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Inequality & absolute value (Mgmat)

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Source: — Data Sufficiency |
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by outreach » Tue Feb 16, 2010 8:53 pm
1)

LET X=2 ,Y=1
satisfies x·|y| > y2?
x=2,y=-1
satisifes since mod of -1 is 1
X=-1 ,Y=-2
does not satisy x·|y| > y2?
insufficient

2)
we do not what is x
insufficient


using 1 and 2 we can solve. hence answer is C
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by sars72 » Tue Feb 16, 2010 9:11 pm
(1) x > y
x=2, y = 1 --> 2>1? -> yes
x=2, y=0 --> 0>0? --> no

conflicting answers --> A,D are eliminated!
(2) y > 0
x=4, y = 0.25 --> 1>0.0625 --> yes
x=0, y= 1 -> 0> 1 --> no

conflicting answers --> B is eliminated!

combining both -> always true

--> C is the answer
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by thephoenix » Wed Feb 17, 2010 12:55 am
joyseychow wrote:Is x·|y| > y2?

(1) x > y

(2) y > 0


OA is C
when ever GMAT throws an openended eqn go for the extreme values
here as it is not mentioned that whether x is an integer or not or +ve or -ve , u can easily put two diff value either a fraction vs int or +ve vs -ve , however the +ve -ve test is always easier

if y is -ve say -2 and xis +ve 2
satisfies s1)

LHS of eqn becomes 4
and RHS becomes 4----->LHS=RHS and ans is no

now let y=2 and x=3
LHS=6
RHS=4---->LHS > RHS........ans is yes

so insuff

s2)Y>0
let x=-2 and y=3------>LHS=-6-------->RHS=9--------->LHS<RHS
let x=4 and y=3 ------>LHS=12 and RHS=9-------->LHS>RHS
two ans insuff

now
combining

x>y>0----> bth are +ve
combinataions can be 3>2>0----->LHS>RHS
or 1/2>1/4>0----->LHS=1/8>1/16=RHS------->LHS>RHS
ans yes
one ans and therfore suff
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