NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 09:00 It is currently 26 Apr 2024, 09:00
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If 4x-12 >= x + 9, which of the following must be true

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
saxenagarima
Intern
Intern
Joined: 07 Sep 2010
Posts: 4
Own Kudos [?]: 90 [90]
Given Kudos: 4
Send PM
If 4x-12 >= x + 9, which of the following must be true [#permalink] New post   26 Sep 2010, 10:48
5
Kudos
85
Bookmarks
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

63% (00:49) correct 37% (00:54) wrong based on 1867 sessions
Hide Show timer Statistics
If 4x-12 >= x + 9, which of the following must be true

A. x > 6
B. x < 7
C. x > 7
D. x > 8
E. x < 8
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92945
Own Kudos [?]: 619191 [21]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: MGMAT Inequalities [#permalink] New post   26 Sep 2010, 13:53
11
Kudos
10
Bookmarks
Expert Reply
saxenagarima wrote:
Bunuel wrote:
saxenagarima wrote:
If 4x-12 >= x + 9, which of the following must be true

a) X > 6
b) X < 7
C) X > 7
D) X > 8
E) X < 8

I doubt the OA in MGMAT solutions


Given: \(4x-12\geq{x + 9}\) --> \(3x\geq{21}\) --> \(x\geq{7}\).

Only A is always true, as ANY \(x\) from the TRUE range \(x\geq{7}\) will be more than 6.

Answer: A.



But with A) x can be 6.1, which will not satisfy the given equation.....
shouldn't option C) be valid choice ....


It should be other way around.

We are given that \(x\geq{7}\). The question is: which of the following is true about \(x\)?

\(x>6\) is true about \(x\), because as \(x\) is more than (or equal to) 7 then it's definitely more than 6.

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.
General Discussion
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92945
Own Kudos [?]: 619191 [4]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: MGMAT Inequalities [#permalink] New post   26 Sep 2010, 10:52
3
Kudos
1
Bookmarks
Expert Reply
saxenagarima wrote:
If 4x-12 >= x + 9, which of the following must be true

a) X > 6
b) X < 7
C) X>7
D) X>8
E) X < 8

I doubt the OA in MGMAT solutions


Given: \(4x-12\geq{x + 9}\) --> \(3x\geq{21}\) --> \(x\geq{7}\).

Only A is always true, as ANY \(x\) from the TRUE range \(x\geq{7}\) will be more than 6.

Answer: A.

Similar question to practice: if-it-is-true-that-x-2-and-x-7-which-of-the-following-m-129093.html
avatar
saxenagarima
Intern
Intern
Joined: 07 Sep 2010
Posts: 4
Own Kudos [?]: 90 [0]
Given Kudos: 4
Send PM
Re: MGMAT Inequalities [#permalink] New post   26 Sep 2010, 11:32
Bunuel wrote:
saxenagarima wrote:
If 4x-12 >= x + 9, which of the following must be true

a) X > 6
b) X < 7
C) X > 7
D) X > 8
E) X < 8

I doubt the OA in MGMAT solutions


Given: \(4x-12\geq{x + 9}\) --> \(3x\geq{21}\) --> \(x\geq{7}\).

Only A is always true, as ANY \(x\) from the TRUE range \(x\geq{7}\) will be more than 6.

Answer: A.



But with A) x can be 6.1, which will not satisfy the given equation.....
shouldn't option C) be valid choice ....
User avatar
Joy111
Manager
Manager
Joined: 18 Oct 2010
Posts: 59
Own Kudos [?]: 552 [0]
Given Kudos: 26
Send PM
Re: MGMAT Inequalities [#permalink] New post   25 May 2012, 03:47
Bunuel wrote:
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.


just for the sake of learning please tell me how to evaluate option E. |X|^2>1

is it |x|>1 and |x|>-1

if |x|>1 then -1 >x>1

if |x|>-1 then how do we evaluate this part, confused here.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92945
Own Kudos [?]: 619191 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: MGMAT Inequalities [#permalink] New post   25 May 2012, 05:27
Expert Reply
Joy111 wrote:
Bunuel wrote:
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.


just for the sake of learning please tell me how to evaluate option E. |X|^2>1

is it |x|>1 and |x|>-1

if |x|>1 then -1 >x>1

if |x|>-1 then how do we evaluate this part, confused here.


|x|^2>1 is the same as x^2>1, so it holds true for x<-1 and x>1.

