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Source: — Data Sufficiency |
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by pemdas » Thu Jan 26, 2012 9:56 am
st(1) sqrt(x)=y, implies x and y are positive and x=y^2. To answer the question x^y<y^x?
(y^2)^y is compared with y^(y^2) OR
y^2y VERSUS y^(y^2), obviously Not Sufficient, as for y=1, we get 1=1 BUT for y=3 we have 3^6 and 3^9

st(2) To answer the question x^y<y^x? we plug in, 2y^y VERSUS y^2y again Not Sufficient

combining st(1&2): x=y^2 and x=2y we get, y^2=2y OR y=2 and x=4
To answer the question x^y<y^x? 4^2 VERSUS 2^4 we answer No as x^y=y^x Sufficient

c

sud21 wrote:Is x^y less than or equal to y^x?
1). rootx=y
2). x=2y
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by ArunangsuSahu » Thu Jan 26, 2012 11:35 am
(C)
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by Anurag@Gurome » Thu Jan 26, 2012 7:43 pm
sud21 wrote:Is x^y less than or equal to y^x?
1). rootx=y
2). x=2y
(1) √x = y
Consider the following values of x and y:
1. x = 1/4 and y = 1/2 => x^y = (1/4)^(1/2) = 1/2 > y^x = (1/2)^(1/4)
2. x = 4, y = 2 => x^y = y ^x; NOT sufficient.

(2) x = 2y
Consider the following values of x and y:
1. x = 2 and y = 1 => x^y = (2)^(1) = 2 > y^x = (1)^(2) = 1
2. x = 4, y = 2 => x^y = y ^x; NOT sufficient.

Combining (1) and (2), √x = y = x/2 => (√x)² = (x/2)²
=> x = x²/4
=> 4x = x²
=> (x² - 4x) = 0
=> x(x - 4) = 0

Thus either (x = 0 and y = 0) or (x = 4 and y = 2)
For both of the cases x^y is equal to y^x; SUFFICIENT.

The correct answer is C.
Anurag Mairal, Ph.D., MBA
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