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

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CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
Followers: 9

Kudos [?]: 348 [0], given: 4

If + |R| = 0, what are the possible values of R [#permalink]  30 Sep 2007, 15:06
If [R^(3)] + |R| = 0, what are the possible values of R?
VP
Joined: 08 Jun 2005
Posts: 1147
Followers: 6

Kudos [?]: 127 [0], given: 0

possible solutions for R = -1,0

CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
Followers: 9

Kudos [?]: 348 [0], given: 4

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: 1147
Followers: 6

Kudos [?]: 127 [0], given: 0

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: 2764
Location: New York City
Followers: 9

Kudos [?]: 348 [0], given: 4

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: 2764
Location: New York City
Followers: 9

Kudos [?]: 348 [0], given: 4

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: 5078
Location: Singapore
Followers: 22

Kudos [?]: 184 [0], given: 0

R^3 + |R| = 0

Possible values:
R = 0
R = -1
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