Inequality Algebric Solution required

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Inequality Algebric Solution required

by navdeepbajwa » Fri Oct 09, 2009 11:13 pm
Can you solve this algebrically


If x and y are integers, does x^y * y^-x = 1?

(1) x^x > y

(2) x > y^y

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question
Source: — Data Sufficiency |

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by Katrusya » Sat Oct 10, 2009 7:51 am
I think the answer is D
x^y * y^-x = 1 -> (x^y)/(y^x)=1 -> x^y=y^x - this can be true only if x=y=1, or y=x=0
neither of options gives us this solutions, hence
if 1 is true, then (x^y)/(y^x)definetely doesn't =1 - sufficient
if 2 is true, then (x^y)/(y^x)definetely doesn't =1 - sufficient

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by mehravikas » Sat Oct 10, 2009 4:22 pm
I think the answer should be B.

Statement 1 - x^x > y

x = 2, y = 2 therefore x^x > y and x^y * y^-x = 1

x = 3, y = 2, therefore x^x > y but x^y * y^-x != 1

Statement 2 - x > y^y

x = 10, y = 2, satisfies statement 2 and x^y * y^-x != 1
x = 28, y = 3, satisfies statement 2 and x^y * y^-x != 1

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by nithi_mystics » Sat Oct 10, 2009 4:37 pm
B is the answer
Thanks
Nithi