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# If + |R| = 0, what are the possible values of R

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CEO
Joined: 21 Jan 2007
Posts: 2739
Location: New York City
If + |R| = 0, what are the possible values of R [#permalink]

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30 Sep 2007, 16:06
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If [R^(3)] + |R| = 0, what are the possible values of R?
VP
Joined: 08 Jun 2005
Posts: 1145

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30 Sep 2007, 16:10
possible solutions for R = -1,0

CEO
Joined: 21 Jan 2007
Posts: 2739
Location: New York City

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30 Sep 2007, 16:17
KillerSquirrel wrote:
possible solutions for R = -1,0

Given: [R^(3)] + |R| = 0

the absolute of any number is positive. Therefore, |R| is any positive number.

[R^(3)] + + = 0
[R^(3)] must be negative in order for the equation to balance out to 0.

if R is negative, raised to an odd exponent, [R^(3)] will be negative. Therefore, R is positive negative number that is the opposite of |R|.

How did you get -1, 0?
VP
Joined: 08 Jun 2005
Posts: 1145

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30 Sep 2007, 16:22
R = -1

(-1^(3)) + |-1| = 0

-1+1 = 0

or

R = 0

(0^(3)) + |0| = 0

0+0 = 0

CEO
Joined: 21 Jan 2007
Posts: 2739
Location: New York City

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30 Sep 2007, 18:03
KillerSquirrel wrote:
R = -1

(-1^(3)) + |-1| = 0

-1+1 = 0

or

R = 0

(0^(3)) + |0| = 0

0+0 = 0

Is there a way to approach this without plugging in the variables? I cant just pull them out the air when im taking the GMAT
CEO
Joined: 21 Jan 2007
Posts: 2739
Location: New York City

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30 Sep 2007, 18:18
bmwhype2 wrote:
KillerSquirrel wrote:
R = -1

(-1^(3)) + |-1| = 0

-1+1 = 0

or

R = 0

(0^(3)) + |0| = 0

0+0 = 0

Is there a way to approach this without plugging in the variables? I cant just pull them out the air when im taking the GMAT

all right. figured it out.

absolute values can be positive or zero.
therefore, R from |R| is 0 or any positive number.
If R is 0, then Rcubed is zero. This is possible only when 0 is the base.

If R is positive 1, then Rcubed must be -1 to balance the equation. R from Rcubed must be -1.

If R is positive 2, the equation cannot balance.....

Therefore, R= 0 or -1.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

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01 Oct 2007, 00:27
R^3 + |R| = 0

Possible values:
R = 0
R = -1
01 Oct 2007, 00:27
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