1. If x and y are non-negative, is (x + y)
greater than xy?
(1) x = y
(2) x + y is greater than x2 + y2
* x2 means x square.
Thanks..
Problem 1 -Data Sufficiency
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Stmt 1 - make x = y in the eqtn x+y>xy, x = y,
x^2 - 2x<0, which gives us 0<x<2, but x can be greater than 2 hence insufficient
Stmt 2 - x+y>x^2 + y^2 can only be true if 0<x<1 and 0<y<1. An interesting thing to note here is a boundary condition, wherein x or y could be = 1 but the other has to be still less than 1 and the equation holds. Now, when 0<x<1 and 0<y<1,
x+y>xy holds. Hence SUFFICIENT.
Ans B
OA please?
x^2 - 2x<0, which gives us 0<x<2, but x can be greater than 2 hence insufficient
Stmt 2 - x+y>x^2 + y^2 can only be true if 0<x<1 and 0<y<1. An interesting thing to note here is a boundary condition, wherein x or y could be = 1 but the other has to be still less than 1 and the equation holds. Now, when 0<x<1 and 0<y<1,
x+y>xy holds. Hence SUFFICIENT.
Ans B
OA please?
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imo ber.twi.fb wrote:1. If x and y are non-negative, is (x + y)
greater than xy?
(1) x = y
(2) x + y is greater than x2 + y2
* x2 means x square.
Thanks..
stem 1
x=y
putting in given situation
is 2x>x2
this can be true for 1, but not for 3 so insufficient
stem 2
x+y>x2+y2
add -2xy on both sides
x+y-2xy>(x-y)^2
x+y>(x-y)^2+2xy
since x and y both greater than 0
x+y is more than xy +xy + (x-y)^2
so x+y>xy
sufficient
IMOB
wats the OA
Success is a journey.....enjoy every moment of it
mj78ind wrote:Stmt 1 - make x = y in the eqtn x+y>xy, x = y,
x^2 - 2x<0, which gives us 0<x<2, but x can be greater than 2 hence insufficient
Stmt 2 - x+y>x^2 + y^2 can only be true if 0<x<1 and 0<y<1. An interesting thing to note here is a boundary condition, wherein x or y could be = 1 but the other has to be still less than 1 and the equation holds. Now, when 0<x<1 and 0<y<1,
x+y>xy holds. Hence SUFFICIENT.
Ans B
OA please?
Hi.
Answer is B. But I would like to have more clear explanation for this.
Thanks..