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# Range

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Intern
Joined: 25 Oct 2010
Posts: 43

Kudos [?]: 154 [0], given: 13

WE 1: 3 yrs

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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

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

Kudos [?]: 154 [0], given: 13

Manager
Joined: 30 Sep 2010
Posts: 56

Kudos [?]: 60 [0], given: 0

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11 Nov 2010, 09:24
y^2 < 64
OR |y| < 8
OR -8< y< 8

Kudos [?]: 60 [0], given: 0

Manager
Joined: 01 Nov 2010
Posts: 173

Kudos [?]: 50 [0], given: 20

Location: Zürich, Switzerland

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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.

Kudos [?]: 50 [0], given: 20

Retired Moderator
Joined: 02 Sep 2010
Posts: 793

Kudos [?]: 1186 [0], given: 25

Location: London

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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

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 $$-8<y<8$$
_________________

Kudos [?]: 1186 [0], given: 25

Re: Range   [#permalink] 11 Nov 2010, 14:18
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