 3. D. x ≠ 3 > we know that x < 3 or x > 3. Thus x cannot be 3. Thus this option is true. E. x < 3 > this option is not necessarily true since x could be more than 3, for example 4, which will make this options not true. Answer: D. Similar questions to practice: ifxxxwhichofthefollowingmustbetrueaboutx68886.htmlif4x12x9whichofthefollowingmustbetrue101732.htmlAll must or could be true questions: search.php?search_id=tag&tag_id=193Hope it helps.
_________________
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



Intern
Joined: 23 Feb 2013
Posts: 8

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
13 Mar 2013, 00:35
Now I get it. I have to eliminate an option (even if its true) in a MUST BE TRUE questions, if there is any other choice that satisfies the conditions equally (Like and A and B). The only option that has no other alternative and satisfies the condition of the question is considered correct (Like D). Thanks Vinaymimani and Bunuel.
_________________
A Ship in port is safe but that is not what Ships are built for !



Manager
Joined: 15 Apr 2013
Posts: 86
Location: India
Concentration: Finance, General Management
WE: Account Management (Other)

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
16 May 2013, 10:00
1
This post received KUDOS
Hi,
It seems I have got a Problem here. what If X equals 3 ( Condition in D is satisfied since X is not 3 it is 3 ; I am fine if the variable in the condition is Mod X instead of X).
Can Someone Pls clarify?



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1122
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
16 May 2013, 10:05
pavan2185 wrote: Hi,
It seems I have got a Problem here. what If X equals 3 ( Condition in D is satisfied since X is not 3 it is 3 ; I am fine if the variable in the condition is Mod X instead of X).
Can Someone Pls clarify? \(\frac{x}{3}>1\) you can see it as \(x>3\) or x>3, x<3 If \(x=3\) \(\frac{3}{3}>1\) and this is 1>1 which is false. x cannot be 3, it's inside the range of values (\(3\leq{}x\leq{}3\)) that x cannot assume Hope it's clear now. Let me know
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Manager
Joined: 15 Apr 2013
Posts: 86
Location: India
Concentration: Finance, General Management
WE: Account Management (Other)

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
16 May 2013, 11:46
1
This post received KUDOS
Zarrolou wrote: pavan2185 wrote: Hi,
It seems I have got a Problem here. what If X equals 3 ( Condition in D is satisfied since X is not 3 it is 3 ; I am fine if the variable in the condition is Mod X instead of X).
Can Someone Pls clarify? \(\frac{x}{3}>1\) you can see it as \(x>3\) or x>3, x<3 If \(x=3\) \(\frac{3}{3}>1\) and this is 1>1 which is false. x cannot be 3, it's inside the range of values (\(3\leq{}x\leq{}3\)) that x cannot assume Hope it's clear now. Let me know Hi, Thanks for the quick response. I got that can not be 3, I just proposed that as a contradiction to the OA which is D here. Option D says It must be true that X does not equal 3. while It is correct, IMO It is not the only restriction we have here. X can not equal 3 as well ( Just as you explained ). so IMO Correct answer should reflect x > 3. Here None of the options reflect that condition. Am I missing something very basic here? Pavan.



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1122
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
16 May 2013, 11:56
1
This post received KUDOS
pavan2185 wrote: Hi, Thanks for the quick response. I got that can not be 3, I just proposed that as a contradiction to the OA which is D here. Option D says It must be true that X does not equal 3. while It is correct, IMO It is not the only restriction we have here. X can not equal 3 as well ( Just as you explained ). so IMO Correct answer should reflect x > 3. Here None of the options reflect that condition. Am I missing something very basic here? Pavan. It's simple: from the quesion we know that x cannot assume values \(3\leq{}x\leq{3}\) Of course D is not the only possible answer. You said "Here None of the options reflect that condition", but here we are not asked to find the range of possible values! We have to check if the values A,B,... fit with the condition above. Also x≠2 or ≠1 must be true for example, but we have to answer by looking at the possible answer. So which must be true? A. x > 3 B. x < 3 C. x = 3 D. x ≠ 3 <This one is correct E. x < 3 Hope it's clear now
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15947

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
17 Sep 2014, 03:34
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



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15947

Re: If x / 3 > 1, which of the following must be true? [#permalink]
Show Tags
22 Sep 2015, 02:13
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




Re: If x / 3 > 1, which of the following must be true?
[#permalink]
22 Sep 2015, 02:13



Go to page
1 2
Next
[ 24 posts ]




