Take, y = 3 => x = 9 ----> x > yGHong14 wrote:x^y < y^x is x < y?
x = y²
Sufficient or not?
Take, y = 0.5 => x = 0.25 ----> x < y
NOT sufficient.
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Inequality
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Take, y = 0.5 => x = 0.25 ----> x < y
NOT sufficient.
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Dont' we have to take into account this condition that x^y < y^x?
Continuing with Anurag's numbers:
If y = 3 , x = 9
(9) ^ 3 < (3) ^ 9
True
If y = 1/2 x = 1/4
(1/4)^ (1/2) < (1/2) ^(1/4)
1/2 < (1/2)^(1/4)
True
Hence this condition is insuff.
Continuing with Anurag's numbers:
If y = 3 , x = 9
(9) ^ 3 < (3) ^ 9
True
If y = 1/2 x = 1/4
(1/4)^ (1/2) < (1/2) ^(1/4)
1/2 < (1/2)^(1/4)
True
Hence this condition is insuff.
statement: x=y^2 --> Sqrt(x)=|y|. Condition for y>0 i) when y is even, x >y; ii) when y is odd, x<y. We are let to decide with more than one statement, hence Not Sufficient.GHong14 wrote:x^y < y^x is x < y?
x=y^2
Sufficient or not?
since x = y^2GHong14 wrote:x^y < y^x is x < y?
x=y^2
Sufficient or not?
x ^y < y^x will be :
y^(2y) < y ^(y^2)
so , 2y = y^2 ; 2 < y
since y > 2 ... it confirms that y is +ve and greater than 2.
so it is sufficient.
statement: x=y^2 --> Sqrt(x)=|y|.
x=9, y={-3;3} --> x^y < y^x= 9^3 < 3^9 BUT 9^-3 > -3^9, hence not Sufficient
x=9, y={-3;3} --> x^y < y^x= 9^3 < 3^9 BUT 9^-3 > -3^9, hence not Sufficient
earnest10 wrote:since x = y^2GHong14 wrote:x^y < y^x is x < y?
x=y^2
Sufficient or not?
x ^y < y^x will be :
y^(2y) < y ^(y^2)
so , 2y = [<] y^2; //2y<y^2 --> sqrt(2y)< |y|, it's not correct to say that 2<y, because |y| = {-ve;+ve}, for example y=|3| while 2*3<3*3, 2*(-3)>(-3)*(-3); so it is not always possible for 2 < y// 2 < y
since y > 2 ... it confirms that y is +ve and greater than 2.
so it is sufficient.
