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# Range

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Intern
Joined: 25 Oct 2010
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Range [#permalink]

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11 Nov 2010, 07:01
I have a doubt regarding range

If y^2 <64, then what is the range in which y exists

Answer: -8<y<8

I want to know the steps involved in solving this. And the logic.
Thanks or the help.
Manager
Joined: 30 Sep 2010
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Re: Range [#permalink]

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11 Nov 2010, 09:24
y^2 < 64
OR |y| < 8
OR -8< y< 8
Manager
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Re: Range [#permalink]

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11 Nov 2010, 12:35
1. Square of a negative or positive number is always positive.
2. Range of a set of numbers is defined as the greatest value in the data set minus the least value.
This indicates, y must fall within the +ve and -ve limits of 8.

Thus, the range of y should be 7 -(-7) = 14.
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Re: Range [#permalink]

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11 Nov 2010, 14:18
student26 wrote:
I have a doubt regarding range

If y^2 <64, then what is the range in which y exists

Answer: -8<y<8

I want to know the steps involved in solving this. And the logic.
Thanks or the help.

$$y^2<64$$
$$y^2-64<0$$
$$(y+8)(y-8)<0$$

Such an expression will be less than 0, if one term is negative and the other is positive. This will only happen when y is between 8 and -8 (Below -8, both terms are negative and above 8, both terms are positive)

Hence the range of $$y$$ is $$-8<y<8$$
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Re: Range   [#permalink] 11 Nov 2010, 14:18
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# Range

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