As for |x|>-1: it holds true for ANY value of x, because absolute value of a number is always non-negative.

Hope it helps.
User avatar
Joy111
Manager
Manager
Joined: 18 Oct 2010
Posts: 59
Own Kudos [?]: 552 [0]
Given Kudos: 26
Send PM
Re: MGMAT Inequalities [#permalink] New post   25 May 2012, 06:57
Bunuel wrote:
Joy111 wrote:
Bunuel wrote:
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.


just for the sake of learning please tell me how to evaluate option E. |X|^2>1

is it |x|>1 and |x|>-1

if |x|>1 then -1 >x>1

if |x|>-1 then how do we evaluate this part, confused here.


|x|^2>1 is the same as x^2>1, so it holds true for x<-1 and x>1.

As for |x|>-1: it holds true for ANY value of x, because absolute value of a number is always non-negative.

Hope it helps.


ok , thank you for that .

Now suppose |x|>-1 was one of the options of the question , then couldn't this have been one of the solutions .

can you please show how |x|>-1 fails to satisfy all the values of x in the equation

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|>-1

now for all values of x i.e x=-1/2, x=3 ,x=4, option E also is also satisfied .

seems to me that both A and E ,could be the solutions? please correct me . Thank you.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92945
Own Kudos [?]: 619191 [2]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: MGMAT Inequalities [#permalink] New post   25 May 2012, 07:21
1
Bookmarks
Expert Reply
Joy111 wrote:
ok , thank you for that .

Now suppose |x|>-1 was one of the options of the question , then couldn't this have been one of the solutions .

can you please show how |x|>-1 fails to satisfy all the values of x in the equation

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|>-1

now for all values of x i.e x=-1/2, x=3 ,x=4, option E also is also satisfied .

seems to me that both A and E ,could be the solutions? please correct me . Thank you.


The question in my example is as follows:

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

For this question E cannot be correct since if x=-1/2 then |x|^2>1 does not hold true.

Hope it's clear.
avatar
dcastan2
Intern
Intern
Joined: 28 Apr 2012
Posts: 13
Own Kudos [?]: 55 [0]
Given Kudos: 51
Send PM
Re: MGMAT Inequalities [#permalink] New post   11 Dec 2012, 21:21
Bunuel wrote:
saxenagarima wrote:
If 4x-12 >= x + 9, which of the following must be true

a) X > 6
b) X < 7
C) X>7
D) X>8
E) X < 8

I doubt the OA in MGMAT solutions


Given: \(4x-12\geq{x + 9}\) --> \(3x\geq{21}\) --> \(x\geq{7}\).

Only A is always true, as ANY \(x\) from the TRUE range \(x\geq{7}\) will be more than 6.

Answer: A.


Bunuel,
I must be reading the question incorrectly because I feel that after you get x>=7 you think 7=7 and 8>7 so the answer of x could 7 or 8 but since it is asking which is always greater than the answer would be D. 8. I don't see why we would look at it as x>6 when we solved the equation and got x>=7. How would the question need to be worded for that to be the case because I am really confused. I don't feel that in other OG questions we we replaced the x with a number smaller when it is asking what number is greater than or equal to a number larger. If that's the case, that means C, D, and E were the trap answers? I'd appreciate your help. Thanks!

If , then which of the following must be true about :
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.

And for this one I know it can't be A-D, but for E, x could be -9 which wouldn't necessarily mean that it is greater than 5? Would you choose it anyways?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92945
Own Kudos [?]: 619191 [1]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: MGMAT Inequalities [#permalink] New post   12 Dec 2012, 02:23
1
Kudos
Expert Reply
dcastan2 wrote:
Bunuel wrote:
saxenagarima wrote:
If 4x-12 >= x + 9, which of the following must be true

a) X > 6
b) X < 7
C) X>7
D) X>8
E) X < 8

I doubt the OA in MGMAT solutions


Given: \(4x-12\geq{x + 9}\) --> \(3x\geq{21}\) --> \(x\geq{7}\).

Only A is always true, as ANY \(x\) from the TRUE range \(x\geq{7}\) will be more than 6.

Answer: A.


