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# IF it is true that x > -2 and x < 7, which of the

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Director
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IF it is true that x > -2 and x < 7, which of the [#permalink]  03 Sep 2005, 05:05
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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
C. x < 2
D. -7 < x < 2
E. None of the above

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Manager
Joined: 06 Aug 2005
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No it is B.

x>-7

The range is -2 < x < 7

A and C split that range so it can't be right.
D has numbers other way round.
Intern
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E.

the values of x will be: -2<x<7

(-6 is greater than -7 but x can't be -6, so D is wrong)
SVP
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Re: PS Inequalities [#permalink]  03 Sep 2005, 20:10
rahulraao wrote:
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

hmmm.... i thought i have answered it. Anyway, B is correct.
Intern
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B says x>-7, even 10 is greater than -7, but 10 cannot be the value ox x
Intern
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E should be the right answer.

Since x> -2 and x<7, x can be any number between these two values but x cannot be more than 7 or less than -2.

a) x>2 includes values that are more than 7, so it is not correct
b) x> -7 incudes values that are less than -2, so it is not correct
c) x< 2 includes values that can be less -2, so it is not always correct
d)x > -7 is inconsistent with the statement that x> -2
e) using poe E is the correct answer
Intern
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B is absolutely right. Rests are wrong.
It says "IF it is true that x > -2 and x < 7". In other words, -2<x<7.
THEREFORE, x logically is GREATER than -7, for all x.

D is wrong with x=5, for instance.

Hope this help.

tibeo - vietnam
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SVP
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acid_burn wrote:
E should be the right answer.

Since x> -2 and x<7, x can be any number between these two values but x cannot be more than 7 or less than -2.

a) x>2 includes values that are more than 7, so it is not correct
b) x> -7 incudes values that are less than -2, so it is not correct
c) x< 2 includes values that can be less -2, so it is not always correct
d)x > -7 is inconsistent with the statement that x> -2
e) using poe E is the correct answer

This is a classical question and classical mistake in answering this kind of questions.

When it says x<7 then it MUST be true that x is less than 8, or 9, etc. But x>-2, so it must be true that it is greater than -3, -4 etc. X may or may not be less than 6 if all we know is that it is less then 7. It may or may not be less than -1 if all we know is that it is greater than -2.

If the question is asked differently, then answer would be different. For example if the question is like this:
Which of the following statement will ensure x is less than 7 and greater than -2?
Then you would need to look at it from another perspective. If x is less than 7, 6 or 5 etc., then we would be able to ensure x is less than 7. If x is greater than -2, -1 or 0 etc., then we would be able to ensure x is less than -2.

Basically all we are deriving at is if one (A) is true, then the other (B) is always true. But we just need to know which one is A and which one is B.
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Director
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Guys,

Nice explanations! I really liked HongHu's logic! Thanks man!

OA is B
OA reasoning is almost in line with HongHu's logic, but rather unclear!
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