If it is true that x-2 and x

Question

If it is true that x > -2 and x < 7, which of the following must be true? A. x > 2 B. x > -7 C. x< 2 D. -7 < x < 2 E. none of the above.

Bunuel · Accepted Answer

Option D is not correct since x could be 2-7 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 -11 , 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 -11 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.

EMPOWERgmatRichC · Answer

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

Bunuel · Answer

Given: -2<x<7.

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

Answer: B.

kuttingchai · Answer

Bunuel what is the reason B must be true ??? the range is -2 2 - no because x can be between -2 -7 -- the answer is true, is it because the values of x are always >-7 C. x< 2 - no because x can be between 21 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 · Answer

Check other similar questions from  Trickiest Inequality Questions Type: Confusing Ranges  (part of our  Special Questions Directory ).

Raxit85 · Answer

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!!

EMPOWERgmatRichC · Answer

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

ScottTargetTestPrep · Answer

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

kskumar · Answer

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

avigutman · Answer

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).

SUV0508 · Answer

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

Bunuel · Answer

I think your doubt is addresses couple of times above.

Check other similar questions from  Trickiest Inequality Questions Type: Confusing Ranges  (part of our  Special Questions Directory ).

Hope it helps.

BLTN · Answer

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

ArnauG · Answer

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.

Nsp10 · Answer

Bunuel ,

In the example you mentioned, what if instead of "or" there is "and"?
 If  -1<x<0  and  x>1 , then which of the following must be true about  x :

What should the answer be in that case? 
kindly help

Bunuel · Answer

The word "and" there would mean both conditions, –1 < x < 0 and x > 1, must be true  simultaneously . But that’s impossible, since x cannot be both less than 0 and greater than 1 at the same time. So the condition is invalid, and no value of x can satisfy it.

suburbMBA · Answer

This helped drive the point home. Really solid example.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards