Nice absolute value Q

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Tue Mar 03, 2009 3:24 pm

If xyz ≠ 0, is x (y + z) ≥ 0?
(1) │y + z│ = │y│ + │z│
(2) │x + y│ = │x│ + │y│

OA : C

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Source: Beat The GMAT — Data Sufficiency | Tue Mar 03, 2009 3:24 pm

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

by lilu » Tue Mar 03, 2009 6:35 pm

Statement 1:
ly+zl=lyl+lzl

This statement shows us that both y and z are either positive or both are negative.
Ex. l3+2l=l3l+l2l
or
l-3-2l=l-3l+l- 2l

but this is not enough to tell whether the whole expression x (y + z) is greater or equal to 0
INSUFF

Statement 2 is similar to Statement 1 and tells us that both x and y are either positive or negative.
Is not suff on its own.

Both statements taken together tell us that all three values are either all positive or all negative.

Ex.
3*(2+5)=21, that's greater than 0
or
(-3)*(-2-5)=21, that's greater than 0
so both statements tell us that the expression >0

Ans is C

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Tue Mar 03, 2009 7:25 pm

Lilu,
Good solution. Thats exactly the point in general if |x+y| = |x|+|y| they are both postive or both negative or both 0.

Since xyz <>0 either x,y,z cant be 0 in this problem

Regards,
Cramya

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