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

Given: -2<x<7.

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

Answer: B.

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

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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

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

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).

Such a weird question. Pretty sure x>-7 means x∈(-7, +∞)
And that includes all those numbers which are not in the range -2<x<7
Hence I dont know how are we saying that x>-7 is a MUST be true statement

I think your doubt is addresses couple of times above.

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Hope it helps.

The question bewildered me. The easiest way to tack is to consider the border limits.

x > -2 and x < 7 - >> 7 > x> -2
So, we can take border values: -1 and 6

A. x > 2 ; 6 > 2 but -1 does not
B. x > -7 ; -1 > -7 and 6 > - 7
C. x< 2 ; -1 <2 but 6 does not
D. -7 < x < 2 ; does not work for 6

Maybe it helps someone

To determine which statements must be true given the conditions x > -2 and x < 7, let's evaluate each option:

A. x > 2: This statement is not necessarily true. Since x can be greater than -2 but less than or equal to 7, it doesn't guarantee that x is greater than 2.

B. x > -7: This statement is true. Since x is greater than -2, it is also greater than -7.

C. x < 2: This statement is not necessarily true. While x is less than 7, it can still be greater than or equal to 2.

D. -7 < x < 2: This statement is not necessarily true. While x is greater than -2, it can still be equal to or greater than 2.

E. none of the above: This is not the correct answer since option B, "x > -7," must be true given the conditions.

Therefore, the correct answer is B. x > -7.