GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 05 Dec 2019, 11:23

### 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

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

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 07 Sep 2010
Posts: 5
If 4x-12 >= x + 9, which of the following must be true  [#permalink]

### Show Tags

26 Sep 2010, 10:48
2
36
00:00

Difficulty:

35% (medium)

Question Stats:

60% (00:50) correct 40% (00:55) wrong based on 948 sessions

### HideShow 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
Math Expert
Joined: 02 Sep 2009
Posts: 59561
Re: MGMAT Inequalities  [#permalink]

### Show Tags

26 Sep 2010, 13:53
10
5
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.

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
Math Expert
Joined: 02 Sep 2009
Posts: 59561
Re: MGMAT Inequalities  [#permalink]

### Show Tags

26 Sep 2010, 10:52
3
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.

Similar question to practice: if-it-is-true-that-x-2-and-x-7-which-of-the-following-m-129093.html
Intern
Joined: 07 Sep 2010
Posts: 5
Re: MGMAT Inequalities  [#permalink]

### Show Tags

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.

But with A) x can be 6.1, which will not satisfy the given equation.....
shouldn't option C) be valid choice ....
Intern
Joined: 07 Sep 2010
Posts: 5
Re: MGMAT Inequalities  [#permalink]

### Show Tags

26 Sep 2010, 14:07
Thanks a lot Bunuel......
Manager
Joined: 18 Oct 2010
Posts: 71
Re: MGMAT Inequalities  [#permalink]

### Show Tags

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.
Math Expert
Joined: 02 Sep 2009
Posts: 59561
Re: MGMAT Inequalities  [#permalink]

### Show Tags

25 May 2012, 05:27
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.
Manager
Joined: 18 Oct 2010
Posts: 71
Re: MGMAT Inequalities  [#permalink]

### Show Tags

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.
Math Expert
Joined: 02 Sep 2009
Posts: 59561
Re: MGMAT Inequalities  [#permalink]

### Show Tags

25 May 2012, 07:21
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.
Intern
Joined: 28 Apr 2012
Posts: 14
Re: MGMAT Inequalities  [#permalink]

### Show Tags

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.

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?
Math Expert
Joined: 02 Sep 2009
Posts: 59561
Re: MGMAT Inequalities  [#permalink]

### Show Tags

12 Dec 2012, 02:23
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.

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.
Intern
Joined: 28 Apr 2012
Posts: 14
Re: MGMAT Inequalities  [#permalink]

### Show Tags

12 Dec 2012, 13:03
Yes, thank you Bunuel!
Intern
Joined: 28 Jan 2012
Posts: 2
Location: Viet Nam
Concentration: Entrepreneurship, Nonprofit
GMAT 1: 650 Q47 V33
GPA: 3.7
WE: Investment Banking (Non-Profit and Government)
Re: If 4x-12 >= x + 9, which of the following must be true  [#permalink]

### Show Tags

13 Dec 2012, 16:02
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?
Math Expert
Joined: 02 Sep 2009
Posts: 59561
Re: If 4x-12 >= x + 9, which of the following must be true  [#permalink]

### Show Tags

14 Dec 2012, 02:27
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.
Math Expert
Joined: 02 Sep 2009
Posts: 59561
Re: If 4x-12 >= x + 9, which of the following must be true  [#permalink]

### Show Tags

19 Jun 2013, 04:52
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All Must or Could be True Questions to practice: search.php?search_id=tag&tag_id=193
Intern
Joined: 26 Sep 2012
Posts: 10
Location: United States
GMAT Date: 06-27-2014
GPA: 3.2
Re: If 4x-12 >= x + 9, which of the following must be true  [#permalink]

### Show Tags

14 Jan 2014, 06:47
I fell for D. It says which of the following must be true. x>8 holds good for all values.

Senior Manager
Joined: 15 Sep 2011
Posts: 305
Location: United States
WE: Corporate Finance (Manufacturing)
Re: If 4x-12 >= x + 9, which of the following must be true  [#permalink]

### Show Tags

30 Jun 2015, 18:31
Good question and great comments. The questions asks, not what x is, but what must be true for the "if" statement. If statement reduces to,
$$x\geq{7}$$

So, the answer must fit the form, "if [answer choice], then $$xgeq\{7}$$.

A) x>6 if x>6, then $$x\geq{7}$$. True.
B) x<7 if x<7, then $$x\geq{7}$$ is not true since x could equal 4.
C) x>7 if x>7, then $$x\geq{7}$$ is not true since x cannot equal 7.
D) x>8 if x>8, then $$x\geq{7}$$ is not true since x cannot equal 7 .
E) x<8 if x<8, then $$x\geq{7}$$ is not true since x cannot equal something like 10.

Hope this helps
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: If 4x - 12 > x + 9, which of the following must be true  [#permalink]

### Show Tags

13 Oct 2015, 00:11
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. $$x > 7$$

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!
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Manager
Joined: 19 Oct 2016
Posts: 64
Location: India
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)
Re: If 4x-12 >= x + 9, which of the following must be true  [#permalink]

### Show Tags

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.

Similar question to practice: http://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
Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: If 4x-12 >= x + 9, which of the following must be true  [#permalink]

### Show Tags

08 Feb 2017, 19:55
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.

_________________

# Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: If 4x-12 >= x + 9, which of the following must be true   [#permalink] 08 Feb 2017, 19:55

Go to page    1   2    Next  [ 22 posts ]

Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne