Option D is not correct since x could be 2<x<7. Otherwise your reasoning is correct.

We are given that \(-2<x<7\). The question is which of the following is true about \(x\)?

\(x>-7\) is true about \(x\), because as \(x\) is more than -2 then it's definitely more than -7.

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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Given: -2<x<7.

Now, any x from this true range is more than -7, so x>-7 must be true.

Answer: B.
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Bunuel

what is the reason B must be true ???

the range is -2<x<7


A. x > 2 - no because x can be between -2<x<2
B. x > -7 -- the answer is true, is it because the values of x are always >-7
C. x< 2 - no because x can be between 2<x<7
D. -7 < x < 2 - no beacuse x can be between -7<x<-2 ????
E. none of the above. - i actually went for E answer choice

in the another problem we had similar situation
ANY x from the ranges -1<x<0 and x>1 will definitely be more the -1. I didnot understood the reason there as well???

if-x-x-x-which-of-the-following-must-be-true-about-x-68886.html

Bunuel, what difficulty would you say this problem is? 600-700 sounds awfully high, I was putting it more in the mid 500's.

I'd say the difficulty level is ~600.
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Hi All,

This question has a real "quirky" design to it. To get the correct answer, you have to focus on the limitations given in the prompt. Consider ALL of the possibilities for X IN THE PROMPT, then select the answer that is TRUE for all of THOSE values.

To get you thinking in the proper way, consider the following....

If you KNOW that X = 0, is it true that X > -1?

Yes.

If you KNOW that 3 > X > 0, is it true that X > -10?

Yes.

Notice the pattern in the logic. I'm NOT presenting the idea that X is everything greater than -10. I'm just asking if, given the limitations, that the statement is TRUE.

As it stands, this type of "quirky design" doesn't show up on Test Day all that often, but plenty of standard questions WILL ask you for "what must be true?"

GMAT assassins aren't born, they're made,
Rich
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Brunel need your Help on this....

How can we say that option (B) X > -7 is correct because we are limited by X<7 and so our answer X>-7 could even yield an answer of X=8,9,..... (which is not correct answer/range)

Hence I selected option (E)

You are neglecting the fact that when we say -2<x<7, all these values ARE >-7. You pick any value in this range (-2<x<7) and you can very well say that x>-7. This isnt the case with options A,C and D.

Think of it this way. If I ask you to pick 1 number from -2<x<7, will it be >-7? The answer is ALWAYS YES. This is the reason why B is the correct answer. It is a tricky question.

Hope this helps.
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Engr2012 I understood that, but we should have been picking that option if we would have no other option to select for.

But in this case we have an option (E) none of the above, which can very well supersede the option for X>-7.

Please let me know if I am still missing on something else here.

In this particular question and for that matter for all must be true questions, you can only be sure of your answer if you can quote 1 example that will negate the given options.

For this question, (B) was a clear winner. Any number falling in the range -2<x<7 will always be true for x>-7. There is no example of a number that lies in the range -2<x<7 that does not satisfy x>-7. Had there been a single case of such a number, E would have been the correct answer.

Hope this helps.
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Check other similar questions from Trickiest Inequality Questions Type: Confusing Ranges (part of our Special Questions Directory).
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as from the given statement x takes value of -2<x<7 , it will always take value which is greater than -7 so b is the right option.

Hi, Bunuel / chetan2u / VeritasKarishma,

As problem is asking Must be true (instead of could be true) and potentially correct option, None of the above, is given, why can't OA be E?
Given: -2<x<7.
If, x = -6, then No,
If anything between -2 and 7, then Yes. So, doesn't the OA proves to be "could be true" instead of Must be true??
Plz shed some lights.
Thanks!!

Hi Raxit85,

This question has a real "quirky" design to it. To get the correct answer, you have to focus on the limitations given in the PROMPT. Consider ALL of the possibilities for X in the PROMPT, then select the answer that is TRUE for all of THOSE values.

To get you thinking in the proper way, consider the following....

If you KNOW that X = 0, is it true that X > -1?

Yes.

If you KNOW that 3 > X > 0, is it true that X > -10?

Yes - because ALL of the possible values of X are greater than -10.

Notice the pattern in the logic. I'm NOT presenting the idea that X is everything greater than -10. I'm just asking if, given the limitations, that the statement is TRUE.

As it stands, this type of "quirky design" doesn't show up on Test Day all that often, but plenty of standard questions WILL ask you for "what must be true?"

GMAT assassins aren't born, they're made,
Rich
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x > -2 and x < 7

=> All possible values of 'x': -2 < x < 7.

Only option that fits the given range is x > -7 as it says x > -2.

Answer B
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If it is true that x > -2 and x < 7, which of the following must be true?

A. x > 2
B. x > -7 CORRECT
C. x< 2
D. -7 < x < 2
E. none of the above.
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Solution:

If x > -2 and x < 7, the value of x is between -2 and 7. Because all of these values are greater than -7, then we know that x > -7.

This type of problem gives rise to a lot of confusion. Let’s consider two easier examples, to display the logic used in this question. If we know that x = 0, is it true that x > -5? Yes, it is. Here’s another one: If 3 < x < 7, is it true that x >1? Yes, it is true (because all possible values of x (any number between 3 and 7) are greater than 1). Notice that in both of these examples, we are NOT trying to reconstruct the domain of x, as this was already accomplished in the question stem. Rather, we are simply making a true statement about the value(s) of x.

Answer: B
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avigutman can you explain the above question using a Number line?

kskumar We know that x lives somewhere inside this region:
--------(-2)----------------------(7)------------

If it's helpful, you can insert 0 in the appropriate place, as well as any other numbers from the answer choices (-7 and 2).
It's important to note that the answer choices do not represent facts. The only fact here is the number line above. The answer choices are just questions.
Here's an analogy:
Fact: Avi is in Toronto
Which of the following must be true?
1) Avi is in Canada
2) Avi is in France
3) Avi is a doctor

Only 1 must be true. 2 is definitely false, and 3 may or may not be true.
Now, some might say how do you know 1 must be true? What if Avi is in Vancouver??
Well, the fact is that Avi is in Toronto, and the question is whether Avi is definitely in Canada. Not the other way around. So the direction of the logic is very important here.

If we apply that logic to the original question, using the number line, we should be able to answer it correctly.
Knowing that x lives somewhere inside that yellow range, yes, we can say definitively that x lives to the right of (-7).
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