If 4x-12 >= x + 9, which of the following must be true : GMAT Problem Solving (PS)
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# If 4x-12 >= x + 9, which of the following must be true

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

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26 Sep 2010, 09:48
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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
[Reveal] Spoiler: OA
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26 Sep 2010, 09:52
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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
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26 Sep 2010, 10:32
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 ....
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26 Sep 2010, 12:53
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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.
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26 Sep 2010, 13:07
Thanks a lot Bunuel......
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25 May 2012, 02:47
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.
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25 May 2012, 04:27
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.
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25 May 2012, 05:57
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.
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25 May 2012, 06:21
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.
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11 Dec 2012, 20:21
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?
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12 Dec 2012, 01:23
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.
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12 Dec 2012, 12:03
Yes, thank you Bunuel!
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Re: If 4x-12 >= x + 9, which of the following must be true [#permalink]

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13 Dec 2012, 15:02
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?
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Re: If 4x-12 >= x + 9, which of the following must be true [#permalink]

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14 Dec 2012, 01:27
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.
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Re: If 4x-12 >= x + 9, which of the following must be true [#permalink]

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19 Jun 2013, 03:52
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

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Re: 4x - 12 ≥ x + 9, which of the following must be true? [#permalink]

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27 Dec 2013, 07:26
uwengdori wrote:
A) x>6
B) x<7
C) x>7
D) x>8
E) x<8

This is MGMAT's problem set question (algebra 5th edition pg 104)
The answer's reasoning is that for C), one of the most possible answers, can include 7, 7.3, 8 , 9.2 itself, so it's wrong which makes sense.

However, what I don't get is the reasoning behind A being the correct answer is that x could be 7, 7.3, 8, 9.2. Then, what about 6.3, 6.4 and so on?

4(6.4) - 12 ≥ 6.4 + 9
25.6 - 12 ≥ 15.4
13.5 ≥ 15.4

and this is wrong. Clarification on this would be appreciated.
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Re: If 4x-12 >= x + 9, which of the following must be true [#permalink]

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14 Jan 2014, 04:55
Bunuel,
I don't understand why OA is x>6
we already know for a fact that x>=7 so why not choose x>7 like the answer suggest .You have said that x>6 will always be true but so will be x>7.

Why cant we select the answer that is directly within the x>=7 range?
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Re: If 4x-12 >= x + 9, which of the following must be true [#permalink]

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14 Jan 2014, 05:47
I fell for D. It says which of the following must be true. x>8 holds good for all values.

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

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14 Jan 2014, 06:01
mumbijoh wrote:
Bunuel,
I don't understand why OA is x>6
we already know for a fact that x>=7 so why not choose x>7 like the answer suggest .You have said that x>6 will always be true but so will be x>7.

Why cant we select the answer that is directly within the x>=7 range?

aryabhatta wrote:
I fell for D. It says which of the following must be true. x>8 holds good for all values.

if-4x-12-x-9-which-of-the-following-must-be-true-101732.html#p788920
if-4x-12-x-9-which-of-the-following-must-be-true-101732.html#p1089335
if-4x-12-x-9-which-of-the-following-must-be-true-101732.html#p1153990

Similar question to practice: if-it-is-true-that-x-2-and-x-7-which-of-the-following-m-129093.html

Hope this helps.
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Re: If 4x-12 >= x + 9, which of the following must be true [#permalink]

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21 Jun 2015, 17:56
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Re: If 4x-12 >= x + 9, which of the following must be true   [#permalink] 21 Jun 2015, 17:56

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