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Re: If it is true that x > -2 and x <7, which of the following m [#permalink]

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29 Jun 2012, 07:19

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???

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???

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.

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?"

Re: If it is true that x > -2 and x <7, which of the following m [#permalink]

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26 Feb 2016, 18:43

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)

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.

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.

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