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]

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

[Reveal] Spoiler: OA

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Re: MGMAT Inequalities [#permalink]

26 Sep 2010, 10:52

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.
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Re: MGMAT Inequalities [#permalink]

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 ....

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Re: MGMAT Inequalities [#permalink]

26 Sep 2010, 13:53

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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.

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.
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Re: MGMAT Inequalities [#permalink]

26 Sep 2010, 14:07

Thanks a lot Bunuel......

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Re: MGMAT Inequalities [#permalink]

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.

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Re: MGMAT Inequalities [#permalink]

25 May 2012, 05:27

Joy111 wrote:

Bunuel wrote:

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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Re: MGMAT Inequalities [#permalink]

25 May 2012, 06:57

Bunuel wrote:

Joy111 wrote:

Bunuel wrote:

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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Re: MGMAT Inequalities [#permalink]

25 May 2012, 07:21

Joy111 wrote:

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

10 Aug 2012, 08:07

4x-12>=x+9
3x>=21
x>=7

Only option A must be true. The rest of the options need not be true
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Re: MGMAT Inequalities [#permalink]

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?

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Re: MGMAT Inequalities [#permalink]

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.

Answer: A.

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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Re: MGMAT Inequalities [#permalink]

12 Dec 2012, 13:03

Yes, thank you Bunuel!

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

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?

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

14 Dec 2012, 02:27

Moralhazard wrote:

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] 14 Dec 2012, 02:27

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

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