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Range of a 1 element set? and square root doubt

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Director
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Range of a 1 element set? and square root doubt [#permalink] New post 19 Feb 2013, 07:09
Bunuel/Karishma,

1) What is the range of a 1 element set?

2) say x square > 2

then root(x)> root 2
=> |x| >root 2

=>

x>root 2 and x< -ve root 2

Is this right? Kindly explain.
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Re: Range of a 1 element set? and square root doubt [#permalink] New post 19 Feb 2013, 07:18
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Sachin9 wrote:
Bunuel/Karishma,

1) What is the range of a 1 element set?

2) say x square > 2

then root(x)> root 2
=> |x| >root 2

=>

x>root 2 and x< -ve root 2

Is this right? Kindly explain.


1. The range of a one element set is 0.

2. x^2 > 2

x^2 - 2 > 0

(x + \sqrt{2})(x - \sqrt{2}) > 0

So,x < -\sqrt{2} or x > \sqrt{2}
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Director
Director
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Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 548
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 2

Kudos [?]: 34 [0], given: 562

Re: Range of a 1 element set? and square root doubt [#permalink] New post 19 Feb 2013, 07:26
MacFauz wrote:
Sachin9 wrote:
Bunuel/Karishma,

1) What is the range of a 1 element set?

2) say x square > 2

then root(x)> root 2
=> |x| >root 2

=>

x>root 2 and x< -ve root 2

Is this right? Kindly explain.


1. The range of a one element set is 0.

2. x^2 > 2

x^2 - 2 > 0

(x + \sqrt{2})(x - \sqrt{2}) > 0

So,x < -\sqrt{2} or x > \sqrt{2}


Thanks mate but what I have deduced above is correct?

And why is the range of 1 element set 0? I know SD is zero because you get zero by substituting the number in its formula.
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : end-of-my-gmat-journey-149328.html#p1197992

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Moderator
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User avatar
Joined: 02 Jul 2012
Posts: 1227
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
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Re: Range of a 1 element set? and square root doubt [#permalink] New post 19 Feb 2013, 07:38
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Sachin9 wrote:
MacFauz wrote:
Sachin9 wrote:
Bunuel/Karishma,

1) What is the range of a 1 element set?

2) say x square > 2

then root(x)> root 2
=> |x| >root 2

=>

x>root 2 and x< -ve root 2

Is this right? Kindly explain.


1. The range of a one element set is 0.

2. x^2 > 2

x^2 - 2 > 0

(x + \sqrt{2})(x - \sqrt{2}) > 0

So,x < -\sqrt{2} or x > \sqrt{2}


Thanks mate but what I have deduced above is correct?

And why is the range of 1 element set 0? I know SD is zero because you get zero by substituting the number in its formula.

The range of a set is the difference between the set's highest element and lowest element.. In a single element set both are the same and hence the difference is 0.
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Re: Range of a 1 element set? and square root doubt [#permalink] New post 19 Feb 2013, 20:30
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Expert's post
Sachin9 wrote:
Bunuel/Karishma,

1) What is the range of a 1 element set?

2) say x square > 2

then root(x)> root 2
=> |x| >root 2

=>

x>root 2 and x< -ve root 2

Is this right? Kindly explain.


Yes, this is another way of putting it.

x^2 > 2
This is equivalent to |x|^2 > 2
Taking square root since both sides are positive,
|x| > \sqrt{2}

So x > \sqrt{2} or x < - \sqrt{2}

Though, I feel that tackling it using inequalities is more straight forward.
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Re: Range of a 1 element set? and square root doubt   [#permalink] 19 Feb 2013, 20:30
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