Bunuel,
I must be reading the question incorrectly because I feel that after you get x>=7 you think 7=7 and 8>7 so the answer of x could 7 or 8 but since it is asking which is always greater than the answer would be D. 8. I don't see why we would look at it as x>6 when we solved the equation and got x>=7. How would the question need to be worded for that to be the case because I am really confused. I don't feel that in other OG questions we we replaced the x with a number smaller when it is asking what number is greater than or equal to a number larger. If that's the case, that means C, D, and E were the trap answers? I'd appreciate your help. Thanks!

If , then which of the following must be true about :
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.

And for this one I know it can't be A-D, but for E, x could be -9 which wouldn't necessarily mean that it is greater than 5? Would you choose it anyways?


I think you are confused about what is given and what is asked.

Given that \(x\geq{7}\), so \(x\) is some number which is more than or equal to 7. Now, the question asks, what must be true about \(x\) (which we know is more than or equal to 7).

If \(x\) is more than or equal to 7, then it must be true that \(x\) is greater than 6, thus A must be true.

The same with another example in your post: given that \(x=5\). The question asks, what must be true about \(x\). Since, \(x=5\), thus it's true to say that it's greater than -10.

Hope it's clear.
avatar
Moralhazard
Intern
Intern
Joined: 28 Jan 2012
Posts: 2
Own Kudos [?]: 13 [1]
Given Kudos: 3
Location: Viet Nam
Concentration: Entrepreneurship, Nonprofit
Schools: Haas '15 (S) Babson '15 (A) Sloan '15 (S) Weatherhead '15 (A$)
GMAT 1: 650 Q47 V33
GPA: 3.7
WE:Investment Banking (Non-Profit and Government)
Send PM
Re: If 4x-12 >= x + 9, which of the following must be true [#permalink] New post   13 Dec 2012, 16:02
1
Kudos
Hi Bunuel,
I am not quite satisfied with the OA. Since the question is not clear if x is an integer, for example x = 6.5 <7 => then it is not true. So the correct choice answer should be C

What do you think?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92945
Own Kudos [?]: 619191 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: If 4x-12 >= x + 9, which of the following must be true [#permalink] New post   14 Dec 2012, 02:27
Expert Reply
Moralhazard wrote:
Hi Bunuel,
I am not quite satisfied with the OA. Since the question is not clear if x is an integer, for example x = 6.5 <7 => then it is not true. So the correct choice answer should be C

What do you think?


We are not told that x is an integer but it has nothing to do with the question.

x cannot be 6.5 because we are told that \(x\geq{7}\).

Option C (x>7) is not always true, since x can be 7 and in this case x>7 won't hold true.

Hope it's clear.
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5962
Own Kudos [?]: 13391 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: If 4x - 12 > x + 9, which of the following must be true [#permalink] New post   13 Oct 2015, 00:11
Expert Reply
arhumsid wrote:
If \(4x - 12 > x + 9\), which o f the following must be true?

A. \(x > 6\)
B. \(x < 7\)
C. \(x > 7\)
D. \(x > 8\)
E. \(x < 8\)

Im confused with the 'must be true' part. Once you choose an answer, please explain why others cant be correct.


Solving \(4x - 12 > x + 9\)
i.e. \(4x - x > 12 + 9\)
i.e. \(3x > 21\)
i.e. \(x > 7\)

Answer: option C

A. \(x > 6\) is Incorrect because as per this option x may be 6.5 whereas x must be Essentially Greater than 7
B. \(x < 7\) is Completely Incorrect because x must be Essentially Greater than 7
C. \(x > 7\) is CORRECT (Exactly what we have derived)
D. \(x > 8\) is Incorrect because as per this option x can NOT be 7.5 whereas x must be Essentially Greater than 7 which can be 7.5 as well
E. \(x < 8\) is Incorrect because as per this option x can NOT be 8.5 whereas x must be Essentially Greater than 7 and can be anything greater than 8 as well

