Absolute value & Inequality

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boazkhan: Master | Next Rank: 500 Posts; Posts: 135; Joined: Tue Oct 13, 2009 10:27 am; Thanked: 3 times

by boazkhan » Fri Apr 02, 2010 9:56 am

Is |a| + |b| > |a + b| ?

(1) a^3 > b^3

(2) b < 0

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Source: Beat The GMAT — Data Sufficiency | Fri Apr 02, 2010 9:56 am

suryapal: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Wed Mar 10, 2010 6:11 am; Thanked: 1 times

by suryapal » Fri Apr 02, 2010 10:02 am

my answer is E ... is it ???

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Fri Apr 02, 2010 10:27 am

boazkhan wrote:Is |a| + |b| > |a + b| ?

(1) a^3 > b^3

(2) b < 0

Step 1 of the Kaplan Method for DS: Analyze the Stem

When will the left side be greater than the right side?

Well, if a and b have the same sign, then the two sides will be equal.

If a and b have different signs, then the right side will be bigger.

So, here's the real question:

Do a and b have the same sign?

(1) a and b could both be positive or a could be positive and b negative: insufficient.

(2) nothing about a: insufficient.

Together: they could both be negative or a could be positive and b negative: still insufficient, choose E.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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boazkhan: Master | Next Rank: 500 Posts; Posts: 135; Joined: Tue Oct 13, 2009 10:27 am; Thanked: 3 times

by boazkhan » Fri Apr 02, 2010 1:11 pm

Thanks Stuart!

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Fri Jun 25, 2010 9:14 pm

Minor edit (thanks to viidyasagar) for noticing:

if the signs are different, the left side will be bigger, not the right side (the solution is the same).

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