Modulus:GPREP

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zaarathelab: Master | Next Rank: 500 Posts; Posts: 217; Joined: Sun Jan 10, 2010 1:39 pm; Thanked: 7 times; Followed by:1 members

Modulus:GPREP

by zaarathelab » Sun Dec 18, 2011 11:23 pm

Ok so this has been discussed before. Can you tell me where I am going wrong

Let x= -5

Sqrt (-(-5)*|-5|) = sqrt (5*|-5| = sqrt (5*-5) = 25i (when |-5| comes out of the modulus sign for algebraic manipulation it retains its original sign i.e. -5) - - - don't we follow this rule for other modulus questions?

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Source: Beat The GMAT — Data Sufficiency | Sun Dec 18, 2011 11:23 pm

pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pm; Thanked: 158 times; Followed by:21 members

by pemdas » Mon Dec 19, 2011 12:21 am

hey no, |-5| is 5.

the mod or absolute is always positive, Think about mode not as -ve or +ve number, but distance on the number line to the left and/or right. Mod is the distance and the numbers with diff. signs are the directors (left, right)

You are right |x| can be x=<0 and x>0, but only inside the mod like x=-2, |x|=|-2|

when you are solving inequalities and want to know the direction along the number line for the diff. values of x you consider several cases for x, when x=<0 and x>0. But only with the inequalities, in all other cases you apply |x|=positive value

Especially here, as the root(even number, i.e. squared, fourth, sixth, etc.) of negative number is not defined for GMAT (according to math conventions in exam). It may be the 3rd root (-27) for example which is correct as -3^3=-27 but not sq root (-3), because -3^2 is always 9.

In general, math (not GMAT) allows for the root of negative number to be assigned, then it's a complex number. In GMAT all numbers are real numbers.

zaarathelab wrote:Ok so this has been discussed before. Can you tell me where I am going wrong

Let x= -5

Sqrt (-(-5)*|-5|) = sqrt (5*|-5| = sqrt (5*-5) = 25i (when |-5| comes out of the modulus sign for algebraic manipulation it retains its original sign i.e. -5) - - - don't we follow this rule for other modulus questions?

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