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saxenagarima
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If 4x-12 >= x + 9, which of the following must be true 26 Sep 2010, 10:48
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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
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If 4x-12 >= x + 9, which of the following must be true 26 Sep 2010, 13:53
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saxenagarima
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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

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 ....
Show more

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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If 4x-12 >= x + 9, which of the following must be true 26 Sep 2010, 10:52
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saxenagarima
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
Show more

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
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If 4x-12 >= x + 9, which of the following must be true 26 Sep 2010, 11:32
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Bunuel
saxenagarima
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.
Show more


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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If 4x-12 >= x + 9, which of the following must be true 25 May 2012, 03:47
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Bunuel

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.
Show more

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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If 4x-12 >= x + 9, which of the following must be true 25 May 2012, 05:27
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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.
Show more

|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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If 4x-12 >= x + 9, which of the following must be true 25 May 2012, 06:57
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Bunuel

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.
Show more

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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If 4x-12 >= x + 9, which of the following must be true 25 May 2012, 07:21
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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.
Show more

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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If 4x-12 >= x + 9, which of the following must be true 11 Dec 2012, 21:21
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Bunuel
saxenagarima
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.
Show more

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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If 4x-12 >= x + 9, which of the following must be true 12 Dec 2012, 02:23
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Bunuel
saxenagarima
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?
Show more

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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If 4x-12 >= x + 9, which of the following must be true 13 Dec 2012, 16:02
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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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If 4x-12 >= x + 9, which of the following must be true 14 Dec 2012, 02:27
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Moralhazard
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?
Show more

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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If 4x-12 >= x + 9, which of the following must be true 13 Oct 2015, 00:11
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arhumsid
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.
Show more

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!
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If 4x-12 >= x + 9, which of the following must be true 06 Feb 2017, 10:26
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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

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
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Just wanted to let you know your post made me realize and go OHHHHHHHHHHHH! I get it now. Thanks B
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If 4x-12 >= x + 9, which of the following must be true 08 Feb 2017, 19:55
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saxenagarima
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
Show more

Let’s solve the given inequality:

4x - 12 ≥ x + 9

3x ≥ 21

x ≥ 7

Thus, x must be greater than 6.

Answer: A
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If 4x-12 >= x + 9, which of the following must be true 09 Nov 2020, 22:16
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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
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If 4x-12 >= x + 9, which of the following must be true 10 Nov 2020, 02:03
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4x - 12 ≥ x + 9

=> 4x - x ≥ 9 + 12

=> 3x ≥ 21

=> x ≥ 7

Option A: x > 6 satisfies it.

Answer A
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If 4x-12 >= x + 9, which of the following must be true 08 Apr 2021, 10:57
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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 ?

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If 4x-12 >= x + 9, which of the following must be true 21 Oct 2021, 10:32
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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
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If 4x-12 >= x + 9, which of the following must be true 11 Apr 2025, 09:51
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