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Properties of numbers

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Properties of numbers

by anishprabhu » Wed Feb 18, 2009 3:10 pm
If x not equal to -y, is (x-y)/(x+y) >1

A. x>0
B. y<0

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Can anyone find fault with the below solution:
Solving algebraically,

Is (x-y)/ (x+y) > 1
is X-y > x+y
is -y > y
which is nothing but is Y negative.

Since B. states y<0 ans must be B
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by cramya » Wed Feb 18, 2009 3:15 pm
Is (x-y)/ (x+y) > 1
is X-y > x+y


Not allowed since we dont know anything about sign of x+y

If x+y was positive then what you did might work but lets say x+y was negative then the inequality reverses. The sign is something that needs to be watched out for when manipulating INEQUALITY PROBS.

Hope this helps!

Regards,
CR
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by anishprabhu » Wed Feb 18, 2009 4:48 pm
Thank You

For those wondering, the OA is E
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Re: Properties of numbers

by x2suresh » Wed Feb 18, 2009 8:38 pm
anishprabhu wrote:If x not equal to -y, is (x-y)/(x+y) >1

A. x>0
B. y<0

---------------------------------------------------


Can anyone find fault with the below solution:
Solving algebraically,

Is (x-y)/ (x+y) > 1
is X-y > x+y
is -y > y
which is nothing but is Y negative.

Since B. states y<0 ans must be B


(x-y)/(x+y) >1

--> (x-y)/(x+y) -1>0
--> 2x/x+y >0
--> 2/(1+y/x) >0

y/x> -1 --> +ve
y/x<-1 --> -ve

not sufficient

E
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by shargaur » Wed Mar 04, 2009 9:38 am
(x-y)/(x+y) >1

--> (x-y)/(x+y) -1>0
--> 2x/x+y >0
--> 2/(1+y/x) >0

y/x> -1 --> +ve
y/x<-1 --> -ve

==================
(x-y)/(x+y) >1
=> (x-y -x -y)/x+y >0
=> -2y/x+y >0
=> 2/{(x/y) + 1} < 0
=> x/y +1 < 0
=> x/y < -1
=> x<0 or y>0
or x>0 or y< 0 = > C
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