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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.

Re: If 4x-12 >= x + 9, which of the following must be true [#permalink]
10 Aug 2012, 07:07

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

Only option A must be true. The rest of the options need not be true _________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+

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?

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.

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

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

Expert's post

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.

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

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

Re: If 4x-12 >= x + 9, which of the following must be true [#permalink]
14 Jan 2014, 06:01

Expert's post

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.

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