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

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Senior Manager
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if it is true that x> -2 and x>7 ,which of the [#permalink]  18 Nov 2003, 10:11
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if it is true that x> -2 and x>7 ,which of the following must be ture?
A.x>2
B. X>-7
C.x<2
D.-7<x<2
E.none.
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shubhangi

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both A and B true. X, for sure, is >2 as X>7. And, whatever be the case, X will be >-7 as X>-2 and X>7...

isn't this ambiguous:?:
Senior Manager
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no its not.. actually its problme of inequality..
and you are wrong abt the first choice.. try once again
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shubhangi

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when you say X>7, it has to be greater than 2. And, when X>-2, it has to be greater than -7.

may be I am missing something.
Senior Manager
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infact .. when u see x is < or> than the negetive number the sign get changed .. imean in this case.. if x >-2 then it gets -2<x<7....then its not true to say x>2 st choice is wrong..
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shubhangi

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shubhangi,

What in the world are you talking about?
Director
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When you multiply by a negative and flip the inequality sign, you have to multiply x by a negative, too.

Is this what you're neglecting?
Manager
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shubhangi,

I think there is an error in the original problem. I've seen a few problems like this one and the problem you posted doesn't make sense. Could you verify it?
Director
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this problem doesn't seems logical...when you switch signs (-ve, +ve), you will have -x<2 from x>-2. that's just the same story.
chasing my tail off.
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Error [#permalink]  18 Nov 2003, 11:21
Hi shubhangi,
I agree with the wondergmat. I think there is an error in the original problem. By the way, is the question from OG ?
Sarnia
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Question does look strange but technically it is not wrong.

"it is true that x> -2 and x>7" implies x >7 always. For example 8 would satisfy that statement.

So the answer should be E
Intern
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shubhangi wrote:

If D is the answer, it's certain that the question is malformed. Please check the source.
Senior Manager
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if it is true that x> -2 and x>7 ,which of the following must be ture?
Now the values of x that will always satisfy above 2 inequalities will be:
x > 7.
Seems like choices are messed up.

Tips on inequalities (basics):
1) Multiply an inequality by a negative number and sign of inequality changes, for eg:
x < -2
or -x > 2 (multiply both sides by -1)

2) If two set of numbers a,b & x,y are positive
and x*a > y*b such that x < y
then a > b ( i remember seeing one question that tested this)
for example:
3*x^2 > 4*y^2 (here x^2, y^2 are positive numbers -squares)
Then, X^2 > Y^2

whereas, if 4*x^2 > 3*y^2
Then, i cannot conclude anything..!!

If X, Y are average of two sets of data then X, Y are always positive.

3) Mutiplying by a positive number, adding or subtracting any number (positive or negative) [u]does't change the sign of inequality.[/u]For example:
3 > -5 -----------a
then 9 > -15 (3 mutiplied on both sides of eq a)
Also, 0 > -8 (3 subtracted from both sides of eq a)
Also, 6>-2 (3 added on both sides of eq a)

thanks (kindly correct me if made a mistake...)
Director
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fyi..

found this problem in OG.. the question, actually, is X>-2 and X<7.

anyway, got decent information on inequalities..
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