I hope this helps and clears your doubt!
User avatar
B
rishit1080
Manager
Manager
Joined: 19 Oct 2016
Posts: 54
Own Kudos [?]: 64 [0]
Given Kudos: 29
Location: India
Concentration: Marketing, Leadership
Schools: IIMA (I)
GMAT 1: 580 Q46 V24
GMAT 2: 540 Q39 V25
GMAT 3: 660 Q48 V34
GPA: 3.15
WE:Psychology and Counseling (Health Care)
Send PM
Re: If 4x-12 >= x + 9, which of the following must be true [#permalink] New post   06 Feb 2017, 10:26
Bunuel wrote:
saxenagarima wrote:
If 4x-12 >= x + 9, which of the following must be true

a) X > 6
b) X < 7
C) X>7
D) X>8
E) X < 8

I doubt the OA in MGMAT solutions


Given: \(4x-12\geq{x + 9}\) --> \(3x\geq{21}\) --> \(x\geq{7}\).

Only A is always true, as ANY \(x\) from the TRUE range \(x\geq{7}\) will be more than 6.

Answer: A.

Similar question to practice: https://gmatclub.com/forum/if-it-is-true ... 29093.html



Just wanted to let you know your post made me realize and go OHHHHHHHHHHHH! I get it now. Thanks B
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3043
Own Kudos [?]: 6277 [0]
Given Kudos: 1646
Send PM
Re: If 4x-12 >= x + 9, which of the following must be true [#permalink] New post   08 Feb 2017, 19:55
Expert Reply
saxenagarima wrote:
If 4x-12 >= x + 9, which of the following must be true

A. x > 6
B. x < 7
C. x > 7
D. x > 8
E. x < 8


Let’s solve the given inequality:

4x - 12 ≥ x + 9

3x ≥ 21

x ≥ 7

Thus, x must be greater than 6.

Answer: A
User avatar
L
Fdambro294
VP
VP
Joined: 10 Jul 2019
Posts: 1392
Own Kudos [?]: 542 [0]
Given Kudos: 1656
Send PM
If 4x-12 >= x + 9, which of the following must be true [#permalink] New post   09 Nov 2020, 22:16
4x - 12 >/= x + 9

after algebraic manipulation, you end up with:

x >/= 7


Q asks: Which of the following must be True?

the Question is effectively asking: which statement in the Answer Choices is a TRUE Statement for Every Possible Value that X can Take?

X can take every value from 7 - to - infinite

-C- X > 7

Since X can take the value of 7, the Statement X > 7 can be FALSE


-A- X > 6

for every value that X can take based on our GIVEN Constraint X >/= 7, we can say "yes, this X Value is greater than > 6"

-A- must be True
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
Own Kudos [?]: 16599 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: If 4x-12 >= x + 9, which of the following must be true [#permalink] New post   10 Nov 2020, 02:03
Expert Reply
4x - 12 ≥ x + 9

=> 4x - x ≥ 9 + 12

=> 3x ≥ 21

=> x ≥ 7

Option A: x > 6 satisfies it.

Answer A
User avatar
S
Mugdho
Manager
Manager
Joined: 27 Feb 2019
Posts: 95
Own Kudos [?]: 132 [0]
Given Kudos: 495
Send PM
Re: If 4x-12 >= x + 9, which of the following must be true [#permalink] New post   08 Apr 2021, 10:57
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.[/quote]


Hey Bunuel if we take x>-1 in 3rd example, like x=10, then this doesn’t satisfy x<0.. So what's the logic here ?

Posted from my mobile device
avatar
B
Trest
Intern
Intern
Joined: 22 Jul 2019
Posts: 13
Own Kudos [?]: 23 [1]
Given Kudos: 29
Send PM
Re: If 4x-12 >= x + 9, which of the following must be true [#permalink] New post   21 Oct 2021, 10:32
1
Kudos
What I found helped for must-be true questions is to find the statement that is OUTSIDE the range and is also true.

Given x >= 7, we can eliminate all the choices from B to E since points 7 and 8 they fall within that range.

A is the only option outside the range x >= 7 and the statement is also true.

These links helped: https://gmatclub.com/forum/veritas-prep ... l#p1858991
https://gmatclub.com/forum/veritas-prep ... l#p1772059
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32686
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If 4x-12 >= x + 9, which of the following must be true [#permalink] New post   06 Feb 2024, 07:53
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 Club Bot
gmatclubot
Re: If 4x-12 >= x + 9, which of the following must be true [#permalink]
06 Feb 2024, 07:53
Moderators:
Bunuel
Math Expert
92945 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions