Tricky Problem

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mlaboda: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Sun Jan 25, 2009 2:34 pm; Thanked: 1 times

by mlaboda » Wed May 06, 2009 8:20 pm

Thanks for the help!
Is it true that the cube root of A < A?

1. A < 0

2. A > -1

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Source: Beat The GMAT — Data Sufficiency | Wed May 06, 2009 8:20 pm

mikeCoolBoy: Master | Next Rank: 500 Posts; Posts: 119; Joined: Tue Jan 20, 2009 10:16 pm; Thanked: 9 times; GMAT Score:730

by mikeCoolBoy » Wed May 06, 2009 11:54 pm

IMO C

1) not sufficient
A = -1/2 ---> -1/8 > -1/2
A = -2 ----> -8 < -2
2) not sufficient

A = 2 ---> 8 > 2
A = 1/2 ---> 1/8 < 1/2

both together -1 < A < 0 A = -1/2 ---> -1/8 > -1/2 sufficient

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bjp2008: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Tue Sep 30, 2008 6:36 am

by bjp2008 » Thu May 07, 2009 8:30 am

mikeCoolBoy wrote:IMO C

1) not sufficient
A = -1/2 ---> -1/8 > -1/2
A = -2 ----> -8 < -2
2) not sufficient

A = 2 ---> 8 > 2
A = 1/2 ---> 1/8 < 1/2

both together -1 < A < 0 A = -1/2 ---> -1/8 > -1/2 sufficient

Not able to understand A = -2 ----> -8 < -2.
If A= -2 cube root of A will be greater than -2. Even take more -ve number the cube root will always be greater than A. So (A) should be the answer.

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lilu: Master | Next Rank: 500 Posts; Posts: 148; Joined: Wed Dec 10, 2008 5:13 pm; Location: SF, CA; Thanked: 12 times

by lilu » Thu May 07, 2009 9:02 am

bjp2008 wrote:
mikeCoolBoy wrote:IMO C

1) not sufficient
A = -1/2 ---> -1/8 > -1/2
A = -2 ----> -8 < -2
2) not sufficient

A = 2 ---> 8 > 2
A = 1/2 ---> 1/8 < 1/2

both together -1 < A < 0 A = -1/2 ---> -1/8 > -1/2 sufficient
Not able to understand A = -2 ----> -8 < -2.
If A= -2 cube root of A will be greater than -2. Even take more -ve number the cube root will always be greater than A. So (A) should be the answer.

As mikeCoolBoy showed, if you have -1/2, -1/2^3=-1/8, which is greater than -1/2,so a greater cube of negative numbers is relevant for NEGATIVE FRACTIONS ONLY
And -2^3=-8, so -8<-2, so a cube will be less than the number for EVERYTHING LESS THAN ONE
And you can also notice than -1^3=-1, so here is another condition that proves that the first statement is INSUFF

The more you look, the more you see.

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